Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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SENSOR-BASED WIRELESS COMMUNICATION SYSTEMS USING
COMPRESSIVE SAMPLING
FIELD
100021 This disclosure generally relates to wireless communication systems
and
more particularly to methods, devices and systems for using compressive
sampling in a
sensor-based wireless communication system.
BACKGROUND
100031 Wireless communications systems are widely deployed to provide, for
example, a broad range of voice and data-related services. Typical wireless
communications systems consist of multiple-access communication networks that
allow
users to share common network resources. Examples of these networks are time
division multiple access ("TDMA") systems, code division multiple access
("CDMA")
systems, single carrier frequency division multiple access ("SC-FDMA")
systems,
orthogonal frequency division multiple access ("OFDMA") systems, or other like
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systems. An OFDMA system is supported by various technology standards such as
evolved universal terrestrial radio access ("E-UTRA"), Wi-Fi, worldwide
interoperability for microwave access ("WiMAX"), ultra mobile broadband
(`UMB"),
and other similar systems. Further, the implementations of these systems are
described
by specifications developed by various standards bodies such as the third
generation
partnership project (-3GPP") and 3GPP2.
[00041 As wireless communication systems evolve, more advanced network
equipment is introduced that provide improved features, functionality and
performance.
Such advanced network equipment may also be referred to as long-term evolution
("LIE") equipment or long- term evolution advanced ("LTE-A") equipment. LTE
builds on the success of high-speed packet access ("HSPA") with higher average
and
peak data throughput rates, lower latency and a better user experience,
especially in
high-demand geographic areas. LTE accomplishes this higher performance with
the use
of broader spectrum bandwidth, OFDMA and SC-FDMA air interfaces, and advanced
antenna methods.
[00051 Communications between user equipment and base stations may be
established using single-input, single-output systems ("SISO"), where only one
antenna
is used for both the receiver and transmitter; single-input, multiple-output
systems
("SIMO"), where multiple antennas are used at the receiver and only one
antenna is used
at the transmitter; and multiple- input, multiple-output systems ("MEMO"),
where
multiple antennas are used at the receiver and transmitter. Compared to a SISO
system,
SIM may provide increased coverage while MLMO systems may provide increased
spectral efficiency and higher data throughput if the multiple transmit
antennas, multiple
receive antennas or both are utilized.
f0006] In these wireless communication systems, signal detection and
estimation in
noise is pervasive. Sampling theorems provide the ability to convert
continuous-time
signals to discrete-time signals to allow for the efficient and effective
implementation of
signal detection and estimation algorithms. A well-known sampling theorem is
often
referred to as the Shannon theorem and provides a necessary condition on
frequency
bandwidth to allow for an exact recovery of an arbitrary signal. The necessary
condition
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is that the signal must be sampled at a minimum of twice its maximum
frequency, which
is also defined as the Nyquist rate. Nyquist rate sampling has the drawback of
requiring
expensive, high-quality components requiring substantial power and cost to
support
sampling at large frequencies. Further, Nyquist-rate sampling is a function of
the
maximum frequency of the signal and does not require knowledge of any other
properties of the signal.
100071 To avoid some of these difficulties, compressive sampling provides a
new
framework for signal sensing and compression where a special property of the
input
signal, sparseness, is exploited to reduce the number of values needed to
reliably
represent a signal without loss of desired information.
BRIEF DESCRIPTION OF THE DRAWINGS
100081 To facilitate this disclosure being understood and put into practice
by persons
having ordinary skill in the art, reference is now made to exemplary
embodiments as
illustrated by reference to the accompanying figures. Like reference numbers
refer to
identical or functionally similar elements throughout the accompanying
figures. The
figures along with the detailed description are incorporated and form part of
the
specification and serve to further illustrate exemplary embodiments and
explain various
principles and advantages, in accordance with this disclosure, where:
100091 FIG. 1 illustrates one embodiment of a sensor-based wireless
communication
system using compressive sampling in accordance with various aspects set forth
herein.
100101 FIG. 2 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in accordance with various
aspects
set forth herein.
100111 FIG. 3 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in accordance with various
aspects
set forth herein.
100121 FIG. 4 illustrates one embodiment of a compressive sampling system
in
accordance with various aspects set forth herein.
[00131 FIG. 5 is a flow chart of one embodiment of a compressive sampling
method
in accordance with various aspects set forth herein.
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100141 FIG. 6 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in accordance with various
aspects
set forth herein.
100151 FIG. 7 illustrates one embodiment of an access method in a sensor-
based
wireless communication system using compressive sampling in accordance with
various
aspects set forth herein.
100161 FIG. 8 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in accordance with various
aspects
set forth herein.
100171 FIG. 9 illustrates one embodiment of a quantizing method of a
detector in a
sensor-based wireless communication system using compressive sampling in
accordance
with various aspects set forth herein.
100181 FIG. 10 is a chart illustrating an example of the type of sparse
representation =
matrix and sensing matrix used in a sensor-based wireless communication system
using
compressive sampling in accordance with various aspects set forth herein.
100191 FIG. 11 illustrates one embodiment of a wireless device, which can
be used
in a sensor-based wireless communication system using compressive sampling in
accordance with various aspects set forth herein.
(00201 FIG. 12 illustrates one embodiment of a sensor, which can be used in
a
sensor- based wireless communication system using compressive sampling in
accordance with various aspects set forth herein.
100211 FIG. 13 illustrates one embodiment of a base station, which can be
used in a
sensor-based wireless communication system using compressive sampling in
accordance
with various aspects set forth herein.
100221 FIG. 14 illustrates simulated results of one embodiment of detecting
a
wireless device in a sensor-based wireless communication system using
compressive
sampling in accordance with various aspects set forth herein.
[00231 FIG. 15 illustrates simulated results of the performance of one
embodiment
of a sensor-based wireless communication system using compressive sampling in
accordance with various aspects set forth herein.
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[00241 FIG. 16 illustrates simulated results of the performance of one
embodiment
of a sensor-based wireless communication system using compressive sampling in
accordance with various aspects set forth herein.
100251 FIG. 17 illustrates simulated results of the performance of one
embodiment
of a sensor-based wireless communication system using compressive sampling in
accordance with various aspects set forth herein.
100261 FIG. 18 illustrates simulated results of the performance of one
embodiment
of a sensor-based wireless communication system using compressive sampling in
accordance with various aspects set forth herein.
100271 FIG. 19 illustrates simulated results of the performance of one
embodiment
of a sensor-based wireless communication system using compressive sampling in
accordance with various aspects set forth herein.
[00281 FIG. 20 is an example of deterministic matrices used in one
embodiment of a
sensor-based wireless communication system using compressive sampling in
accordance
with various aspects set forth herein.
[00291 FIG. 21 is an example of random matrices used in one embodiment of a
sensor- based wireless communication system using compressive sampling in
accordance with various aspects set forth herein.
[00301 FIG. 22 illustrates an example of an incoherent sampling system in a
noise-
free environment.
[00311 FIG. 23 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in accordance with various
aspects
set forth herein.
[00321 FIG. 24 illustrates an example of a prior art lossless sampling
system.
[00331 FIG. 25 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in a noisy environment in
accordance with various aspects set forth herein.
[00341 FIG. 26 illustrates another embodiment of an access method in a
sensor-
based wireless communication system using compressive sampling in accordance
with
various aspects set forth herein.
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100351 FIG. 27 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in a noisy environment in
accordance with various aspects set forth herein.
100361 FIG. 28 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in accordance with various
aspects
set forth herein.
100371 FIG. 29 illustrates
another embodiment of a sensor-based wireless =
communication system using compressive sampling in accordance with various
aspects
set forth herein.
100381 FIG. 30 illustrates a proposed target operating region of a sensor-
based
wireless communication system using compressive sampling in accordance with
various
aspects set forth herein.
100391 FIG. 31 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in accordance with various
aspects
set forth herein.
100401 FIG. 32 illustrates embodiments of frequency domain sampling of a
sensor-
based wireless communication system using compressive sampling in accordance
with
various aspects set forth herein.
100411 FIG. 33 is a block diagram of a remote sampler of a sensor-based
wireless
communication system using compressive sampling in accordance with various
aspects
set forth herein.
100421 Skilled artisans will appreciate that elements in the accompanying
figures are
illustrated for clarity, simplicity and to further help improve understanding
of the
embodiments, and have not necessarily been drawn to scale.
DETAILED DESCRIPTION =
100431 Although the following discloses exemplary methods, devices and
systems
for use in sensor-based wireless communication systems, it will be understood
by one of
ordinary skill in the art that the teachings of this disclosure are in no way
limited to the
examplaries shown. On the contrary, it is contemplated that the teachings of
this
disclosure may be implemented in alternative configurations and environments.
For
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example, although the exemplary methods, devices and systems described herein
are
described in conjunction with a configuration for aforementioned sensor-based
wireless
communication systems, the skilled artisan will readily recognize that the
exemplary
methods, devices and systems may be used in other systems and may be
configured to
correspond to such other systems as needed. Accordingly, while the following
describes
exemplary methods, devices and systems of use thereof, persons of ordinary
skill in the
art will appreciate that the disclosed exemplaries are not the only way to
implement' such
methods, devices and systems, and the drawings and descriptions should be
regarded as
illustrative in nature and not restrictive.
[0044] Various techniques described herein can be used for various sensor-
based
wireless communication systems. The various aspects described herein are
presented as
methods, devices and systems that can include a number of components,
elements,
members, modules, nodes, peripherals, or the like. Further, these methods,
devices and
systems can include or not include additional components, elements, members,
modules,
nodes, peripherals, or the like. In addition, various aspects described herein
can be
implemented in hardware, firmware, software or any combination thereof. It is
important to note that the terms "network" and "system" can be used
interchangeably.
Relational terms described herein such as "above" and "below", "left" and
"right", "first" and "second", and the like may be used solely to distinguish
one entity or
action from another entity or action without necessarily requiring or implying
any actual
such relationship or order between such entities or actions. The term "or" is
intended to
mean an inclusive "or- rather than an exclusive "or." Further, the terms "a"
and "an" are
intended to mean one or more unless specified otherwise or clear from the
context to be
directed to a singular form.
[0045] The wireless communication system may be comprised of a plurality of
user
equipment and an infrastructure. The infrastructure includes the part of the
wireless
communication system that is not the user equipment, such as sensors, base
stations,
core network, downlink transmitter, other elements and combination of
elements. The
core network can have access to other networks. The core network, also
referred to as a
central brain or remote central processor, may include a high-powered
infrastructure
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component, which can perform computationally intensive functions at a high
rate with
acceptable financial cost. The core network may include infrastructure
elements, which
can communicate with base stations so that, for instance, physical layer
functions may
=
also be performed by the core network. The base station may communicate
control
information to a downlink transmitter to overcome, for instance, communication
impairments associated with channel fading. Channel fading includes
how a radio frequency ("RF") signal can be bounced off many reflectors and the
properties of the resulting sum of reflections. The core network and the base
station
may, for instance, be the same the same infrastructure element, share a
portion of the
same infrastructure element or be different infrastructure elements.
[00461 A base station may be referred to as a node-B ("NodeB"), a base
transceiver
station ("BTS"), an access point ("AP"), a satellite, a router, or some other
equivalent
terminology. A base station may contain a RF transmitter, RF receiver or both
coupled
to a antenna to allow for communication with a user equipment.
[00471 A sensor may be referred to as a remote sampler, remote conversion
device,
remote sensor or other similar terms. A sensor may include, for instance, an
antenna, a
receiving element, a sampler, a controller, a memory and a transmitter. A
sensor may be
interfaced to, for instance, a base station. Further, sensors may be deployed
in a wireless
communication system that includes a core network, which may have access to
another
network.
100481 A user equipment used in a wireless communication system may be
referred
to as a mobile station ("MS"), a terminal, a cellular phone, a cellular
handset, a personal
digital assistant ("PDA"), a smartphone, a handheld computer, a desktop
computer, a
laptop computer, a tablet computer, a netbook, a printer, a set-top box, a
television, a
wireless appliance, or some other equivalent terminology. A user equipment may
= contain an RF transmitter, RF receiver or both coupled to an antenna to
communicate
with a base station. Further, a user equipment may be fixed or mobile and may
have the
ability to move through a wireless communication system. Further, uplink
communication refers to communication from a user equipment to a base station,
sensor
or both. Downlink communication refers to communication from a base station,
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downlink transmitter or both to a user equipment.
[00491 FIG. 1 illustrates one embodiment of sensor-based wireless
communication
system 100 using compressive sampling with various aspects described herein.
In this
embodiment, system 100 can provide robust, high bandwidth, real-time wireless
communication with support for high-user density. System 100 can include user
equipment 106, sensors 110 to 113, base station 102, core network 103 and
other
network 104. User equipment 106 may be, for instance, a low cost, low power
device.
Base station 102 can communicate with user equipment 106 using, for instance,
a
plurality of low-cost, low-power sensors 110 to 113.
10050J In FIG. 1, system 100 contains sensors 110(0 113 coupled to base
station
102 for receiving communication from user equipment 106. Base station 102 can
be
coupled to core network 103, which may have access to other network 104. In
one
embodiment, sensors 110 to 113 may be separated by, for instance,
approximately ten
meters to a few hundred meters. In another embodiment, a single sensor 110 to
113 may
be used. A person of ordinary skill in the art will appreciate in deploying a
sensor-based
wireless communication system that there are tradeoffs between the power
consumption
of sensors, deployment cost, system capacity, other factors and combination
factors. For
instance, as sensors 110 to 113 become more proximally spaced, the power
consumption
of sensors 110 to 113 may decrease while the deployment cost and system
capacity may
increase. Further, user equipment 106 may operate using a different RF band
than used
with the underlying wireless network when in close proximity to sensors 110 to
113.
100511 In the current embodiment, sensors 110 to 113 can be coupled to base
station
102 using communication links 114 to 117, respectively, which can support, for
instance, a fiber- optic cable connection, a coaxial cable connection, other
connections
or any combination thereof. Further, a plurality of base stations 102 may
communicate
sensor-based information between each other to support various functions.
Sensors 110
to 113 may be designed to be low cost with, for example, an antenna, an RF
front-end,
baseband circuitry, interface circuitry, a controller, memory, other elements,
or
combination of elements. A plurality of sensors 110 to 113 may be used to
support, for
instance, antenna array operation, SIMO operation, MEMO operation, beamforming
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operation, other operations or combination of operations. A person of ordinary
skill in
the art will recognize that the aforementioned operations may allow user
equipment 106
to transmit at a lower power level resulting in, for instance, lower power
consumption.
[0052] In system 100, user equipment 106 and base station 102 can
communicate
using, for instance, a network protocol. The network protocol can be, for
example, a
cellular network protocol, Bluetooth protocol, wireless local area loop
("WLAN")
protocol or any other protocol or combination of protocols. A person of
ordinary skill in
the art will recognize that a cellular network protocol can be anyone of many
standardized cellular network protocols used in systems such as LTE, UMTS,
CDMA,
GSM and others. The portion of the network protocol executed by sensors 110 to
113
may include, for instance, a portion of the physical layer functions. A person
of
ordinary skill in the art will recognize that reduced functionality performed
by sensors
110 to 113 may result in lower cost, smaller size, reduced power consumption,
other
advantages or combination of advantages.
[0053j Sensors 110 to 113 can be powered by, for instance, a battery power
source,
an alternating current ("AC") electric power source or other power sources or
combination of power sources. Communication including real-time communication
among sensors 110 to 113, user equipment 106, base station 102, core network
103,
other network 104 or any combination thereof may be supported using, for
instance, an
automatic repeat request ("ARQ") protocol.
[0054] In the current embodiment, sensors 110 to 113 can compress a
received
uplink signal (r) transmitted from user equipment 106 to form a sensed signal
("y").
Sensors 110 to 113 can provide the sensed signal ('y') to base station 102
using
communication links 114 to 117, respectively. Base station 102 can then
process the
sensed signal ("y"). Base station 102 may communicate instructions to sensors
110 to
113, wherein the instructions can relate to, for instance, data conversion,
oscillator
tuning, beam steering using phase sampling, other instructions or combination
of
instructions. Further, user equipment 106, sensors 110 to 113, base station
102, core
network 103, other network 104 or any combination thereof may communicate
including
real-time communication using, for instance, a medium access control ("MAC")
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ARQ protocol, other similar protocols or combination of protocols. Also, user
equipment 106, sensors 110 to 113, base station 102, core network 103, other
network
104 or any combination thereof may communicate using, for instance, presence
signaling codes which may operate without the need for cooperation from
sensors 110 to
113; space-time codes which may require channel knowledge; fountain codes
which
may be used for registration and real-time transmission; other communication
codes or
combination of communication codes. Some of these communication codes may
require, for instance, applying various signal processing techniques to take
advantage of
any inherent properties of the codes.
100551 In FIG. 1, base station 102 may perform functions such as
transmitting
system overhead information; detecting the presence of user equipment 106
using
sensors 110 to 113; two-way, real-time communication with user equipment 106;
other
functions or combination of functions. A person of ordinary skill in the art
will
recognize that sensors 110 to 113 may be substantially less expensive than
base station
102 and core network 103.
100561 Sampling is performed by measuring the value of a continuous-time
signal at
a periodic rate, aperiodic rate, or both to form a discrete-time signal. In
the current
embodiment, the effective sampling rate of sensors 110 to 113 can be less than
the actual
sampling rate used by sensors 110 to 113. The actual sampling rate is the
sampling rate
of, for instance, an analog- to-digital converter ("ADC"). The effective
sampling rate is
measured at the output of sensors 110 to 113, which corresponds to the
bandwidth of
sensed signal ("y"). By providing a lower effective sampling rate, sensors 110
to 113
can consume less power than other sensors operating at the actual sampling
rate without
any compression. Redundancy can be designed into the deployment of a system so
that
the loss of a sensor would minimally affect the performance of the system. For
many
types of signals, reconstruction of such signals can be performed by base
station 102,
core network 103, other network 104, or any combination thereof.
100571 In the current embodiment, sensors 110 to 113 may each contain a
direct
sequence de-spreading element, a fast Fourier transform ("FFT-) element, other
elements or combination of elements. Base station 102 can send to sensor 110
to 113
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instructions, for instance, to select direct sequence codes or sub-chip timing
for a de-
spreading element, to select the number of frequency bins or the spectral band
for an
FFT element, other instructions or combination of instructions. These
instructions may
be communicated at, for example, one-millisecond intervals, with each
instruction being
performed by sensor 110 to 113 within one tenth of a millisecond after being
received.
Further, user equipment 106 may transmit and receive information in the form
of slots,
packets, frames or other similar structures, which may have a duration of, for
instance,
one to five milliseconds. Slots, packets, frames and other similar structures
may include
a collection of time-domain samples successively captured or may describe a
collection
of successive real or complex values.
100581 In FIG. 100, system 100 can include the communication of system
overhead
information between user equipment 106, base station 102, core network 103,
other
network 104, sensors 110 to 113 or any combination thereof. The system
overhead
information may include, for instance, guiding and synchronizing information,
wireless
wide area network information, WLAN information, other information or
combination
of information. A person of ordinary skill in the art will recognize that by
limiting the
need for user equipment 106 to monitor the underlying network, extraneous
networks or
both may reduce its power consumption. "
100591 In FIG. 1, user equipment 106 may transmit uplink signals at a low
transmission power level if user equipment 106 is sufficiently proximate to
sensors 110
to 113. Sensors 110 to 113 can compressively sample the received uplink
signals ("g")
to generate sensed signals ("y"). Sensors 110 to 113 can send sensed signals
("y") to
base station 102 using communication link 114 to 117, respectively. Base
station 102
may perform, for instance, layer 1 functions such as demodulation and
decoding; layer 2
functions such as packet numbering and ARQ; and higher-layer functions such as
registration, channel assignment and handoff. Base station 102 may have
substantial
computational power to perform computationally intensive functions in real
time, near-
real time or both.
100601 In the current embodiment, base station 102 may apply link
adaptation
strategies using, for instance, knowledge of the communication channels such
as the
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antenna correlation matrix of user equipment 106; the number of sensors 110 to
113 in =
proximity to user equipment 106; other factors or combination of factors. Such
adaptation strategies may require processing at periodic intervals, for
instance, one-
millisecond intervals. Such strategies may allow for operating, for instance,
at the
optimum space-time multiplexing gain and diversity gain. Also, a plurality of
base
stations 102 may communicate between each other to perform, for instance,
dirty paper
coding ("DPC"), which is a technique for efficiently transmitting downlink
signals
through a communication channel that is subject to some interference that is
known to
base station 102. To support these techniques, other base stations that
receive
extraneous uplink signals from user equipment 106 may provide the uplink
signals ("f)
to base station 102 associated with user equipment 106. A person of ordinary
skill in the
art will recognize that a plurality of user equipment 106 can communicate with
base =
station 102.
100611 FIG. 2 illustrates another embodiment of a sensor-based wireless
communication system 200 using compressive sampling in accordance with various
aspects set forth herein. In this embodiment, system 200 can provide robust,
high
bandwidth, real-time wireless communication with support for high-user
density.
System 200 includes user equipment 206, sensors 210 to 213, base station 202,
core
network 203 and other network 204. In this embodiment, sensors 210 to 213 may
perform a portion of layer 1 functions such as receiving an uplink signal and
performing
compressive sampling. Further, base station 202 may send instructions to
sensors 210 to
213 using communication link 214 to 217, respectively. Such instructions may
be, for
example, to compress using a specific multiple access code such as a direct
sequence
code or an OFDM code. Further, base station 202 may send instructions to
sensors 210
to 213 to perform, for instance, sampling at twice the sampling rate, which
may be at a
specific phase.
100621 Base station 202 may perform computationally intensive functions to,
for =
instance, detect the presence of user equipment 206 in the sensed signals
("y") received
from sensors 210 to 213. Once the presence of user equipment 206 is detected,
base
station 202 may configure sensors 210 to 213 to improve the reception of
uplink signals
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(7') from user equipment 206. Such improvements may be associated with timing,
frequency, coding, other characteristics or combination of characteristics.
Further, user
equipment 206 may transmit uplink signals (T) using, for instance, a fountain
code.
For high bandwidth, low power communication, user equipment 206 may use a
fountain
code to transmit uplink signals
containing, for instance, real-time speech. The packet transmission rate for
such uplinlc
signals may be, for instance, in the range of 200 Hz to 1 kHz. Sensors 210 to
213 may
have limited decision-making capability with substantial control by base
station 202.
100631 In FIG. 2, sensors 210 to 213 may be densely deployed, for instance,
one
sensor 210 to 213 in approximately every one hundred meters separation
distance, one
sensor 210 to 213 in approximately every ten meters separation distance, other
configurations or combination of configurations. Sensors 210 to 213 may
contain or be
co-located with a downlink transmitter, which is used to support the
transmission of
downlink signals received from base station 202. Further, base station 202 may
use a
communication link to provide downlink signals to a remote downlink
transmitter such
as, a traditional cellular tower with antenna sectorization, a cellular
transmitter mounted
on a building or light pole, a low power unit in an office, other elements or
combination
of elements. The deployment of such remote downlink transmitters may be to
support,
for example, building deployment, street light deployment, other deployments
or
combination of deployments. Further, it will be understood that a plurality of
user
equipment 206 can communicate with base station 202.
100641 FIG. 3 illustrates another embodiment of a sensor-based wireless
communication system 300 using compressive sampling in accordance with various
aspects set forth herein. In this embodiment, system 300 represents a multiple
access
system. System 300 includes user equipment 306, sensor 310, base station 302
and
downlink transmitter 308. In FIG. 3, sensor
310 can include a receiving element for downconverting uplink signals. A
person of
ordinary skill in the art will appreciate the design and implementation
requirements for
such a receiving element.
[00651 In FIG. 3, base station 302 can be coupled to downlink transmitter
308,
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wherein downlink transmitter 308 can be co-located, for instance, with a
cellular tower.
Base station 302 may contain, for instance, a collector for collecting sensed
signals from
sensor 310, a detector for detecting information signals contained in the
sensed signals, a
controller for controlling sensor 310, other elements or combination of
elements. Base
station 302 and downlink transmitter 308 may be co-located. Further, downlink
transmitter 308 can be coupled to base station 302 using communication link
309, which
can support, for instance, a fiber-optic cable connection, a microwave link, a
coaxial
cable connection, other connections or any combination thereof. The
configuration of
system 300 may be similar to a conventional cellular system such as, a GSM
system, a
UMTS system, a LTE system, a CDMA system, other systems or combination of
systems. A person of ordinary skill in the art will recognize that these
systems exhibit
arrangements of user equipment, base stations, downlink transmitters, other
elements or
combination of elements.
100661 In the current embodiment, user equipment 308 and base station 302
can
communicate using a network protocol to perform functions such as random
access;
paging; origination; resource allocation; channel assignment; overhead
signaling
including timing, pilot system identification, channels allowed for access;
handover
messaging; training or pilot signaling; other functions or combination of
functions.
Further, user equipment 308 and base station 302 may communicate voice
information,
packet data information, circuit-switched data information, other information
or
combination of information.
100671 FIG. 4 illustrates one embodiment of a compressive sampling system
in
accordance with various aspects set forth herein. System 400 includes
compressive
sampler 431 and detector 452. In FIG. 4, compressive sampler 431 can
compressively
sample an input signal (V") using sensing waveforms ("9i ") of sensing matrix
("O") to
generate a sensed signal ("y"), where coj refers to the jth waveform of
sensing matrix
("(I)"). The input signal ("r) can be of length N, the sensing matrix ("O")
can have M
sensing waveforms ( " ") of length N and the sensed signal ("y") can be of
length M,
where Mean be less than N. An information signal ("x") can be recovered if the
input
signal ('r) is sufficiently sparse. A person of ordinary skill in the art will
recognize the
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characteristics of a sparse signal. In one definition, a signal of length N
with S non-zero
values is referred to as S-sparse and includes N minus S ("N-S") zero values.
100681 In the current embodiment, compressive sampler 431 can compressively
sample the input signal ("f") using, for instance, Equation (1).
100691 = (f. (PO. k E J such that c (i ...N) (1)
100701 where the brackets () denote the inner product, correlation function
or other
similar functions.
100711 Further, detector 452 can solve the sensed signal ('Y) to find the
information
signal ("x") using, for instance, Equation (2).
100721 min t(x- E R N ) 111,(1i1) subject to yik (vik,Tx"). (lc E (2)
[0073) where 11-11i is the norm, which is the sum of the absolute values
of the
elements of its argument and the brackets (I) denote the inner product,
correlation
function or other similar functions. One method, for instance, which can be
applied for
I minimization is the simplex method. Other methods to solve the sensed signal
("y")
to find the information signal ("x") include using, for instance, the l o norm
algorithm,
other methods or combination of methods.
100741 Incoherent sampling is a form of compressive sampling that relies on
sensing
waveforms Op ") of the sensing matrix ("O") being sufficiently unrelated to
the sparse
representation matrix ("T"), which is used to make the input signal (T)
sparse. To
minimize the required number of sensing waveforms("Ti ") of sensing matrix
("0"), the
coherence ("10 between the sparse representation waveforms ("I/ ") of the
sparse
representation matrix ("T") and the sensing waveforms ("T./ ") of sensing
matrix ("O")
should represent that these waveforms are sufficiently unrelated,
corresponding to a
lower coherence ("p"), where yi refers to the jth waveform of the sparse
representation
matrix ("T"). The coherence (",u") can be represented, for instance, by
Equation 3.
= max N11(0k, tP))11
100751 15k,J.S 11 (3)
100761 where ll Dzi is the I I norm, which is the sum of the absolute
values of the
elements of its argument and the brackets (7) denote the inner product,
correlation
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function or other similar functions.
100771 FIG. 5 is a flow chart of an embodiment of a compressive sampling
method
500 in accordance with various aspects set forth herein, which can be used,
for instance,
to design a compressive sampling system. In FIG. 5, method 500 can start at
block 570,
where method 500 can model an input signal ('r) and discover a sparse
representation
matrix ("T") in which the input signal (T) is S-sparse. At block 571, method
500 can
choose a sensing matrix ("0"), which is sufficiently incoherent with the
sparse
representation matrix ("T"). At block 572, method 500 can randomly,
deterministically
or both select M sensing waveforms ("pj ") of sensing matrix ("O"), where Al
may be
greater than or equal to S. At block 573, method 500 can sample input signal
(7') using
the selected M sensing waveforms ("(pi ") to produce a sensed signal ("y"). At
block
574, method 500 can pass the sparse representation matrix ("T"), the sensing
matrix
("V) and the sensed signal ("y") to a detector to recover an information
signal ("x").
100781 FIG. 6 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in accordance with various
aspects
set forth herein. In this embodiment, system 600 can provide robust, high
bandwidth,
real-time wireless communication with support for high-user density. System
600
includes user equipment 606, sensor 610 and base station 602. In FIG. 6,
system 600
can allow user equipment 606 to communicate with, for instance, the underlying
cellular
system even if sensor 610, for instance, fails to operate. System 600 may
allow sensors
610 to be widely distributed consistent with, for instance, office-building
environments.
System 600 may allow for base station 602 to not be limited by, for instance,
computational capacity, memory, other resources or combination of resources.
System
600 may allow for downlink signals to be provided by, for instance, a
conventional
cellular tower. System 600 may allow user equipment 606 to minimize power
consumption by limiting its transmission power level to, for instance,
approximately ten
to one hundred microwatts. System 600 may allow for sensor 610 to be coupled
to base
station 602 using communication link 614, wherein communication link 614 can
support, for instance, a fiber-optic cable connection, a coaxial cable
connection, other
connections or any combination thereof. System 600 may allow for sensor 610 to
be
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operated by power sources such as a battery, a photovoltaic power source, an
alternating
current ("AC") electric power source, other power sources or combination of
power
sources.
[00791 In FIG. 6, system 600 may allow for sensor 610 to be substantially
less ex
pensive than base station 602. Further, system 600 may allow for sensor 610 to
operate
using battery power for an extended period such as approximately one to two
years. To
achieve this, a person of ordinary skill in the art will recognize that
certain functions
such as signal detection, demodulation and decoding may have to be performed
by, for
instance, base station 602.
100801 In FIG. 6, sensor 610 can have a receiving element such as an
antenna
coupled to an RF downconversion chain, which are used for receiving uplink
signals
("f"). In this disclosure, uplink signal (r) can also be referred to as uplink
signal ("g").
Uplink signal ("g") includes channel propagation effects and environmental
effects on
uplink signal ("f). For instance, channel gain ("a") 621 of channel 620 can
represent,
for instance, channel propagation effects while channel noise ("v") 622 of
channel 620
can represent, for instance, environment noise effects. Further, sensor 610
can support a
communication link to send, for instance, sensed signals ("y") to base station
602.
Sensor 610 may not have the computational capability to, for instance,
recognize when
user equipment 606 is transmitting an uplink signal ('r). Sensor 610 may
receive
instructions from base station 602 associated with, for instance, RF
downconversion,
compressive sampling, other functions or combination of functions.
[00811 There are many methods for a user equipment to access a wireless
communication system. One type of access method is, for instance, the Aloha
random
access method, which is performed when an unrecognized user equipment attempts
to
access the network. Two-way communication with a base station may take place,
for
instance, after the user equipment has been given permission to use the system
and any
uplink and downlink channels have been assigned.
[0082) FIG. 7 illustrates one embodiment of an access method 700 in a
sensor-based
wireless communication system using compressive sampling in accordance with
various
aspects set forth herein. Various illustrative structures are shown in the
lower portion of
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FIG. 7 to facilitate understanding of method 700. Further, FIG. 7 illustrates
base station
702 twice but should be interpreted as one and the same base station 702.
Accordingly,
method 700 includes communication amongst base station 702, user equipment
706,
sensor 710 or any combination thereof. User equipment 706 can have, for
instance, a
power-on event 770 and begin observing overhead messages 771 sent from base
station
702. A person of ordinary skill in the art will recognize that a base station
can
communicate with a user equipment using, for instance, broadcast
communication,
point-to-multipoint communication, point-to-point communication or other
communication methods or combination of communication methods. Overhead
messages 771 may contain system parameters including, for instance, the length
of
message frames, the value of M associated with the number of sensing waveforms
("of
") and the sparseness S of the uplink signals ("r) being sent.
100831 In FIG. 7, base station 702 may send, for instance, an overhead
message to
configure user equipment 706 to use sparseness Si and sparse representation
matrix
("T"), as shown at 772. User equipment 706 may then send, for instance,
presence
signals using sparseness Si, as represented by 780. Presence signals can
include any
signal sent by user equipment 706 to base station 702 that can be
compressively
sampled. In another embodiment, user equipment 706 may send presence signals
using
Si, as shown at 780, when it determines that it is approaching base station
702. In this
situation, user equipment 706 may determine that it is approaching base
station 702 via,
for instance, overhead messages 771 sent by base station 702, another base
station or
both.
(00841 In FIG. 7, base station 702 may also send, for instance, an overhead
message
containing system information such as framing, timing, system identification,
other
system information or combination of information, as shown at 773. In
addition, base
station 702 may instruct sensor 710 to use, for instance, Ai/ sensing
waveforms ("ei ")
of sensing matrix ("0"), as represented by 791. Sensor 710 may then
continuously
process received uplink signals (r) and send sensed signals ("y") using Mi
sensing
waveforms ("cif ") of sensing matrix ("D") to base station 702, as shown at
790.
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[00851 In FIG. 7, base station 702 may send, for instance, an overhead
message to
configure user equipment 706 to use sparseness 52 and sparse representation
matrix
("T"), as represented by 774. User equipment 706 may then send, for instance,
presence
signals using sparseness 52, as shown by 781. In addition, base station 702
may instruct
sensor 710 to use, for instance, M2 sensing waveforms ("pi") of sensing matrix
(-0"), as
represented by 792. Sensor 710 may then continuously process received uplink
signals
("f) and send to base station 702 sensed signals ("y") using M2 sensing
waveforms ("9
j ") of sensing matrix On, as shown at 793. User equipment 706 may continue to
send
presence signals using S2, as shown by 781, until, for instance, base station
702 detects
the presence signals using 52, as shown at 794. At which point, base station
702 may
send to user equipment 706 a recognition message including, for instance, a
request to
send a portion of its electronic serial number ("ESN") and to use sparseness
S3 and a
sparse representation matrix ("T"), as represented by 775. Further, base
station 702 may
send to sensor 710 an instruction to use, for instance, a new value of M3 and
a new
sensing matrix ("0"), as shown at 795. Sensor 710 may then continuously
process
received uplink signals ("f") and send to base station 702 sensed signals
("y") using M3
sensing waveforms ("coi ") of sensing matrix ("0"), as shown at 796.
100861 In FIG. 7, user equipment 706 may send to base station 702 an uplink
message containing a portion of its ESN using S3, as represented by 782. Once
base
station 702 has received this uplink message, base station 702 may send to
user
equipment 706 a downlink message requesting user equipment 706 to send, for
instance,
its full ESN and a request for resources, as shown at 776. User equipment 706
may then
send an uplink message containing its full ESN and a request for resources
using S3, as
represented by 783. After base station 702 receives this uplink message, base
station
702 may verify the full ESN of user equipment 706 to determine its eligibility
to be on
the system and to assign it any resources, as represented by 798. Base station
702 may
then send to user equipment 706 a downlink message to assign it resources, as
shown at
777.
00871 Sensor 710 may continuously receive uplink signals (7) of a frequency
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bandwidth ("B") centered at a center frequency (fc"). Sensor 710 can
downconvert the
uplink signal ("r) using a receiving element and then perform compressive
sampling.
Compressive sampling is performed, for instance, by sampling the received
uplink signal
(T) and then computing the product of a sensing matrix ("0") and the samples
to
generate a sensed signal ("y-). Sampling may be performed, for instance, at
the
frequency bandwidth ("B-) corresponding to the Nyquist rate, consistent with
preserving
the received uplink signal (r) according to Shannon's theorem. The received
uplink
signal (r) can be sampled, for instance, periodically, aperiodically or both.
100881 The sampling process can result in N samples, while computing the
product ,
of a sensing matrix OD") and the N samples can result in M values of sensed
signal
("y"). The sensing matrix (-0") may have dimensions of N by M. These resulting
M
values of sensed signal ("y") can be sent over a communication link to base
station 702.
Compressive sampling can reduce the number of samples sent to base station 702
from
N samples for a conventional approach to M samples, wherein M can be less than
N. If
sensor 710 does not have sufficient system timing, sampling may be performed
at a
higher sampling rate resulting in, for instance, 2N samples. For this
scenario, sensor 710
may compute the product of a sensing matrix ("(I)") and the 2N samples of
uplink signal
(7') resulting in 2M samples of sensed signal ("y"). Thus, the compressive
sampler may
reduce the number of samples sent to base station 702 from 2N samples for a
conventional approach to 2M samples, wherein M may be less than N. For this
scenario,
the sensing matrix ("CD") may have dimensions of 2N by 2M.
[0089] The compressive sampler may compute sensed signal ("y") by
correlating the
sampled received uplink signal (y") with, for instance, independently selected
sensing
waveforms ("ipi ") of the sensing matrix ("O"). Selection of the sensing
waveforms ("q./
") of the sensing matrix ("(I)") may be without any knowledge of the
information signal
("x"). However, the selection of M may rely, for instance, on an estimate of
the
sparseness S of the received uplink signal (y-). Therefore, the selected M
sensing
waveforms NJ -) of the sensing matrix ("0") may be independent of the sparse
representation matrix ("T"), but M may be dependent on an estimate of a
property of the
received uplink signal (V"). Further, the sparseness S of received uplink
signal ("f')
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may be controlled, for instance, by base station 702 sending to user equipment
706 a
downlink message recognizing user equipment 706 and configuring user equipment
706
to use sparseness S3 and a new sparse representation matrix ("T") 775.
100901 Successful detection of the information signal ("x") by base station
702 may
require M to be greater than or equal to the sparseness S. The lack of
knowledge of
sparseness S may be overcome, for instance, by base station 702 estimating
sparseness S
and adjusting thereafter. For example, base station 702 may initialize M to,
for instance,
the value of N, which may correspond to no compression benefit. As base
station 702
estimates the activity level of the frequency band B received at sensor 710,
base station
702 may, for instance, adjust the value of M. By doing so, base station 702
can affect
the power consumption of sensor 710 by, for instance, adjusting the number of
M
sensing waveforms ("pi "); thus, adjusting the bandwidth of the sensed signals
("y") sent
to base station 702 over the communication link.
100911 Further, base station 702 may send an instruction to sensor 710 to,
for
instance, periodically increase the value of M to allow base station 702 to
evaluate
thoroughly the sparseness S in the frequency band B. In addition, base station
702 may
send to sensor 710 an instruction as to the method of selecting sensing
waveforms ("pi
") such as, random selection, selection according to a schedule, other
selection methods
or combination of selection methods. In some instances, sensor 710 may need to
communicate its selection of sensing waveforms ("pi ") to base station 702.
100921 User equipment 706 can send presence signals to notify base station
702 of
its presence. Each presence signal may be an informative signal generated by,
for
instance, selecting and combining sparse representation waveforms ("NI] ") of
sparse
representation matrix (V"). The selection of sparse representation waveforms
("igi ")
of sparse representation matrix ("T") may be configured, for instance, by an
overhead
message sent by base station 702. For example, base station 702 may broadcast
an
overhead message that specifies a subset of sparse representation waveforms
("Iv ") of
sparse representation matrix ("tP").
100931 Base station 702 may also broadcast a downlink overhead message for
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unrecognized user equipment 706 to use a specific sparse representation
waveform ("iii
") of sparse representation matrix ("T"), which can be referred to as a pilot
signal ("410
"). Sensor 710 can continuously receive uplink signals ('T), compressively
sample
uplink signals (r) to generate sensed signal ("y"), and send sensed signals
("y") to base
station 702. Base station 702 can then detect the pilot signal ("To") in the
sensed signal
("y"). Once the pilot signal ("4/ 0") is ,detected, base station 702 may
estimate the
channel gain ("a ") between user equipment 706 and sensor 710 and may instruct
any
user equipment 706, which had sent the pilot signal ("41 0") to send, for
instance, a
portion of its ESN. If a collision occurs between uplink transmissions from
different
user equipment 706, collision resolution methods such as the Aloha algorithm
may be
used to separate subsequent uplink transmission attempts by different user
equipment
706.
10094J Sensor 710 may also operate irrespective of the communication
between base
station 702 and user equipment 706. Base station 702 may instruct sensor 710
to use,
for instance, M sparse representation waveform ("yi ") of sparse
representation matrix
("T"). Further, base station 702 may vary the value of M based on
anticipating, for
instance, the amount of uplink signal ('f') activity by user equipment 706.
For example,
if base station 702 anticipates that the sparseness S of uplink signal (T) is
changing, it
may instruct sensor 710 to change the value of M. For a certain deterministic
sensing
matrix ("O"), when M equals the value of N, sensing matrix ("CD") in sensor
710 may
effectively become a discrete Fourier transform ("DFT").
100951 FIG. 8 illustrates another embodiment of a sensor-based wireless
communication system 800 using compressive sampling in accordance with various
aspects set forth herein. In this embodiment, system 800 can provide robust,
high
bandwidth, real-time wireless communication with support for high-user
density. In
FIG. 8, system 800 includes user equipment 806, sensor 810 and base station
802. Base
station 802 can receive sensed signals("y") from sensor 810 as input to
detector 851 of
base station 802 to generate an estimate of information signal ("x"), also
referred to as
Base station 802 can then quantize this estimate to generate, for instance, a
quantized
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estimate of the information signal ("x"), also referred to as I. The estimate
of the
information signal ("x") may be determined using, for instance, the simplex
algorithm,
norm algorithm, to norm algorithm, other algorithms or combination of
algorithms.
In this embodiment, all of the elements of the estimate of the information
signal ("x")
may have non-zero values. Therefore, a hard decision of the estimate of the
information
signal ("x") may be performed to determine the information signal ("x"), which
consists
of, for instance, S non-zero values and N minus S ("N-S") zero values.
(00961 FIG. 9 illustrates one embodiment of a quantizing method 900 of a
detector
in a sensor-based wireless communication system using compressive sampling in
accordance with various aspects set forth herein. FIG. 9 refers to steps
within base
station 902 and steps within quantizer 953 within base station 902. Method 900
starts at
sensor 910, which can send sensed signal ("y") to base station 902. At block
952,
method 900 can solve sensed signal ("y") to determine an estimate of the
information
signal ("x"), also referred to as g . At block 970, method 900 can order the
elements of
the estimate of the information signal ("x"), for instance, from the largest
value to the
smallest value.
100971 In FIG. 9, the information signal ("x") is applied to quantizer 953.
At block
971, method 900 can determine the sparseness S using, for instance, the sensed
signal
(-y"), the estimate of the information signal ("x") or both. Further, base
station 902 may
fix the value of S for a user equipment, by sending a downlink message to the
user
equipment. Base station 902 may also periodically scan for appropriate values
of S by
sending different values of S to the sensor and determining the sparseness S
of uplink
signal (V") during some period of time, for instance, one to two seconds.
Because user
equipment may make multiple access attempts, base station 902 may have the
opportunity to recognize a bad estimate of S and instruct the sensor to adjust
its value of
M. With a sufficiently low duty cycle on the scanning for S, the power
consumption
advantages of using a sensor-based wireless communication network can be
preserved.
In this way, compressive sampling activities by sensor 910 may adaptively
track the
sparseness of the signals, which may affect it. Therefore, sensor 910 may
minimize its
power consumption even while continuously performing compressive sampling.
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100981 At block 972, method 900 can use the sparseness S determined at
block 971
to retain indices of the largest S elements of the estimate of the information
signal ("x").
At block 973, method 900 can use the S indices determined at block 972 to set
the
largest S elements of the estimate of the information signal ("x") to first
value 974. At
block 975, method 900 can then set the remaining N-S elements of the estimate
of the
information signal ("x") to second value 976. The output of quantizer 953 can
be a
quantized estimate of the information signal ("x"), referred to as i First
value 974 may
be, for instance, a logical one. Further, second value 976 may be, for
instance, a logical
zero.
[00991 FIG. 10 is chart 1000 illustrating an example of the type of sparse
representation matrix and sensing matrix used in sensor-based wireless
communication
system 100, 200, 300, 400, 600 and 800 using compressive sampling in
accordance with
various aspects set forth herein. In one embodiment, a sensor-based wireless
communication system using compressive sampling may use random matrices for
the
sparse representation matrix ("T") and the sensing matrix ("0"). The random
matrices
are composed of, for instance, independently and identically distributed
("ud") Gaussian
values.
(001001 In another embodiment, a sensor-based wireless communication system
using
compressive sampling may use deterministic matrices for the sparse
representation
matrix ("T") and the sensing matrix ran. The deterministic matrices are
composed of,
for instance, an identity matrix for the sparse representation matrix ("T")
and a cosine
matrix for the sensing matrix ("O"). A person of ordinary skill in the art
would
recognize that many different types and combinations of matrices might be used
for a
sensor-based wireless communication system using compressive sampling.
1001011 FIG. 11 illustrates one embodiment of user equipment 1100, which can
be
used in sensor-based wireless communication system 100, 200, 300, 400, 600 and
800
using compressive sampling in accordance with various aspects set forth
herein. In FIG.
11, user equipment 1100 can include modulator 1140 for modulating an uplink
message
to form an information signal ("x"). Generator 1141 can receive the
information signal
("x") and can apply a sparse representation matrix ("T") 1143 to the
information signal
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("x") to generate an uplink signal (7'), which is transmitted by uplink
transmitter 1142
using, for instance, antenna 1364. User equipment 1100 can also include a
downlink
receiver 1148 for downconverting a downlink signal received by antenna 1164.
The
received downlink signal can then be processed by demodulator 1149 to generate
a
downlink message.
1001021 In this embodiment, user equipment 1100 can include oscillator 1162
for
clocking user equipment 1100 and maintaining system timing, power supply 1163
such
as battery 1361 for powering user equipment 1100, input/output devices 1367
such as a
keypad and display, memory 1360 coupled to controller 1147 for controlling the
operation of user equipment 1100, other elements or combination of elements. A
person
of ordinary skill in the art will recognize the typical elements found in a
user's
equipment.
1001031 FIG. 12 illustrates one embodiment of a sensor 1200, which can be
used in
sensor-based wireless communication system 100, 200, 300, 400, 600 and 800
using
compressive sampling in accordance with various aspects set forth herein. In
FIG. 12,
sensor 1200 can include receiving element 1230 for downconverting an uplink
signal
("j") received by, for instance, antenna 1264. Compressive sampler 1231 can
apply a
sensing matrix ("0") 1233 to the uplink signal (7') to generate a sensed
signal ("y"),
which can be sent using sensor transmitter 1232.
1001041 In this embodiment, sensor 1200 can include oscillator 1262 for
clocking
sensor 1200 and maintaining system timing, power supply 1263 such as battery
1261 for
powering user equipment 1100, memory 1260 coupled to controller or state
machine
1237 for controlling the operation of sensor 1200, other elements or
combination of
elements. Controller 1237 may be implemented in hardware, software, firmware
or any
combination thereof. Further, controller 1237 may include a microprocessor,
digital
signal processor, memory, state machine or any combination thereof.
1001051 FIG. 13 illustrates one embodiment of base station 1300, which can
be used
in sensor-based wireless communication system 100, 200, 300, 400, 600 and 800
using
compressive sampling in accordance with various aspects set forth herein. In
FIG. 13, in
the uplink direction, base station 1300 can include collector 1350 for
collecting sensed
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signal ("y"). Detector 1351 can receive the collected sensed signal ("y") and
can use a
sensing matrix ("O") 1233 and a sparse representation matrix ("T") 1143 to
estimate and
detect information signal ("x") from the collected sensed Signal ("y").
Controller 1357
may evaluate the detected information signal ") to determine the uplink
message. In
the downlink direction, base station 1300 can include a modulator 1359 for
modulating a
downlink message and downlink transmitter interface 1358 for sending the
modulated .
downlink signals.
[00106] In this embodiment, base station 1300 can include oscillator 1362
for
clocking base station 1300 and maintaining system timing, power supply 1363
for
powering base station 1300, memory 1360 coupled to controller 1337 for
controlling the
operation of base station 1300, sensor controller 1355 for controlling a
sensor, downlink -
transmitter controller for controlling a downlink transmitter, other elements
or
combination of elements.
[00107] In one embodiment, sensor-based wireless communication system 100,
200,
300, 400, 600 and 800 may use a plurality of sensors 110 to 113,210 to 213,
310, 610,
710, 810, 1200 and 1310 to process uplink signal (r) to allow for the joint
detection of
a presence signal at base station 102, 202, 302, 602, 702, 802 and 1302 by
using antenna
array signal processing techniques, MIMO signal processing techniques,
beamforrning
techniques, other techniques or combination of techniques. The use of a
plurality of
sensors 110 to 113, 210 to 213, 310, 610, 710, 810, 1200 and 1310 may allow
the value
ofM to be lower at each sensor 110 to 113, 210 to 213, 310, 610, 710, 810,
1200 and
1310. Therefore, the power consumption of each sensor 110 to 113, 210 to 213,
310,
610, 710, 810, 1200 and 1310 may be reduced by placing the plurality of
sensors 110 to
113,210 to 213, 310, 610, 710, 810, 1200 and 1310, for instance, in a more
dense
deployment.
1001081 In another embodiment, sensor-based wireless communication system 100,
200, 300, 400, 600 and 800 may deploy sensors 110 to 113,210 to 213, 310, 610,
710,
810, 1200 and 1310 to allow typically two sensors 110 to 113,210 to 213, 310,
610,
710, 810, 1200 and 1310 to receive uplink signals ("j") transmitted by user
equipment
706. Such a deployment may be in an indoor environment where sensors 110 to
113,
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210 to 213, 310, 610, 710, 810, 1200 and 1310 may be deployed by, for
instance, a thirty
meters separation distance with a path loss exponent between two or three.
Sensors 110
to 113,210 to 213, 310, 610, 710, 810, 1200 and 1310 may each be deployed to
cover a
larger area; however, the path loss exponent may be smaller. For successful
detection,
the probability of detecting a single presence signal may be above ten
percent.
[001091 In another embodiment, sensor-based wireless communication system 100,
200, 300, 400, 600 and 800 may deploy sensor 110 to 113,210 to 213, 310, 610,
710,
810, 1200 and 1310 in macrocells to support, for instance, vehicular
communication,
other communication or combination of communication. Further, sensor 110 to
113,
210 to 213, 310, 610, 710, 810, 1200 and 1310 may be deployed in microcells to
support, for instance, pedestrian communication, indoor communication, office
communication, other communication or combination of communication.
[001101 In system 100, 200, 300, 400, 600 and 800, channel 620 and 820 may be
static with channel gain ("a") 621 and 821 and channel noise ("v") 622 and 821
may be
additive white Gaussian noise ("AWGN"). Channel noise ("v") 622 and 821 may
include an additive signal, which may distort the receiver's view of the
information of
interest. The source of the channel noise ("v") may be, for instance, thermal
noise at a
receive antenna, co-channel interference, adjacent channel interference, other
noise
sources or combination of noise sources. Further, sensor 110 to 113, 210 to
213, 310,
610, 710, 810, 1200 and 1310; user equipment 106, 206, 306, 606, 706, 806 and
1100;
base station 102, 202, 302, 602, 702, 802 and 1302; or any combination thereof
may be
sufficiently synchronized in timing, frequency, phase, other conditions or
combination
of conditions thereof. In addition, there may be only one sensor 110 to 113,
210 to 213,
310, 610, 710, 810, 1200 and 1310; one user equipment 106, 206, 306, 606, 706,
806
and 1100; one base station 102, 202, 302, 602, 702, 802 and 1302; or any
combination
thereof.
[001111 The compressive sampling scheme may use a sparse representation matrix
(*V") and a sensing matrix ("(I)") that are, for instance, a random pair, a
deterministic
pair or any combination thereof. For these matrices, base station 102, 202,
302, 602,
702, 802 and 1302, sensor 110 to 113,210 to 213, 310, 610, 710, 810, 1200 and
1310,
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user equipment 106, 206, 306, 606, 706, 806 and 1100, or any combination
thereof may
be provided with, for instance, the sparse representation matrix ("IP"), the
sensing matrix
("D") or both, information such as a seed value to generate the sparse
representation
matrix ("T"), the sensing matrix ("0") or both, or any combination thereof.
Base station
102, 202, 302, 602, 702, 802 and 1302 may know which sparse representation
matrix
("P") and sensing matrix ("D") are being used. Base station 102, 202, 302,
602, 702,
802 and 1302 may instruct sensor 110 to 113, 210 to 213, 310, 610, 710, 810,
1200 and
1310 to use a specific set ofM sensing waveforms ("(pj ") of sensing matrix
("0").
Further, base station 102, 202, 302, 602, 702, 802 and 1302 may instruct user
equipment
106, 206, 306, 606, 706, 806 and 1100 and sensor 110 to 113, 210 to 213, 310,
610, 710,
810, 1200 and 1310 that the uplink signal consists, for instance, of N
intervals or chips.
100112J The aforementioned random matrices, deterministic matrices or both may
be
generated only once or may not change if generated again. Further, these
matrices may
be regenerated after some time, for instance, a few seconds. Also, these
matrices may be
regenerated each time they are to be used. In any case, the detector, which
includes the
solver, of base station 102, 202, 302, 602, 702, 802 and 1302 may know the
sparse
representation matrix ("T") used by user equipment 706 as well as the sensing
matrix
("O") used by the sampler. A person of ordinary skill in the art would
recognize that
this does not mean that the base station must provide the matrices. On the
other hand,
for example, user equipment 106, 206, 306, 606, 706, 806 and 1100 and base
station
102, 202, 302, 602, 702, 802 and 1302 may change the sparse representation
matrix
("T") according to, for instance, a pseudo-noise ("pn") function of the system
time.
Similarly, for example, sensor 110 to 113,210 to 213, 310, 610, 710, 810, 1200
and
1310 and base station 102, 202, 302, 602, 702, 802 and 1302 may change the
sensing
matrix ("0") according to, for instance, a pseudo-noise ("pn") function of the
system
time.
[001131 FIG. 14 illustrates simulated results of one embodiment of detecting a
user
equipment in a sensor-based wireless communication system using compressive
sampling in accordance with various aspects set forth herein, where the
performance of
system 800 was measured using N=10, M=5, S=1 or 2, and random matrices. The
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graphical illustration in its entirety is referred to by 1400. The logarithmic
magnitude of
the signal-to-noise ("SNR") ratio is shown on abscissa 1401 and is plotted in
the range
from 0 decibels ("dB") to 25 dB. The probability of detection ("Pr (detect)")
is shown
on ordinate 1402 and is plotted in the range from zero, corresponding to zero
probability, to one, corresponding to one hundred percent probability. Graphs
1403,
1404 and 1405 represent simulation results for system 800, where N is ten, M
is five, S is
one or two and random iid Gaussian values are used to populate the sparse
representation matrix ("T") and the sensing matrix ("0"). Graph 1403 shows the
probability of detecting one non-zero entry in a quantized estimate of the
information
signal ("x"), where S is one. Graph 1404 shows the probability of detecting
one non-
zero entry in a quantized estimate of the information signal ("x"), where S is
two. Graph
1405 shows the probability of detecting two non-zero entries in a quantized
estimate of
the information signal ("x"), where S is two.
1001141 FIG. 15 illustrates simulated results of the performance of one
embodiment
of a sensor-based wireless communication system using compressive sampling in
accordance with various aspects set forth herein, where the performance of
system 800
was measured using N=20, M=10, S=1 or 2, and random matrices. The graphical
illustration in its entirety is referred to by 1500. The logarithmic magnitude
of the SNR
ratio is shown on abscissa 1501 and is plotted in the range from 0 dB to 25
dB. The
probability of detection ("Pr (detect)") is shown on ordinate 1502 and is
plotted in the
range from zero, corresponding to zero probability, to one, corresponding to
one
hundred percent probability. Graphs 1503, 1504, 1505, 1506 and 1507 represent
=
simulation results for system 800, where Nis twenty, M is ten, S is one or two
and
random iid Gaussian values are used to populate the sparse representation
matrix ("P")
and the sensing matrix ("0"). Graph 1503 shows the probability of detecting
one non-
zero entry in a quantized estimate of the information signal ("x"), where S is
one. Graph
1504 shows the probability of correctly detecting two non-zero entries in a
quantized
estimate of the information signal ("x"), where S is two. Graph 1505 shows the
probability of correctly detecting no non- zero entries in a quantized
estimate of the
information signal ("x"), where S is one. Graph 1506 shows the probability of
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detecting no non-zero entries in a quantized estimate of the information
signal ("x"),
where S is two. Graph 1507 shows the probability of correctly detecting one
non-zero
entry in a quantized estimate of the information signal ("x"), where S is two.
[00115] FIG. 16 illustrates simulated results of the performance of one
embodiment
of a sensor-based wireless communication system using compressive sampling in
accordance with various aspects set forth herein, where the performance of
system 800
was measured using N=10, M=3, S=1, and deterministic or random matrices. The
graphical illustration in its entirety is referred to by 1600. The logarithmic
magnitude of
the SNR ratio is shown on abscissa 1601 and is plotted in the range from 0 dB
to 25 dB.
The probability of detection ("Pr (detect)") is shown on ordinate 1602 and is
plotted in
the range from zero, corresponding to zero probability, to one, corresponding
to one
hundred percent probability. Graphs 1603, 1604, 1605, 1606 and 1607 represent
simulation results for system 800, where N is twenty, M is ten, S is one or
two and
deterministic values are used for the sparse representation matrix ("T") and
the sensing
matrix ("*D"). Graph 1603 shows the probability of correctly detecting one non-
zero
entry in a quantized estimate of the information signal ("x"), where S is one.
Graph
1604 shows the probability of correctly detecting two non-zero entries in a
quantized
estimate of the information signal ("x"), where S is two. Graph 1605 shows the
probability of correctly detecting no non- zero entries in a quantized
estimate of the
information signal ("x"), where S is one. Graph 1606 shows the probability of
correctly
detecting no non-zero entries in a quantized estimate of the information
signal ("x"),
where S is two. Graph 1607 shows the probability of correctly detecting one
non-zero
entry in a quantized estimate of the information signal ("x"), where S is two.
[001161 FIG. 17 illustrates simulated results of the performance of one
embodiment
of a sensor-based wireless communication system using compressive sampling in
accordance with various aspects set forth herein, where the performance of
system 800
was measured using N=10, M=3, S=1, and random or deterministic matrices. The
graphical illustration in its entirety is referred to by 1700. The logarithmic
magnitude of
the SNR ratio is shown on abscissa 1701 and is plotted in the range from 0 dB
to 45 dB.
The probability of detection ("Pr (detect)") is shown on ordinate 1702 and is
plotted in
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the range from zero, corresponding to zero probability, to one, corresponding
to one
hundred percent probability. Graphs 1703, 1704, 1705 and 1706 represent
simulation
results for system 800, where N is ten, M is three and S is one. Graph 1703
shows the
probability of correctly detecting one non-zero entry in a quantized estimate
of the
information signal ("x"), where deterministic matrices are used. Graph 1704
shows the
probability of correctly detecting one non-zero entry in a quantized estimate
of the
information signal ("x"), where iid Gaussian random matrices are used. Graph
1705
shows the probability of correctly detecting no non-zero entries in a
quantized estimate
of the information signal ("x"), where iid Gaussian random matrices are used.
Graph
1706 shows the probability of correctly detecting no non-zero entries in a
quantized
estimate of the information signal ("x"), where deterministic matrices are
used.
1001171 FIG. 18 illustrates simulated results of the performance of one
embodiment
of a sensor-based wireless communication system using compressive sampling in
accordance with various aspects set forth herein, where the performance of
system 800
was measured using N=10, M=5, 5=2, and random matrices. Further, the sparse
representation matrix ("`P") and the sensing matrix ("t) were varied prior to
each
transmission of the information signal ("x"). The graphical illustration in
its entirety is
referred to by 1800. The logarithmic magnitude of the SNR ratio is shown on
abscissa
1801 and is plotted in the range from .0 dB to 50 dB. The probability of
detection ("Pr
(detect)") is shown on ordinate 1802 and is plotted in the range from zero,
corresponding to zero probability, to one, corresponding to one hundred
percent
probability. Graphs 1803, 1804, 1805 and 1806 represent simulation results for
system.
800, where N is ten, M is five, S is two, random lid Gaussian matrices are
used for the
sparse representation matrix ("LP") and the sensing matrix ("D") and the
random
matrices are regenerated prior to each transmission. Graph 1803 shows the
probability
of detecting two non- zero entries in a quantized estimate of the information
signal ("x").
Graph 1804 shows the probability of detecting two non-zero entries in a
quantized
estimate of the information signal ("x"), where any two sensing waveforms
("(pj ") of
sensing matrix ("ED") are substantially incoherent. Graph 1805 shows the
probability of
detecting one non-zero entry in a quantized estimate of the information signal
("x"),
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where any two sensing waveforms ("of ") of sensing matrix ("0") are
substantially
incoherent. Specifically, graph 1804 and graph 1805 also represent the effect
of
rejecting any two sensing waveforms ("of ") of sensing matrix ("an having a
correlation magnitude greater than 0.1. Graph 1806 shows the probability of
detecting
one non-zero entry in a quantized estimate of the information signal ("x").
1001181 FIG. 19 illustrates simulated results of the performance of one
embodiment
o f a sensor-based wireless communication system using compressive sampling in
accordance with various aspects set forth herein, where the performance of
system 800
was measured using N=10, M=3, S=1, random matrices, and various number of
trials.
Further, the sparse representation matrix ("T") and the sensing matrix ("(D")
were varied
prior to each transmission of the information signal ("x"). The graphical
illustration in
its entirety is referred to by 1900. The logarithmic magnitude of the SNR
ratio is shown
on abscissa 1901 and is plotted in the range from 0 dB to 50 dB. The
probability of
detection ("Pr (detect)") is shown on ordinate 1902 and is plotted in the
range from zero,
corresponding to zero probability, to one, corresponding to one hundred
percent
probability. Graphs 1903, 1904, 1905, 1906 and 1907 represent simulation
results for
system 800, where N is ten, M is three, S is one, random lid Gaussian matrices
are used
for the sparse representation matrix ("T") and the sensing matrix ("O") and
the random
matrices are regenerated prior to each transmission. Graph 1903 shows the
probability
of detecting one non-zero entry in a quantized estimate of the information
signal ("x"),
where any two sensing waveforms ("(pi ") of sensing matrix ("cD") are
substantially
incoherent and two hundred trials are performed. Specifically, graph 1903 also
represents the effect of rejecting any two sensing waveforms ("pi ") of
sensing matrix
(NY') having a correlation magnitude greater than 0.1. Graph 1904 shows the
probability of correctly detecting one non-zero entry in a quantized estimate
of the
information signal ("x"), where two hundred trials are performed. Graph 1905
shows the
probability of correctly detecting one non-zero entry in a quantized estimate
of the
information signal ("x"), where four thousand trials are performed. Graph 1906
shows
the probability of correctly detecting one non-zero entry in a quantized
estimate of the
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information signal ("x"), where one thousand trials are performed. Graph 1907
shows
the probability of correctly detecting one non-zero entry in a quantized
estimate of the
information signal ("x"), where two thousand trials are performed.
1001191 FIG. 20 is an example of deterministic matrices used in one embodiment
of a
sensor-based wireless communication system using compressive sampling in
accordance
with various aspects set forth herein. The example of the deterministic
matrices is
collectively referred to as 2000. Matrices 2001 and 2002 are representative of
the
deterministic matrices that can be used in systems 100, 200, 300, 400, 600 and
800,
where N is ten and M is five. Matrix 2001 can represent the transform of the
sensing
matrix ("0"). Matrix 2002 can represent the sparse representation matrix
("T").
1001201 FIG. 21 is an example of random matrices used in one embodiment of a
sensor- based wireless communication system using compressive sampling in
accordance with various aspects set forth herein. The example of the random
matrices is
collectively referred to as 2100. Matrices 2101 and 2102 are representative of
the
random matrices that can be used in systems 100, 200, 300, 400, 600 and 800,
where N
is ten and M is five. Matrix 2101 can represent the transform of the sensing
matrix
("0"). Matrix 2102 can represent the sparse representation matrix ("T").
1001211 A different way of sampling is shown in Figure 22. This figure is
based on
[CW08]. The sampler in Figure 22 is a set of sensing waveforms, (I). The
signal, x, can
be recovered without error if f is sparse. An N dimensional signal is S-
sparse, if in the
representation f =tPx, x only has S nonzero entries (see [CW08, page 23]).
Representation parameters are the parameters which characterize the variables
in the
expression f =Tx. These parameters include the number of rows in P. i.e. N,
the values
of the elements of T, and the number of nonzero entries in x, i.e. S. The
steps of
sampling and recovery in Figure 22 are replaced by a new pair of operations,
sensing
and solving.
1001221 Step 1. Sensing.
1001231 Yk = (f. 490. k Ã1 such that/ c (I ¨N) (4)
(001241 Step 2. Solving.
1001251 nLcE 11-N ) gx" D. (is 1 ) subject to yLk = (04k. (k E j (5)
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1001261 Equations (1) and (2) are from [CW08, equations 4 and 5]. In Eq.
(1), the
brackets C , denote inner product, also called correlation. The II norm,
indicated by
llx1111, is the sum of the absolute values of the elements of its argument.
1001271 In order to use as few sensing waveforms as possible, the coherence
between
the vectors of the basis, T and the vectors used for sensing taken from (1)
must be low
[CW08, equations 3 and 6]. The coherence, p is given by
p(4). %V) = max 1140k, W.) )11
1001281 15.k.j53: (6)
1001291 The Incoherent Sampling Method for designing a sampling system
(compare
with [CW08]) is:
1001301 1 Model! and discover in T which f is S-sparse.
1001311 2 Choose a (I) which is incoherent with T.
1001321 3 Randomly select M columns of (I), where Al5S.
[001331 4 Sample f using the selected co vectors to produce y.
1001341 5 Pass P. (I) and y to an II minimizer, and recover x.
1001351 One method which can be applied for // minimization is the simplex
method
[LY08].
1001361 An embodiment of the invention shown in Figure 23 includes a low power
receiver. The RF portions of the low power receiver can be implemented as
taught in
[ESY05, KJR+06]. The figure represents a multiple access system 2300. The
multiple
Access Schemes that can be used in the system, include FDMA, TDMA, DS-CDMA,
TD/CDMA using FDD and TDD modes [Cas04, pp. 23-45, 109] and OFDM access
scheme [AAN08]. The system includes a user equipment or UE 2206 and an
infrastructure 2210. The UE 2206 includes a mobile station, cellular-radio
equipped
laptop computer, and smart phone. The infrastructure 2210 includes the parts
of the
cellular system, which is not the UE, such as remote samplers 2212, base
station 2216,
central brain, and DL tower 2222. The remote samplers 2212 includes a device
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consisting of an antenna, a down-conversion RF section, a correlating section,
a
controller or state machine for receiving instructions over a backhaul, a
memory for
storing a configuration and optical transmitter to send the correlation
results or value
over a fiber ( back-haul) to the base station 2216. Each base station 2216
will be fed by
more than one remote sampler 2212, in general. Remote samplers 2212 may be
deployed in a system using the Central Brain concept, or in a system not using
the
Central Brain concept.
[001371 Conversion includes representing an input waveform is some other form
suitable for transmission or computation. Examples are shifting the frequency
of a
signal (down conversion), changing from analog to digital form (A to D
conversion).
1001381 The central brain is a high-powered infrastructure component which can
carry out computations at a very high speed with acceptable cost. The central
brain
includes infrastructure components which can communicate with the base
stations
quickly so that many physical layer computing activities can be carried out at
the Central
Brain. Radio control via the base station and the DL tower is not so slow as
to be
infeasible to overcome communications impairments associated with the rate of
fading
of the channel. The Central Brain and the Base Station may physically be the
same
computer or infrastructure component. The base station transmitter is located
at the DL
(downlink) Tower 2222 which includes a conventional cellular tower, cellular
transmitters mounted on buildings, light poles or low power units in offices.
1001391 The downlink, DL 2220 is the flow of information-bearing RF energy
from
the infrastructure to the User Equipment or UE. This includes radio signals
transmitted
by the DL tower 2222 and received by a UE 2206.
[001401 Fading includes descriptions of how a radio signal can be bounced off
many
reflectors and the properties of the resulting sum of reflections. Please see
[BB99, Ch.
13] for more information on fading.
[001411 Environmental parameters includes the range from the LTE to the remote
sampler, the range from the UE to the DL tower, the SNR at any remote sampler
of
interest and any co channel signal which is present and any fading.
1001421 There are several kinds of access in cellular systems. Aloha random
access
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takes place when the UE wishes to reach the infrastructure, but the
infrastructure does
not know the UE is there. Two-way data exchange takes place after the UE has
been
given permission to use the system and UL and DL channels have been assigned.
For
more discussion of access, please see [Cas04, pg. 119].
[001431 "Channels" include permitted waveforms parameterized by time,
frequency,
code and/or space limitations. An example would by a particular TDMA slot- in
a
particular cell sector in a GSM system. User data and/or signaling information
needed
for maintaining the cellular connection are sent over channels.
1001441 The term "Base Station" is used generically to include description of
an
entity which receives the fiber-borne signals from remote samplers, hosts the
11 solver
and Quantizer and operates intelligently (that is, runs computer software) to
recognize
the messages detected by the Quantizer to carry out protocol exchanges with
UEs
making use of the DL. It generates the overhead messages sent over the DL. It
is
functionally part of the Central Brain concept created by RIM. A "Solver"
includes a
device which uses the It distance measure. This distance is measured as the
sum of the
absolute values of the differences in each dimension. For example, the
distance between
(1.0, 1.5, 0.75) and (0, 2.0,0.5) is 11 ¨ 01+11.5 ¨ 2.01+10.75 ¨ 0.51=1.75. A
"Quantizer" includes a device which accepts an estimate as input and produces
one of a
finite set of information symbols or words as output.
1001451 The base station receiver, solver, quantizer, and a controller are
at the point
called "base station" 2216 in the figure. The base station 2216 and DL Tower
2222
could be co- located, and in any event they are completely connected for
signaling
purposes. Uplink 2224 is the flow of information-bearing RF energy from the UE
2206
to the infrastructure 2210. This includes radio signals transmitted by the UE
2206 and
received by one or more remote samplers 2212.
1001461 Cellular systems provide multiple access to many mobile users for real
time
two way communication. Examples of these systems are GSM, IS-95, UMTS, and
UMTS-Wi-Fi [Cas04, pg. 559].
1001471 A mixed macro/micro cellular network includes large cells for vehicles
and
small cells for pedestrians [Cas04, pg. 453. For a general perspective on
cellular system
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design, the GSM or WCDMA systems are suitable reference systems. That is, they
exhibit arrangements of mobile stations (UEs), base stations, base station
controllers and
so on. In those systems various signaling regimes are used depending on the
phase of
communication between the UE and the infrastructure such as random access,
paging,
resource allocation (channel assignment), overhead signaling (timing, pilot
system id,
channels allowed for access), handover messaging, training or pilot signals on
the uplink
and downlink and steady state communication (voice or data, packet or
circuit).
[00148] Feeding an unsampled analog signal to a base station via a fiber was
presented in [CG91]. In Chu, a kind of transducer is attached to an antenna
and feeds a
fiber. The transducer in [CG91.) does not sample the RF signal, it simply
converts it to
optical energy using an analog laser transmitter. Part of the novelty of this
invention is
the number and nature of values sent to the base station from a remote antenna
and how
the number and nature is controlled.
1001491 Figure 24 is often thought of in the.context of lossless sampling. If
the power
spectrum of a signal A(f) is zero for Ifj >fmax, then the time domain signal
a(t) can be
represented based on discrete samples taken at rate 2fmax [Pro83, page 71]. In
this
general scenario, the only thing the sampler knows about A(f) is that it is
zero above
fmax.
[001501 For a radio system in which the sampler is locked to the chip rate, in
general,
lossless sampling would consist of sampling once per chip. For an N chip
waveform,
which includes a frame defined at N discrete, sequential points in time, this
would mean
N samples per chip-level codeword. The frame might be a frame ready for
conversion to
passband for transmission, or it might simply be a frame of boolean, real, or
complex
values inside of a computing device or memory. In one embodiment of this
invention, N
chip waveforms are sensed with M values, where M <N. "Frame" includes a
collection
of time samples captured in sequence. It may also describe a collection of
boolean (or
real or complex) values generated in sequence.
1001511 "Noise" includes an additive signal, which distorts the receiver's
view of the
information it seeks. The source may be thermal noise at receive antenna, or
it may be
co channel radio signals from undesired or other desired sources, or it may
arise from
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other sources. The basic theory of detection of signals in noise is treated in
[BB99, Ch.
2.6]. 0=
1001521 "Performance" includes how well a radio system is doing according to a
designer's intended operation. For instance, the designer may wish that when a
UE
powers up and recognizes an overhead signal, it will send a message alerting
the base
station. The performance of the base station detection of this signal includes
the
probability that the base station will recognize a single transmission of that
message.
The performance varies depending on the system parameters and environmental
factors.
"System parameters" includes the length of message frames, the number of
sensing
waveforms and the sparseness of the messages being sent.
1001531 The Uplink is the flow of information-bearing RF energy from the UE to
the
infrastructure. This includes radio signals transmitted by the UE and received
by one or
more remote samplers. Incoherent sampling includes a kind of compressive
sampling
which relies on sensing waveforms (columns of (I)) which are unrelated to the
basis, tP,
in which the input signal is sparse. This report discloses simple sampling and
low rate
data transmission to conserve battery power at the remote sampler, please see
Figure 25.
Compressive sampling includes a technique where a special property of the
input signal,
sparseness, is exploited to reduce the number of values needed to reliably (in
a statistical
sense) represent a signal without loss of desired information. Here are some
general
points about the inventive architecture.
1001541 I. The overall cellular system continues to operate with full
performance
even if a sampler stops working.
1001551 2. The remote samplers are widely distributed with a spacing of 30 to
300 m
in building/city environments.
100156j 3. The base station is not limited in its computing power.
1001571 4. The cellular system downlink is provided by a conventional cell
tower,
with no unusual RF power limitation.
1001581 5. UE battery is to be conserved, the target payload data transmission
power
level is 10 to 100 It Watts.
1001591 6. Any given remote sampler is connected to the base station by a
fiber optic.
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One alternative for selected sampler deployments would be coaxial cable.
1001601 7. If possible, the remote sampler should operate on battery power.
Using
line power (110 V, 60 Hz in US) is another possibility.
1001611 From the overall system characteristics, we infer the following
traits of a
remote sampler.
1001621 1. The remote sampler is very inexpensive, almost disposable.
1001631 2. The remote sampler battery must last for 1-2 years.
1001641 3. The remote sampler power budget will not allow for execution of
receiver
detection/demodulation/decoding algorithms.
[00165j 4. The remote sampler will have an RF down conversion chain and some
scheme for sending digital samples to the base station.
1001661 5. The remote sampler will not have the computer intelligence to
recognize
when a UE is signaling.
1001671 6. The remote sampler can receive instructions from the base station
related
to down conversion and sampling.
1001681 Examples of modulation schemes are QAM and PSK and differential
varieties [Pro83, pp. 164, 188], coded modulation [BB99, Ch.12].
1001691 From those traits, these Design Rules emerge:
1001701 Rule A: Push all optional computing tasks from the sampler to the base
station.
[001711 Rule B: Drive down the sampler transmission rate on the fiber to the
lowest
level harmonious with good system performance.
1001721 Rule C: In a tradeoff between overall system effort and sampler
battery
saving, overpay in effort.
[00173j Rule D: Make the sampler robust to evolutionary physical layer changes
without relying on a cpu download.
1001741 From the Design Rules, we arrived at the design sketched in Figures 23
and
25.
In this report, we have focused on the problem of alerting the base station
when a
previously- unrecognized UE (User Equipment or mobile station) is present. The
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situation is similar to one of the access scenarios described in [LKL+08,
"Case 1"],
except that we have not treated power control or interference here. There are
well
known methods to control those issues. The sampler operates locked to a system
clock
provided by the base station.
[00175J See Figure 26 for an illustration of the messages being sent in
cellular system
access event that this report is focused on. Figure 26 is one example
situation which
illustrates the UE 2206 sending Presence signals 2314. In the figure, the UE
2206
powers on, observes overhead signals 2312, and begins to send Presence Alert
signals
2314. The term "Presence Signal" includes any signal which is sent by the UE
2206 to
the base station which can be incoherently sampled by sense waveforms. "Sense
waveforms" includes a column from the sensing matrix, <D, which is correlated
with a
frame of the input to obtain a correlation value. The correlation value is
called
Y: where i is the column of4Dused in the correlation. In general, the UE 2206
may use
Presence Alert signals 2314 whenever it determines, through overhead
information
2312, that it is approaching a cell which is not currently aware of the UE
2206. The
remote sampler 2212 sends sense measurements, y, continuously unless M=0.
1001761 Sense parameters are the parameters which characterize the variables
in the
expression. Overhead 2312 is sent continuously. The Presence Alert signal 2314
is sent
with the expectation that it will be acknowledged. The UE and base station
exchange
messages in this way: UL is UE 2206 to remote sampler 2212. The remote sampler
2212 continuously senses, without detecting, and sends sense measurements y to
the
base station 2216 over a fiber optic. The DL is the base station tower 2222 to
UE 2206,
for instance the message 2318 instructing UEs to use sparsity 52 when sending
a
Presence signal 2314. A sparse signal includes an N-chip waveform which can be
created by summing S columns from an NxN matrix. An important characteristic
of this
signal is the value of S, "sparsity". For nontrivial signals, S ranges from
Ito N. An
instruction 2316 changing the value of M used by the remote sampler 2212 is
shown.
An indication is a way of messaging to a UE or instructing a remote sampler as
the
particular value of a particular variable to be used. The figure is not
intended to show
exactly how many messages are sent.
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1001771 The UE also has access to the system clock via overhead transmissions
from
the base station on the downlink (DL). The remote sampler observes a bandwidth
of
radio energy, B, centered at some frequency fc. Generally, it does not treat B
as the only
information it has, so it does provide samples at rate 2B over the fiber to
the base station.
Rather, the sampler obtains N samples of the N chip waveform, and computes M
correlations. The resulting M values are sent over the fiber to the base
station. If the
sampler does not have chip timing lock, it can acquire 2N samples at half-chip
timing
and compute 2M correlations. The reduction in samples sent to the base station
is from
2N for a conventional approach to 2M.
1001781 The sampler is able to compute sensing measurements, y, by correlating
with
independently selected columns of the (I) matrix. Sensing parameters are the
parameters
which characterize the variables in the correlation of the received signal g
with columns
of the (I) matrix. These parameters include the number of elements in y, i.e.
M, the
values of the elements of (1), and the number of chip samples represented by
g, i.e., N.
Selection of the columns of the (I) matrix which are used is without any
knowledge of x
except selection of the value of M itself relies on an estimate of S. So,
which columns of
= (1) are used is independent of but the number of columns of (I) used is
dependent on an
estimate of a property of f. Or, the sparsity of f can be controlled by DL
transmissions
as shown at time tl 7 in Figure 26.
(001791 A necessary condition for successful detection of x at the base
station, is that
the value of M used by the remote sampler must be chosen greater than S. The
lack of
knowledge of S can be overcome by guessing at the base station, and adjusting
thereafter. For instance, M may start out with a maximum value of N, and as
the base
station learns the activity level of the band B, M can be gear shifted to a
lower, but still
sufficiently high, value. In this way, power consumption at the remote
sampler, both in
computing correlations, y, and in transmissions to the base station on the
fiber, can be
kept low. The base station might periodically boost M (via instruction to the
remote
sampler) to thoroughly evaluate the sparsity of signals in the band B. The
base station
can direct the sampler as to which columns it should use, or the sampler may
select the
columns according to a schedule, or the sampler may select the columns
randomly and
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inform the base station as to its selections.
1001801 Detection includes operating on an estimated value to obtain a nearest
point
in a constellation of finite size. A constellation includes a set of points.
For example, if
each point in the constellation is uniquely associated with a vector
containing N entries,
and each entry can only take on the values 0 or 1 (in general, the vector
entries may be
booleans, or reals, or complex) then the constellation has 2N or fewer points
in it.
1001811 The UE 2206, upon powering on, wishes to let the system know of its
existence. To do this, the UE sends a Presence Alert signal 2314. The Presence
Alert
signal is an informative signal constructed by selecting columns out of the
'I' matrix and
summing them. The selection of columns can be influenced by the base station
overhead
signal. For instance, the base station may specify a subset of columns which
are to be
selected from.
1001821 The base station can require, via a DL overhead message 2312, that a
UE
which has not yet been recognized, to transmit one particular column, say 4/0.
This
would act as a pilot. The remote sampler 2212 would operate, according to
Incoherent
Sampling, and send samples y to the base station 2216. The base station 2216
would
then process this signal and detect the presence of ,0, estimate the complex
fading
channel gain, a% between the previously-unrecognized UE and the remote
sampler, and
then instruct any UEs which had been sending Iy0 to commence sending the last
two bits
of their ESN (Electronic Serial Number, a globally unique mobile station
identifier), for
example. -Sampling" includes changing a signal from one which has values at
every
instant of time to a discrete sequence which corresponds to the input at
discrete points in
time (periodic or aperiodic).
1001831 If a collision occurs between transmissions from two different
mobile
stations the uplink (UL), standard Aloha random back-off techniques may be
used to
separate subsequent UL attempts.
1001841 The remote sampler 2212 is unaware of this protocol progress, and
simply
keeps sensing with columns from (11. and sending the samples y to the base
station 2216.
The base station 2216 may instruct the remote sampler 2212 to use a particular
quantity,
M, of sensing columns. This quantity may vary as the base station anticipates
more or
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less information flow from the UEs. If the base station anticipates that S.
which has a
maximum of N, is increasing, it will instruct the remote sampler to increase M
(the
maximum value M can take on is N). For example, in Figure 26, the Recognition
Message can include a new value of S, S , to be used by the UE, and at the
same time
the base station can configure the remote sampler to use a higher value of M,
called Ma
in the figure. In the figure these events occur at times t15 and . At
t17 the base
station expects a message with sparsity SZ and that that message has probably
been
sensed with an adequate value of M, in particular the value called here Ma . A
sequence
of events is illustrated, but the timing is not meant to be precise. In the
limit as M is
increased, if (I) is deterministic (for example, sinusoidal) and complex, when
M takes on
the limiting value N,41:0 in the remote sampler has become a DFT operation
(Discrete
Fourier Transform possibly implemented as an FFT). Continuing with the
scenario
description, once the base station has a portion of the ESNs of all the UEs
trying to
access the system, the base station can tell a particular UE, with a
particular partial ESN,
to go ahead and transmit its full ESN and request resources if it wishes. Or
the base
station may assign resources, after determining that the UE is eligible to be
on this
system.
1001851 The remote sampler / central brain system conducts information
signaling in
a noisy environment and with almost no intelligent activity at the remote
sampler. The
system has the benefit of feedback via a conventional DL. The link budget
includes
design of a radio system to take account of the RF energy source and all of
the losses
which are incurred before a receiver attempts to recover the signal. For more
details,
please see [Cas04, pp. 39-45, 3811. Our initial link budget calculations show
that a UE
may be able to operate at a transmission power of 10 to 100 Watts at a range
of 20 to
30 m if a reuse factor of 3 can be achieved and a received SNR of 0 to 10 dB
can be
achieved. These figures are "order of' type quantities with no significant
digits. For
detection of the presence signal, usually more than one sampler can receive
noisy,
different, versions of f and joint detection can be done. This will allow M to
be lower at
each sampler than if f is only visible at one remote sampler. Thus, the
battery drain at
each sampler is reduced by deploying the samplers in a dense fashion. For
brevity,
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sometimes the noisy version off is referred to as g.
1001861 "Reuse" includes how many non-overlapping deployments are made of a
radio bandwidth resource before the same pattern occurs again geographically.
1001871 For a worst-case design, we assume the signal from the UE only
impinges on
one remote sampler. In general, for indoor transmission, we expect two remote
samplers
to be within a 30 m range with a path loss exponent between 2 and 3. The
design is not
limited to indoor transmission. Outdoors, the range will be larger, but the
path loss
exponent will tend to be smaller. For successful detection, the probability of
detecting a
single transmission should be above 10% (presuming the error mechanism is
noise-
induced and therefore detection attempts will be independent). The remote
sampler can
be deployed in macro cells to support vehicular traffic and microcells to
support
pedestrian or indoor-office communication traffic.
1001881 Coming to a concrete example, then, we have fashioned the following
scenario.
1001891 1. The channel is static (no fading).
1001901 2. The noise is AWGN.
1001911 3. The UE, remote sampler and base station are all locked to a clock
with no
timing, frequency or phase errors of any kind. Impairments such as these can
be dealt
with in standard ways [13B99, Ch. 5.8, Ch. 9].
1001921 4. There is one UE.
1001931 5. The Incoherent Sampling scheme uses a random pair ( , ) or a
deterministic pair (Pei ,4:1>d ), in any case the solver knows everything
except the
signals x, f and noise.
1001941 6. The base station has instructed the sampler to use a specific set
of M
columns of O.
1001951 7. The base station has instructed the UE and the sampler that
transmission
waveforms consist of N intervals or chips.
1001961 Figure 27 is an illustration of one embodiment of the remote sampler/
central
brain cellular architecture in accordance with various aspects set forth
herein. The
information is x 3240. f 3242 is S-sparse, and the base station has estimated
S as
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discussed elsewhere. The input to the remote sampler 3212 is a noisy version
off,
sometimes referred to here as g 3244. The remote sampler 3212 computes M
correlations of g 3244 with pre- selected columns of (1), producing the Mx I
vector y
3215 (Equation I). y 3215 is passed down a fiber optic to the base station
3216.
(00197j "Estimation" is a statistical term which includes attempting to
select a
number, , from an infinite set (such as the reals) which exhibits a minimum
distance,
in some sense, from the true value of x. A frequently used measure of minimum
distance is mean-squared error (MSE). Many estimators are designed to minimize
MSE,
i.e., Expectation ffx ¨ 3T). Statistical operations, such as Expectation, are
covered in
[Pro83, Ch. 1]. In practice, numbers output from estimators are often
represented with
fixed-point values.
(001981 For reals, the correlation, or inner product, of g with (pp is
computed as
= (k)g(k)
k=o , where the kth element of g is denoted g(k).
=
p )9 )
1001991 For complex numbers the correlation would be k=o =, where
9 = denotes complex conjugation.
N--
[19 113 = gccOg = (k)
1002001 The 12 norm of a signal, g, is k=to ; the expression for
reals
is the same, the complex conjugation has no effect in that case.
1002011 The base station 3216 produces first an estimate of x, called 3**
3246, and then
a hard decision called 3248. The estimate 3246 is produced by forming a linear
program and then solving it using the simplex algorithm. The algorithm
explores the
boundaries of a feasible region for realizations of the Nxl vector X which
produce
vectors Y. . The search does not rely on sparsity. The 11 minimization works
because
the signal is sparse, but the minimizer acts without any attempt to exploit
sparsity.
[002021 Hence, the N entries in x' are generally all nonzero. That X which
produces
a Y. which satisfies Y =y and has the minimum sum of absolute values is
selected as 3'
(Equation 5). 37 is generally not equal to x, so a hard decision is made to
find the
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nearest vector to x consisting of S ones and N S zeros.
1002031 Linear programs include a set of equations and possibly inequalities.
The
variables only appear in linear form. For example, if xl and x2 are variables,
variables
of the form xl do not appear.
1002041 The probability that this quantization identifies one or more correct
nonzero
entries in x is what the simulation is designed to determine. There are many
definitions
of "nearest". We determine as follows. The quantizer 3230 first arithmetically-
orders
the elements of -I' and retain the indices of the first S elements (e.g., +1.5
is greater than
-2.1). Secondly, the quantizer sets all the entries of -Z to logical zero.
Thirdly, the
quantizer sets to logical one those elements of with indices equal to the
retained
indices. The result is the output of the quantizer.
1002051 The Quantizer 3230 obtains S from a variety of ways. Examples would be
an
all- knowing genie (for limiting performance determination) or that the base
station has
fixed the value of S to be used by the mobile station, using the DL or that
the base
station periodically "scans" for S by trying different values (via instruction
to the remote
sampler) and determining the sparseness of f during some macro period of time,
e.g., 1-2
seconds. Because UEs will make multiple attempts, the base station has
opportunity to
recognize a miss-estimate of S and instruct the remote sampler to reduce or
increase the
value it is using for S. With a sufficiently low duty cycle on the scanning
for S, the
power-saving aspect of the sensing technique will be preserved. In this way,
the remote
sampler's sensing activities track the sparsity of the signals which impinge
on it. Thus,
the remote sampler is always sampling, in general, but only with a battery
drain
sufficient for the system to operate, and not much more battery drain than
that. In
particular, the remote sampler is not sampling at the full Nyquist rate for
large periods
when there is no UE present at all.
1002061 The y- is notation from [CW08, page 24]. The M is not notation from
[CW08], because that reference does not treat signals corrupted by noise. The
= and
C-notations for estimates and detected outputs are commonly used in the
industry, and
can be seen, for example in [Pro83, page 364, Figure 6.4.4 "Adaptive zero-
forcing
equalizer"].
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1002071 Figure 27 shows the functional pieces and signals in the computer
simulation.
The nature of the matrices used is specified in Table 1. The columns were
normalized to
unit length. Please see examples of these matrices in Figures 20 and 21.
Nature (10:j .45Z1
Random iid Gaussian iid Gaussian
Deterministic 1 if i=j, else 0
cos g
[002081 Table 1: Nature of the Matrices
(00209) The deterministic matrices are generated only once, and would not
change if
generated again. The random matrices might be generated only once, or the
random
matrices may be regenerated after some time, such as a few seconds. Also the
random
matrices may be regenerated each time they are to be used. In any case, the
solver 3228
must know what I' matrix the UE 3206 uses at any time and what (I) matrix the
sampler
3212 uses. This does not mean the solver 3228 must dictate what matrices are
used. If
the tiE is changing 41 according to a pseudo-random ("pn") function of the
system time
(time obtained via the DL overhead), then the solver 3228 can use the same pn
function
generator to find out what 4' was. Unless stated otherwise, the probabilities
given in this
report are for the case where the random matrices were generated once and
fixed for all
SNRs and trials at those SNRs.
1002101 The simulation has been restricted to real numbers to ease
development, but
there is nothing in the schemes presented here that limits their application
to real
numbers. The same building block techniques such as correlation and linear
programming can be applied to systems typically modeled with complex numbers.
This
is true since any complex number a + jb can be written as an all real 2x2
matrix with the
first row being [a -b] and the second row being (b a].
(002111 This may be done at the scalar or the matrix level. Therefore any
complex
set of equations can be recast as an all-real set.
SNR(dB) S Prgotal Miss} Prfj=1 hit} Prfj=2 hit}
0 1 0.67 0.32 n/a
1 0.29 0.71 n/a
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20 1 0.12 0.87 n/a
0 2 0.44 0.46 0.09
2 0.22 0.47 0.30
2 0.16 0.28 0.55
1002121 Table 2: Detector Performance with M=5, N=10. AWGN. IP and (I) with
lid
Gaussian entries. See Figure 27.
1002131 In these simulations, the performance we are looking for is anything
exceeding about 10%. A high number of trials is not needed as the only random
events=
are the noise, the signal and the matrix generation. The data points were
gathered using
100 or 200 trials per point in most cases. In about 0.5% of the trials, our 11
solver
implementation attempted to continue the optimization of x when it should have
exited
with the existing solution. These few trials were tossed out. Even if included
either as
successes or failures, the effect on the results would be imperceptible, since
we are
looking for any performance greater than 10%.
1002141 The data from Table 3 is plotted in Figure 14. S is the number of
nonzero
entries in x and is called "pulses" in Figure 14. The event "j = I hit" means
that the
detector detected exactly one nonzero entry in x correctly. In the case that S
= I, that is
the best the detector can do. The event 1 = 2 hit" means that the detector
detected
exactly two nonzero entries in x correctly.
[002151 I also did a simulation with M = 3,N = 10 and S = 1 (please see Figure
17
discussed below).
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SNR(dB) S Pr{Total Miss} Pr{j=1 hit} Pr{j=2 hit)
0 1 0.64 0.36 n/a
1 0.13 0.87 n/a
1 0.03 0.97 n/a
0 2 0.42 0.49 0.09
10 2 0.13 0.40 0.47
20 2 0.07 0.19 0.74
100216] Table 3: Detector Performance with M=5, N=10. AWGN. W and (1) with
deterministic entries.
100217) Figures 15, 16 and 17 give detection performance for various
combinations
of M, N, S, SNR and nature of the matrices. In each of these plots j is the
number of
nonzero entries in x correctly determined by the combination of the II
minimizer and the
Quantizer (Figure 25).
1002181 For system design, the important probability is the probability
that the
detector gets the message completely right in one observation. The system is
assumed to
use multiple transmissions, each of which will be independent as to
uncontrolled effects
like noise. In that case, the probability of detecting the Presence signal in
C
transmissions or less is 1 ¨ Pr (Miss)C. A Miss can be defined either as the
event j = 0
or the event j<S. When S = 1 and with random matrices, the event j = S occurs
with
probability greater than 10% at SNR below 0 dB, and at S = 2 at SNR of about 3
dB.
The 90% points are at about 12 and 17 dB respectively as seen in Figure 15.
The
performance is better for deterministic matrices and S =,1 as seen in Figure
16.
1002191 In order to see how the detector would work when the sparsity
condition
(M>>S not true) was weak, we generated the data shown in Figure 17 using S = 1
and M
= 3. Both the random and deterministic configurations are able to detect at
low SNR,
but the random configuration saturates near 70% rather than reaching the 90%
point.
The performance for the random configuration is a bit worse than that for M
=5,
N=10(e.g. Pr (detection) = 0.55 at SNR = 10 dB, while with M = 5 this
probability is
0.71). At high SNR, the probability approaches l for the deterministic case,
Figure 17.
1002201 Thus, we see that with increasing M and SNR, we approach Candes noise-
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free result that 100% reliable exact recovery is reached. However, for low M
and a
noisy signal, sometimes the solver produces x is not equal to x. An important
qualitative characteristic is that the degradation is gradual for the
deterministic
configuration. A threshold effect in noise may exist with the random
configuration
unless M >> S. In Figure 17, M =3S, while in all of the other figures M? 5S
for S = I.
1002211 An unusual characteristic of the Incoherent Sampling Method is the
incoherence. Most detectors seek to try many candidate waveforms to see which
one
matches the received waveform and then use some kind of "choose largest"
function to
determine the identity, or index, of the transmitted waveform. A local replica
is a
waveform which has the same identity as a transmitted waveform. In Incoherent
Sampling, the only requirement is that and (I) be weakly related at most. This
means
that a great variety of sense matrices (CDs) could be used for any T. For the
random case,
we explored the effect of changing both matrices every transmission. Results
for this are
shown in Figure 18 and 19. From this we noticed some variation in performance,
even
at high SNR. We confirmed a conjecture that this is due to the generation of
"bad"
matrices with poor autocorrelation properties. High correlation within either
matrix
would weaken the estimation ability, since for it would reduce the support for
distinguishing the values of x on any two correlated columns, and for (I) it
would reduce
the solver's ability to distinguish between candidate contributions from two
correlated
columns of O. To localize the mechanism of these variations at high SNR, we
rejected
(1) matrices where any two columns had a correlation magnitude greater than a
threshold.
In the plots the threshold is 0.1. Studies were done with other thresholds. A
threshold of
0.4 has almost no effect. What we have learned from this is that, yes, there
are wide
variations in the effect of the actual (I) matrix on the performance. Another
way to put
this, is that there are "bad" (1). matrices that we do not want to sense with.
The
performance is a random variable with respect to the distribution of matrices.
This
means that a probability of outage can be defined. In particular, the
probability of outage
is the probability that the probability of detection will fall below a
probability threshold.
For example, the system can be designed so that not only the average
probability of
detection is greater than 40%, but the probability that the probability of
detection will be
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less than 10% is less than 1%. We can reduce the number of "bad" matrices in
order to
reduce the probability of outage. One way to do this is to constrain
correlation in the (1)
matrices. Constraining the 'I' matrices will also be beneficial, especially as
S increases.
1002221 To provide robust high bandwidth real time service and high user
density by
radio, we have created an architecture based on dispersed antennas and
centralized
processing of radio signals. =We call the system Remote Conversion or Remote
Sampling. The mobile stations are simple low power devices, the infrastructure
core is
super-computer- like, and the Base Stations are linked to mobile stations by a
redundant
sea of cheap radio sensors. Figure 28 is a diagram of the cellular network
that we are
proposing here. It shows a series of simple sensors 2712 deployed in large
numbers
such that generally more than one is within the range of the mobile subscriber
(MS)
device 2206. These sensors may also be referred to as remote samplers or
remote
conversion devices in this project. The sensors could be separated in the
range of ten
meters to a few hundreds of meters. There is a deployment tradeoff between the
power
required for the sensors, the ease of deploying the sensors and the amount of
capacity
needed in the system. The UE may use frequency bands much higher than typical
in
cellular telephony.
1002231 The sensors are provided a fiber-optic back haul 2714 to a central
base
station 2716. The backhaul could also be provided by another medium such as
coaxial
cable. There may be several base stations in a deployment where they
communicate and
pass information. The sensors have one or more antennas attached to an RF
front end
and base-band processing that is designed to be inexpensive. The sensors with
one
antenna can be used as an array and can be made into MIMO air interfaces.
1002241 Beam-formed air interfaces allow the MS to transmit at a low power.
The
upper layer protocol used between the MS and the Base Station could be one
from a
standardized cellular network (e.g. LTE). Upper Layer Protocols that
specialize in low
power and short range (e.g. Bluetooth) are alternative models for
communications
between the MS and Base Station. The stack at the sensor will include only a
fraction of
layer one (physical). This is to reduce cost and battery power consumption.
Possibly
the sensors will be powered by AC (110 V power line in US). Low round-trip
time
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hybrid-ARQ retransmission techniques to handle real-time applications can be
used; the
Layer 2 element handling ARQ will not be in the sensor but rather in the BS or
Central
Brain. Areas of Innovation A completely new topology is given here in which
the
sensors compress a high bandwidth mobile signal received at short range and
the
infrastructure makes physical layer calculations at high speed.
1002251 1. Instructions, communication protocols and hardware interfaces
between
the base station and the sensors
[002261 a. remote conversion instructions
1002271 b. oscillator retuning instructions
[002281 c. beam steering (phase sampling) instructions
1002291 2. Communication protocols and hardware interfaces between the MS and
the BS or Central Brain
1002301 a. a high bandwidth MAC hybrid-ARQ link between an MS and the BS
which can support real-time services.
1002311 3. Communication protocols and processing techniques between the MS
and
the central processor / Central Brain
(00232) a. presence-signaling codes which work without active cooperation from
the
sensors
1002331 b. space time codes for this new topology and mixture of channel
knowledge
1002341 c. fountain codes for mobile station registration and real time
transmission
[00235] d. large array signal processing techniques
[00236] e. signal processing techniques taking advantage of the higher
frequency
transmission bands
1002371 4. The Base Stations support activities which include the following:
1002381 a. transmission of system overhead information
1002391 b. detection of the presence of mobile stations with range of one or
more
sensors
1002401 c. two-way real-time communication between the base stations and
mobile
station.
1002411 This memo addresses the sensor or sampler to be used in a cellular
telephony
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architecture. These sensors are cheaper than Base Stations and sample RF
signals of
high bandwidth, for example bandwidth B. The compressed signals are sent over
fiber
to the base station. The sensors often do not perform Nyquist sampling. This
is done for
several reasons. One is that sampling at high rates consumes much energy. We
aim to
provide low-power sensor technology. Redundancy is expected to be designed
into the
system so that loss of single sensors can be easily overcome. For many
important
signals, low-error reconstruction of that signal which is present can be done
at the base
station. A sensor may be equipped with a direct sequence de-spreader, or an
FFT
device. The sensors do not make demodulation decisions. The direct sequence
code
used in the de-spreader, or the sub-chip timing of the de-spreader or the
number of bins
used in the FFT, or the spectral band the FFT is to be applied to by the
sensor are things
which the Base Station tells the sensor through an instruction. In one
embodiment, these
instructions come at 1 ms intervals and the sensor adjusts its sampling or
conversion
within less than 0.1 ms of receiving the instruction. For purposes of
structure, we
assume that the mobile station transmits and receives information packets or
frames of
du-ration I to 5 ms. The format may be circuit-like or non-circuit-like. The
system
overhead information may include guiding and synchronizing information which
cause
the mobile stations to practice and copy good cooperative behavior according
to game
theory. There may also be important information provided that the MS needs to
know
about a possible wireless WAN. By keeping all communications within this sub-
communication network and not having to monitor external networks, battery
power can
be saved. The mobile stations transmit their messages at low power. The
sensors
sample the wireless channel. The sensors in this proposal compress the
samples. The
compressed samples in the present proposal are sent over a fiber channel to
the base
station. The base station is responsible for many layer I activities
(demodulation,
decoding), layer 2 activities (packet numbering, ARQ), and signaling
activities
(registration, channel assignment, handoff). The computational power of the
base
station is high. The base station may use this computing power to solve
equation
systems in real time that would have only been simulated offline in prior
systems. The
base station can use knowledge of the channel (mobile station antenna
correlation
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matrix, number of sensors in view of the mobile station) to determine link
adaptation
strategies on a 1 Ins interval. These strategies will include operating at the
optimum
space time multiplexing gain/ diversity gain trade-off point. Also multiple
base stations
can be in almost instantaneous communication with each other, and optimally
design
transmit waveforms which will sum to yield a distortion-free waveform (dirty
paper
coding) at the simple mobile station. Other base stations which receive
extraneous
uplink energy from the mobile station occasionally supply an otherwise-erased
1 ms
frame interval to the anchoring base station. Figure 29 shows another
schematic of the
proposed system. The sensors 2712 in this proposal are only responsible for
sub-layer 1
activities, i.e., compression at the sample level. The Base Station 2716 in
this proposal
may send instructions to the sensors, such as compress using multiple access
code 16
(this might be a DS code, or OFDM code). The Base Station may send an
instruction
such as perform 2x sampling with phase theta. In other words, the sensor is a
remote
pulling away from an AID path from a conventional base station, like pulling a
comer of
taffy and creating a thin connecting strand. The taffy strand is a metaphor
for the fiber
channel from a sensor to the base station. The base station uses very high
available
computing power to detect the presence of MS signals in the compressed data.
The base
station in this proposal then responds to the detected MS by instructing the
sensor to use
sampling and compressing techniques which will capture well the MS signal
(timing,
frequency, coding particulars which render the compressed data full of the MS
signal,
even though the sensor is unaware of the utility of the instructions). The MS
in this
proposal may transmit with a fountain code, at least for call establishment.
For very high
bandwidth, low power links, the mobile station may transmit real time voice
using a
fountain code. The packet transmission rate should be with period on the order
of 1 to 5
ms. The sensor is primarily not a decision-making device; it is not locally
adaptive;
sensor control is from the Base Station. The sensors are deployed densely in
space, that
is, at least one every 100 m x 100m and possibly one every 10 m x 10 m. The
sensors
may or may not support a DL transmission. The DL might be carried from a
traditional
base station tower with sectorization. The density of such towers would be at
least one
every 1000 m x 1000 in (building deployment) and possibly one every 300 m x
300 m
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(street light deployment).
[002421 FIG. 30 illustrates simulated results of the performance of one
embodiment
of a sensor-based wireless communication system using compressive sampling in
accordance with various aspects set forth herein, where the performance of
system 3000
was measured using N=8, S=1, and varied values of M. The graph depicts the
mutual
information between compressed samples and the transmitted signal for various
values
of M. Based on the simulation results, a proposed target operating region for
the
compressed sampling architecture is identified. The importance of these
observations
lies in the fact that conservation of battery life is a key attribute of the
proposed
compressive sampling architecture. When the value of M is increased, the
samplers
require more battery power. However, if the value ofM is too small, the mutual
information between the transmitted and the received signal may fall below an
acceptable level. Thus, for acceptable system performance, it is necessary to
identify a
value of M to provide a stable system. For this simulation, the sparse
representation
matrix ("T") is Walsh in nature and the sensing matrix ("0") is random in
nature. The
choice of representation and sensing matrices used affects the mutual
information
between the transmitted signal and the compressed samples, depending on the
SNR.
There is a benefit to orthogonalizing the representation matrix for certain
sets of
conditions. Using deterministic matrices aids in increasing the mutual
information,
however, would require more signaling. Thus, there is a tradeoff between
signaling and
battery power, and, correspondingly, between coordinating the matrices and the
value of
M. In cases where the signaling is more limited, then a higher value of M
should be
used. However, if battery life is more critical, then more signaling should be
used.
Additionally, the mutual information between the transmitted signal and the
compressed
samples is a function of the additive noise. Hence, deterministic matrices
should be
used when feasible. However, this once again will increase the signaling
requirements
of the system. Furthermore, choosing representation and sensing matrices that
have
some form of length preservation is advantageous.
1002431 The graphical illustration in its entirety is referred to by 3000. The
logarithmic magnitude of the SNR ratio is shown on abscissa 3009 and is
plotted in the
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range from 0 dB to 35 dB. The mutual information is shown on ordinate 3908 and
is
plotted in the range from -1.0 to 3. Curves 3003, 3004, 3005 and 3006
represent
simulation results for system 3000, where N is eight, S is one, a random ild
Gaussian
matrix is used for the sensing matrix ("0") and a Walsh matrix is used for the
sparse
representation matrix ("P"). Curve 3003 shows a lower bound ("LB") for the
mutual
information when M=1. Curve 3004 shows a LB for the mutual information when
M=2.
Curve 3005 shows a LB for the mutual information when M=3. Curve 3006 shows a
LB
for the mutual information when M=4. 3001 and 3007 represent the upper bound
and
collection of lower bounds respectively. An example of a target operating
region is
shown as Region 3002. A max operation has been performed to retain the best
Monte
Carlo realization of probability of (1) for each M. As shown by the graph, the
worst
bound (0,4) for M=3 is better than the best bound for M=1. The target
operating region
is chosen as the area indicated by Region 3002 in order to obtain reasonable
limits on
signaling delay. The behaviour of the simulated system applies for any linear
modulation system.
[00244] In designing the system, various attributes may be changed or adjusted
to
increase system performance or maximize efficiency. For instance, all UEs of a
system
may be assigned the same value of S while all the Remote Samplers may be
assigned the
same value of M. This is not necessary, as the values of S and Mmay be
different for all
of the UEs and remote samplers. Additionally, for low values of SNR, the value
of S
may be reduced, while for high SNR, the value of S may be increased. These
value
changes are logical since increasing S at a low SNR rate has very little
benefit.
However, at a high SNR rate, increasing S makes sense in order to transfer
more of the
user information. The system would also benefit if the solver is aware of the
value of S
assigned to the UE. It should also be appreciated by those skilled in the art
that
maximum value of M would be 2N in the case of asynchronous sampling because
for
synchronous systems with chip lock, N samples per word are required whereas
for a no
chip lock system, a minimum of 2N samples must be taken. Another aspect of the
current invention is that the controller is able to differentiate between
various types of
signals in a compressive sampling architecture, such as between WCDMA and GSM.
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Thus, the controller can issue instructions to maximize the efficiency of
signal transfer
based on the type of signal it perceives. The system may also be designed so
as to not
require adjustment of time of flight for a UE. For example, in a GSM system,
the
system may require a UE to adjust its transmission based on the fact that the
signal is
time shifted from other signals. However, in the proposed system, these
adjustments
may be taken into account in designing the system by using a long chip period
such that
no adjustment on the part of the UE is required.
1002451 FIG. 31 is a sketch of one embodiment of the present invention in
which
several UEs communicate using compressive sampling. FIG 31 shows UEs 3101,
3102
and 3103 communicating with Remote Samplers 3104, 3105 and 3106. Remote
Samplers 3104, 3105 and 3106 are connected via fiber optic cables 3107 to
solver 3108.
Controller 3109 sends instructions to Remote Samplers 3104, 3105 and 3106 via
fiber.
'optic cables 3107, in addition to sending instructions for Solver 3108
itself. Controller
3109 sends instructions to UEs 3101, 3102 and 3103 through Base Station Tower
3110.
One aspect of the current invention is that UEs 3101, 3102 and 3103 are not
restricted to
any particular remote sampler. Each UE simply transmits and the multiple
remote
samplers simply report the samples they capture. The downlink between the UEs
and
the Controller is accomplished via Base Station Tower 3110. The uplink is
accomplished through Remote Samplers 3104, 3105 and 3106.
1002461 In any given system, if the number of remote samplers is increased,
then the
value of M may be decreased without appreciably harming system performance.
Furthermore, although the current invention seeks to preserve battery life of
a remote
sampler, if there are remote samplers in the system which have significantly
more
energy available than other remote samplers, it would be beneficial to
increase the value
ofM at those remote samplers. In this way, the value of M for other remote
samplers,
which are limited with regards to their energy, may be reduced without
affecting system
performance.
(002471 A further aspect of the proposed architecture is to reduce signal
complexity
based on known channel coefficients. If there are multiple UEs communicating
with
multiple remote samplers, channel coefficients may indicate that due to some
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obstruction, a particular UE communicates almost exclusively with a single
remote
sampler. In such a situation, the channel coefficient matrix associated with
the multiple
UEs may show that the vectors associated with a particular sensed waveform are
insignificant in certain areas. For example, if a UE communicates exclusively
with one
remote sampler, the channel coefficients associated with that UE for the
remaining
remote samplers may be zero. Thus, the signal associated with this UE may be
reconstructed without regard to measurements at any other remote sampler
besides the
one to which the UE is communicating. By separating out this particular
signal, the
complexity of the matrix representing the remaining signals is reduced. This
in turn will
decrease the computational power needed by the solver. Based upon this, the
controller
may issue instructions to the.solver to break the matrices into smaller
matrices to reduce
computational complexity.
002481 FIG. 32 represents a method of frequency domain sampling using
frequency
shifting and filter banks. These are forms of analog or continuous time
correlations for
the proposed system. It should be noted that correlation may be done in
discrete time or
continuous time. 3212 is a diagram of a sparse signal sampler using a filter
bank. 3212
shows recovery of V 3211 using a bank of M narrow band filters 3202. Received
signal
y 3201 is multiplexed and fed into a signal bank of M narrow band filters
3202. The
filter bank performs the matrix operations (I) for the analogue signals. The
output is the
signal y 3203 which is passed to optimizer 3204 which recovers an estimate of
V 3205.
Frequency domain sampling using filter banks is characterized by the following
points:
I. The number of samples, M, is limited by the number of narrow band
filters in
the device.
2. The hardware requirement increases with M, as M narrow band filters are
needed.
3. Memory storage of y may not be required.
4. Non-stationary or time varying signal processing is possible.
1002491 3213 is a diagram of a sparse signal sampler using frequency shifting.
3213
presents a method for recovering the signal directly from the time domain
signal y for
a temporally stationary signal. The voltage controlled oscillator 3207 and
narrow band
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filter 3208 perform the operations of in the analogue domain. Signal y 3206 is
frequency shifted by the VCO 3202 to the pass band of the narrow band filter
3208. It
should be noted that a low pass filter may be used instead of a narrow band
filter with
differing results. The output amplitude and phase is stored in memory 3209
until all M
frequencies are sampled. y 3209 is then passed to the optimizer 3210 which
generates
the estimate of 3211. Frequency domain sampling using frequency shifting is
characterized by the following points:
I. The number of samples M can be dynamically changed by controlling
the
VCO.
2. Memory storage of initially found y values is required to recover the
entire
vector y.
3. The signal must be stationary or slowly time varying.
1002501 FIG. 33 is a block diagram of a remote sampler utilizing continuous
time
sampling concepts described herein. Antenna 3301 receives a sparse signal and
passes
the signal to Downconverter 3305. Due to antenna characteristics, noise 3302
will be
. part of Received signal 3304, and its addition is indicated by adder 3303
(although this
is not an actual structure, the addition of noise 3302 is indicated by an
adder to show the
nature of Received signal 3304). The signal is downconverted at 3305. At 3306,
the
signal is correlated using a configuration received by the remote sampler from
a remote
central processor (not shown). Samples 3307 are then sent to Analog-to-Digital
converter 3308. The converted samples are then sent along fiber optic 3309 to
the solver
(not shown).
1002511 An example of a low cost radio is given in Kaukovuori [KJR+06],
another is
given in Enz [ESY05].
1002521 Using fiber to connect a remote antenna to a base station was proposed
and
tested by Chu [C091].
1002531 Current Intel processors like the QX9775 execute at over I GHz clock
speed,
at over 1 GHz bus speed and with over 1 MB cache. According to Moore's law,
transistor densities will reach 8x their current value by 2015. Based on the
typical clock-
rate-times gate-count reasoning, we can expect roughly 10x the processing
power will be
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available in single processors in 2015. Thus, in 1 ms, 10 million CISC
instructions can
be executed. One microprocessor will direct the physical layer adaptation of
10 sensors
in real time. http://compare.intel.com/pcc/
[00254] The limits on the MIMO multiplexing/diversity tradeoff were derived by
Zheng and Tse, 2L. Zheng and D. Tse, "Diversity and Multiplexing:
A.Fundamental
Tradeoff in Multiple-Antenna Channels, IEEE Transactions on Info. Theory, May
2003,
pp. 1073-1096".
[00255] The present-day conception of dirty paper coding is discussed in, for
example, Ng, "C. Ng, and A. Goldsmith, Transmitter Cooperation in Ad-Hoc
Wireless
Networks: Does Dirty-Paper Coding Beat Relaying?, IEEE ITW 2004, pp. 277-282."
100256] Teaching selfish users to cooperate is discussed, for example, in
Hales, "D.
Hales, From Selfish Nodes to Cooperative Networks Emergent Link-based
incentives in
Peer-to-Peer Networks, IEEE Peer-to-Peer Computing, 2004".
[00257] The concept of multiple nodes receiving cleverly-redundant
transmission is
discussed in Kokalj-Filipovic, "A. Kokalj-Filipovic, P. Spasojevic, R. Yates
and E.
Soljanin, Decentralized Fountain Codes for Minimum-Delay Data Collection, C1SS
2008, pp. 545-550".
[00258] From these tables and figures, we conclude that, yes, it has been
possible to
design a Presence signal and detect at the remote sampler while satisfying
qualitative
design rules. In particular, two combinations P and (1) have been shown to
make
detection of the Presence signal possible with very little signal processing,
and no
decision-making, at the remote sampler. Recall, the Presence signal is a sum
of columns
from the `I' matrix. The probability of detecting the Presence signal with S I
or S =2
nonzero entries in x is sufficiently high for SNRs in the range of 0 to 10 dB.
This is
achieved under the constraint that the remote sampler transmits to the base
station fewer
samples than would be required for conventional conversion of the observed
signal
when the conventional assumption has been made that the signal fully exercises
an N-
dimensional basis. This gain has been brought about by purposefully designing
the
transmitted signal to be sparse, the remote sampler to be simple, and the base
station to
be intelligent and equipped with a separately designed (non-co-located with
the remote
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samplers) downlink connection to mobile stations.
1002591 Appendices A, B, C, D, E, F, and G, which are attached hereto and
incorporated herein by reference, describe technical considerations with
regard to
designing a compressive sampling system. In particular, mutual information in
remote
samplers is discussed in great detail. Additionally, the problem of noise in
sparse signal
sampling is addressed. Appendices C and D present computer programs designed
to
address these issues. Appendix G is the provisional application filed April
15,2009.
1002601 References:
1002611 [AAN08] K. Adachi, F. Adachi, and M. Nakagawa. Cellular mirno channel
capacities of mc-cdma and ofdm. IEEE, 2008.
1002621 [BB991 S. Benedetto and E. Biglieri. Principles of Digital Trans-
mission with
Wireless Applications. Kluwer, New York, 1999.
1002631 [Cas04] J.P. Castro. All IP in 30 COMA Networks. John Wiley & Sons,
Ltd., Chichester, England, 2004.
1002641 [CG91] T.S. Chu and M.J. Gans. Fiber optic microcellular radio. IEEE,
pages
339-344,1991.
1002651 [CR02] S. Cotter and B. Rao. Sparse channel estimation via matching
pursuit
with application to equalization. IEEE Trans. on Communications, pages 374-
377,
March 2002.
1002661 [CW08] E. Candes and M. Wakin. An introduction to compressive
sampling.
IEEE Signal Proc. Mag., pages 21-30, March 2008.
1002671 [ESY05] C. Enz, N. Scolari, and U. Yodprasit. Ultra low-power radio
design
for wireless sensor networks. IEEE Intl. Workshop on RF Integration Tech.,
pages 1-17,
Dec. 2005.
1002681 [JR08] Y. Jin and B. Rao. Performance limits of matching pursuit
algorithms.
IEEE Intl. Sym. Info. Theory, pages 2444¨ 2448, July 2008.
1002691 [KJR+06] J. Kaukovuori, J.A.M. Jarvinen, J. Ryynanen, J. Jussila,
K.
Kivekas, and K.A.I. Halonen. Direct-conversion re-ceiver for ubiquitous
communications. IEEE, pages 103¨ 106,2006.
1002701 [LKL+08] M. Lee, G. Ko, S. Lim, M. Song, and C. Kim. Dynamic spectrum
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access techniques: Tpc-resilient initial access in open spectrum bands. Intl.
Conf. on
Cognitive Radio Oriented Wireless Networks and Comm., pages 1-6, May 2008.
[00271] [LY08] D. Luenberger and Y. Ye. Linear and Nonlinear Programming.
Springer, third edition, 2008.
1002721 [Pro83] John G. Proakis. Digital Communications. McGraw-Hill, New
York,
New York, first edition, 1983.
1002731 [TGS05] J.A. Tropp, A.C. Gilbert, and M.J. Strauss. Simultaneous
sparse
approximation via greedy pursuit. IEEE ICASSP, pages V721¨V724, 2005.
1002741 In various embodiments disclosed herein, multiple user equipments
(UEs)
communicate over the uplink (UL) with the central brain (CB) via a collection
of remote
samplers (RSs). The downlink (DL) is provided by a base station tower.
1002751 The UE transmissions appear at the receiving antenna of any given
RS as a sum
of the respective individual waveforms. The sum present on the RS antenna is
denoted "g." The
RSs use a sampling technique that captures M samples at each RS (M may be
different at
different RSs).
[002761 In a conventional system, for example, N CDMA chips may be sent per
transmit
waveform. If the receiver has chip-lock, then N samples can be retained by the
CDMA receiver
before despreading. In a second example, if a narrowband transmitter, such as
GSM is sending
symbols using 8-PSK or GMSK modulation and a GSM receiver has accurate symbol
timing,.
then 1 sample per symbol is required to identify the transmitted symbol. In
the Remote Sampler
System, given that a UE has transmitted N symbols, the number of samples
passed from a given
RS to the CB is M, where M is less than N when the UE is expected to transmit
an S-sparse
combination of the columns from the 41 matrix in use at the UE, where S is
much less than N.
The M-vector containing these samples is denoted y.
1002771 Several front-end configurations are used in radio design, and
provide a guide for
design of the RS front end. Increasing the amount of supply current available
in the front end
can increase the dynamic range of the particular front end design in use. The
components of the
analog front end are the LNA (low noise amplifier), pu, (phase locked loop),
mixer, attenuator,
IF filters and ADC (Analog to Digital Converter). The influence of circuit
power on dynamic
range is made use of in this disclosure to improve signal detection.
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(002781 Generally, as the PLL is allowed to consume more current the power
in the phase
noise component of the generated signal declines. This causes the signal to
noise ratio (SNR) of
' the received signal to reach a maximum Limit. By increasing the amount of
current supplied to
the PLL, the maximum achievable SNR can be increased.
(00279j There may be some instances in which two UE signals are present of
different
received energy levels. Since the analog front end has finite dynamic range
(DR), the weaker
signal may be present in the remote sampler after A to D conversion (ADC) at a
level only
comparable to the receiver circuit noise level. Suppose that the weaker signal
comes from UE2
and the sparse signal from UE2 is denoted x2. The CB may have a poor success
rate in detecting
x2. To alleviate this, the dynamic range of the ADC is increased based on a
command from the
CB. Thus, the weaker signal is now not overwhelmed by the receiver circuit
noise. When y is
passed to the CB, the CB will have better success detecting x2.
1002801 The CB can adjust M, cp, DR, sample timing, carrier offset and any
other circuit
parameter of the RS by a command sent from the CB to the RS along the
connecting fiber. By
sometimes increasing M and DR to accurately view the antenna signal g, the CB
can determine
the steady state values for M and DR (and other parameters). The CB then
instructs the RS on
what value to use for M and DR (and other parameters). If the CB calculates
that detection of
the received signal is limited by additive thermal noise, the CB may send a
command to increase
current drain in a way which reduces the NF.
(00281] An object of the disclosed system is to minimize current drain in
a given RS when
UEs in the area are not sending data. UE access to the system is broken in to
two phases: i)
Presence Signaling and ii) Payload Transmission. During the Presence Signaling
Phase, the UE
will send sparse signals. RSs which are not supporting one or more UEs in
Payload
Transmission mode, will be sampling with M <N. Many different receiver
configurations are
possible, and some configurations are more optimal for low-duty cycle, narrow-
bandwidth
operation while others are better for high-bandwidth, high dynamic range
operation. In the
present disclosure, the RS front end circuitry may configure some components
(LNA, mixer,
PLL, ADC) for one regime or the other as commanded by the CB according the UL
traffic load
that the CB estimates is offered in the vicinity of a given RS.
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1002821 Because RS current drain will be tailored by the CB to suit UE
demand for
transmission of UL data, the status of RS battery level, for those RSs not
powered by 110 V line
power, will vary from one RS to the next because LTE demand for service is not
geographically
uniform. The CB can maintain estimates of the expected battery lifetime of
each RS and plan to
replenish the batteries of those RSs in need. The CB may adjust current drain
in real time
operation to gather more samples, or samples corresponding to a higher DR or
lower NF, from a
sampler, "RS high", with more battery power, if an RS, "RS_low", which is
closest to a cluster
of active UEs has low battery power. The CB can use the resulting samples from
both RS_high
and RS low to determine the transmitted data.
1002831 Having shown and described exemplary embodiments, further
adaptations of the
methods, devices and systems described herein may be accomplished by
appropriate
modifications by one of ordinary skill in the art without departing from the
scope of the present
disclosure. Several of such potential modifications have been mentioned, and
others will be
apparent to those skilled in the art. For instance, the exemplars,
embodiments, and the like
discussed above are illustrative and are not necessarily required.
Accordingly, the scope of the
present disclosure should be considered in terms of the following claims and
is understood not to
be limited to the details of structure, operation and function shown and
described in the
specification and drawings.
1002841 As set forth above, the described disclosure includes the aspects
set forth below.
