Note: Descriptions are shown in the official language in which they were submitted.
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SENSOR-BASED WIRELESS COMMUNICATION SYSTEMS USING
COMPRESSIVE SAMPLING
FIELD
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
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 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.
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
("LTE") 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.
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 ("MIMO"),
where
multiple antennas are used at the receiver and transmitter. Compared to a SISO
system,
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SIMO may provide increased coverage while MIMO systems may provide increased
spectral efficiency and higher data throughput if the multiple transmit
antennas, multiple
receive antennas or both are utilized.
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
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.
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
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:
FIG. 1 illustrates one embodiment of a sensor-based wireless
communication system using compressive sampling in accordance with various
aspects
set forth herein.
FIG. 2 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in accordance with various
aspects
set forth herein.
FIG. 3 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in accordance with various
aspects
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set forth herein.
FIG. 4 illustrates one embodiment of a compressive sampling system in
accordance with various aspects set forth herein.
FIG. 5 is a flow chart of one embodiment of a compressive sampling method
in accordance with various aspects set forth herein.
FIG. 6 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in accordance with various
aspects
set forth herein.
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.
FIG. 8 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in accordance with various
aspects
set forth herein.
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.
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.
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.
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.
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.
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.
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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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.
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.
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.
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.
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.
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.
FIG. 22 illustrates an example of an incoherent sampling system in a noise-
free environment.
FIG. 23 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in accordance with various
aspects
set forth herein.
FIG. 24 illustrates an example of a prior art lossless sampling system.
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.
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.
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.
FIG. 28 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in accordance with various
aspects
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set forth herein.
FIG. 29 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in accordance with various
aspects
set forth herein.
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.
FIG. 31 illustrates another embodiment of a sensor-based wireless
communication system using compressive sampling in accordance with various
aspects
set forth herein.
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.
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.
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
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
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 examplaries 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.
Various techniques described herein can be used for various sensor-based
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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.
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
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.
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.
A sensor may be referred to as a remote sampler, remote conversion device,
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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.
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,
downlink transmitter or both to a user equipment.
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.
In FIG. 1, system 100 contains sensors 110 to 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
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with the underlying wireless network when in close proximity to sensors 110 to
113.
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, MIMO operation, beamforming
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.
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.
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.
In the current embodiment, sensors 110 to 113 can compress a received
uplink signal (7') 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
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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")
hybrid-
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.
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.
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.
In the current embodiment, sensors 110 to 113 may each contain a direct
sequence de-spreading element, a fast Fourier transform ("Fl-T") 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.
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.
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.
In the current embodiment, base station 102 may apply link adaptation
strategies using, for instance, knowledge of the communication channels such
as the
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
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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 (7') 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.
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.
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
(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 (7') 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 uplink
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.
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
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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.
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.
In FIG. 3, base station 302 can be coupled to downlink transmitter 308,
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.
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
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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.
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 (7') using sensing waveforms ("yi ") of sensing matrix
("0") to
generate a sensed signal ("y"), where yi refers to the jth waveform of sensing
matrix
("0"). The input signal ("f') can be of length N, the sensing matrix ("0") can
have M
sensing waveforms ("9 = ") of length N and the sensed signal ("y") can be of
length M,
where M can 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
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.
In the current embodiment, compressive sampler 431 can compressively
sample the input signal (T) using, for instance, Equation (1).
yk = (f,cpk),k E J such that c (1 /\/} (1)
where the brackets ( ) denote the inner product, correlation function or
other similar functions.
Further, detector 452 can solve the sensed signal ("y") to find the
information signal ("x") using, for instance, Equation (2).
subject to yk = (cpk,)1(i), Vk E J (2)
where II II/iis the / norm, which is the sum of the absolute values of
the elements of its argument and the brackets ( ) denote the inner product,
correlation
function or other similar functions. One method, for instance, which can be
applied for
1 iminimization is the simplex method. Other methods to solve the sensed
signal ("y")
to find the information signal ("x") include using, for instance, the 1 0 norm
algorithm,
other methods or combination of methods.
Incoherent sampling is a form of compressive sampling that relies on
sensing waveforms ("yi ") of the sensing matrix ("0") 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("yi ") of sensing
matrix ("0"), the coherence ("//") between the sparse representation waveforms
("y ")
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of the sparse representation matrix ("tr) and the sensing waveforms ("(pi ")
of sensing
matrix ("0") should represent that these waveforms are sufficiently unrelated,
corresponding to a lower coherence On, where iv,/ refers to the jth waveform
of the
sparse representation matrix ("tr). The coherence ("//") can be represented,
for
instance, by Equation 3.
p.(44:0, = V77 maxi,k,i,NII(Ok,Wilii (3)
where II II/iis the / norm, which is the sum of the absolute values of the
elements of its argument and the brackets ( ) denote the inner product,
correlation
function or other similar functions.
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 (!') and discover a sparse
representation
matrix ("tr) 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 ("tr). At block 572, method 500 can randomly,
deterministically
or both select M sensing waveforms ("yi ") of sensing matrix ("0"), where M
may be
greater than or equal to S. At block 573, method 500 can sample input signal
(!') using
the selected M sensing waveforms ("9 = ") to produce a sensed signal ("y"). At
block
574, method 500 can pass the sparse representation matrix ("tr), the sensing
matrix
("0") and the sensed signal ("y") to a detector to recover an information
signal
("x").
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
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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
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.
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.
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
(7'). In this disclosure, uplink signal (7') can also be referred to as uplink
signal ("g").
Uplink signal ("g") includes channel propagation effects and environmental
effects on
uplink signal (7'). 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 (7'). Sensor 610 may
receive
instructions from base station 602 associated with, for instance, RF
downconversion,
compressive sampling, other functions or combination of functions.
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.
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
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portion of 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
("pi
") and the sparseness S of the uplink signals (7') being sent.
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
("tr), 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.
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, Mi sensing waveforms
("yi ")
of sensing matrix ("0"), as represented by 791. Sensor 710 may then
continuously
process received uplink signals (7') and send sensed signals ("y") using Mi
sensing
waveforms ("yi ") of sensing matrix ("0") to base station 702, as shown at
790.
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
("tr), 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"),
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as represented by 792. Sensor 710 may then continuously process received
uplink
signals (T) and send to base station 702 sensed signals ("y") using M2 sensing
waveforms ("(p = ") of sensing matrix ("0"), 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 S2, 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 ("tr), 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 (!') and send to base station 702
sensed
signals ("y") using M3 sensing waveforms ("pi ") of sensing matrix ("0"), as
shown at
796.
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.
Sensor 710 may continuously receive uplink signals (!') of a frequency
bandwidth ("B") centered at a center frequency ("fc"). Sensor 710 can
downconvert the
uplink signal (T) 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 (T) according to Shannon's theorem. The received
uplink
signal (T) can be sampled, for instance, periodically, aperiodically or both.
The sampling process can result in N samples, while computing the product
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of a sensing matrix ("0") 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 ("0") 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 ("0") may have dimensions of 2N by 2M.
The compressive sampler may compute sensed signal ("y") by correlating
the sampled received uplink signal (7') with, for instance, independently
selected
sensing waveforms ("yi ") of the sensing matrix ("0"). Selection of the
sensing
waveforms ("9 = '') of the sensing matrix ("0") 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 (7'). Therefore,
the selected
M sensing waveforms ("9 = ") of the sensing matrix ("0") may be independent of
the
sparse representation matrix ("tr), but M may be dependent on an estimate of a
property
of the received uplink signal (7'). Further, the sparseness S of received
uplink signal
(7') 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 ("tP") 775.
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.
Further, base station 702 may send an instruction to sensor 710 to, for
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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 ("(p =
") 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
("yj ") to base station 702.
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 (",j ") of
sparse
representation matrix ("tr). The selection of sparse representation waveforms
("y = ")
of sparse representation matrix ("tr) 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
("y j ") of
sparse representation matrix ("tr).
Base station 702 may also broadcast a downlink overhead message for
unrecognized user equipment 706 to use a specific sparse representation
waveform ("yi
") of sparse representation matrix ("tr), which can be referred to as a pilot
signal ("y
"). Sensor 710 can continuously receive uplink signals (!'), compressively
sample
uplink signals (7') to generate sensed signal ("y"), and send sensed signals
("y") to base
station 702. Base station 702 can then detect the pilot signal ("yo ") in the
sensed
signal ("y"). Once the pilot signal ("y ") 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 ("y "), 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.
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 (",j ") of sparse
representation
matrix ("tr). Further, base station 702 may vary the value of M based on
anticipating,
for instance, the amount of uplink signal (T) activity by user equipment 706.
For
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example, if base station 702 anticipates that the sparseness S of uplink
signal (7') is
changing, it may instruct sensor 710 to change the value of M. For a certain
deterministic sensing matrix ("0"), when M equals the value of N, sensing
matrix ("0")
in sensor 710 may effectively become a discrete Fourier transform ("DFT").
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
estimate of the information signal ("x"), also referred to as The estimate
of the
information signal ("x") may be determined using, for instance, the simplex
algorithm, /1
norm algorithm, /0 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.
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 . 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.
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 (7') during some period of time, for instance, one to two seconds.
Because user
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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.
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 X . First
value 974 may
be, for instance, a logical one. Further, second value 976 may be, for
instance, a logical
zero.
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 ("tr) and the sensing matrix ("0"). The random
matrices
are composed of, for instance, independently and identically distributed
("iid') Gaussian
values.
In another embodiment, a sensor-based wireless communication system
using compressive sampling may use deterministic matrices for the sparse
representation
matrix ("tr) and the sensing matrix ("0"). The deterministic matrices are
composed of,
for instance, an identity matrix for the sparse representation matrix ("tr)
and a cosine
matrix for the sensing matrix ("0"). 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.
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
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to form an information signal ("x"). Generator 1141 can receive the
information signal
("x") and can apply a sparse representation matrix ("tr) 1143 to the
information signal
("x") to generate an uplink signal (T), 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.
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 equipment.
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
(7') 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.
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.
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
signal ("y"). Detector 1351 can receive the collected sensed signal ("y") and
can use a
sensing matrix ("0") 1233 and a sparse representation matrix ("tr) 1143 to
estimate and
detect information signal ("x") from the collected sensed signal ("y").
Controller 1357
may evaluate the detected information signal (".X") to determine the uplink
message. In
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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.
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.
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 (7') 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,
beamforming
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
of M 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.
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 (7') transmitted by user
equipment 706.
Such a deployment may be in an indoor environment where sensors 110 to 113,
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.
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
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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.
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.
The compressive sampling scheme may use a sparse representation matrix
("tr) and a sensing matrix ("0") 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,
user equipment 106, 206, 306, 606, 706, 806 and 1100, or any combination
thereof may
be provided with, for instance, the sparse representation matrix ("tr), the
sensing matrix
("0") or both, information such as a seed value to generate the sparse
representation
matrix ("tr), 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
("tr) and sensing matrix ("0") 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 of M sensing waveforms ("pi ") 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.
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
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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 ("tr) used by user equipment 706 as well as the sensing
matrix
("0") 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
("tr)
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.
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
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 ("tr)
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.
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
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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 N is twenty, M is ten, S is one or two and
random iid
Gaussian values are used to populate the sparse representation matrix ("tr)
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 correctly 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.
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 ("tr) and
the sensing
matrix ("0"). 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.
FIG. 17 illustrates simulated results of the performance of one embodiment
of a sensor-based wireless communication system using compressive sampling in
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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
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.
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, S=2, and random matrices. Further, the sparse
representation matrix ("tr) and the sensing matrix ("0") 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 iid Gaussian matrices are used for the sparse
representation
matrix ("tr) and the sensing matrix ("0") 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 ("pi ") of sensing matrix ("0")
are
substantially incoherent. Graph 1805 shows the probability of detecting one
non-zero
entry in a quantized estimate of the information signal ("x"), where any two
sensing
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waveforms ("(pi ") of sensing matrix ("0") are substantially incoherent.
Specifically,
graph 1804 and graph 1805 also represent the effect of rejecting any two
sensing
waveforms ("(pi ") of sensing matrix ("0") 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").
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, 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 ("tr) and the sensing matrix ("0")
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 iid Gaussian matrices
are used
for the sparse representation matrix ("tr) and the sensing matrix ("0") 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 ("yi ") of sensing matrix ("0") are
substantially
incoherent and two hundred trials are performed. Specifically, graph 1903 also
represents the effect of rejecting any two sensing waveforms ("yi ") of
sensing matrix
("0") 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
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.
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
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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").
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").
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, J. The signal,
x, can
be recovered without error if f is sparse. An N dimensional signal is S-
sparse, if in the
representation f =Tx, 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 T, 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.
Step 1. Sensing.
yk= (f,cpk),k E J such that/ c (1 ...N} (4)
Step 2. Solving.
subject to yk = (cpk, Vk E J (5)
Equations (1) and (2) are from [CW08, equations 4 and 5]. In Eq. (1), the
brackets ( ), denote inner product, also called correlation. The 11 norm,
indicated by
11x111, is the sum of the absolute values of the elements of its argument.
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, is given by
((1), T) = max],k,i,N11(0k,Cui)11], (6)
The Incoherent Sampling Method for designing a sampling system (compare
with [CW08]) is:
1 Model f and discover in T which f is S-sparse.
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2 Choose a al which is incoherent with tlf.
3 Randomly select M columns of (to, where M>S.
4 Sample fusing the selected q) vectors to produce y.
Pass tP, (I) and y to an // minimizer, and recover x.
One method which can be applied for ii minimization is the simplex
method [LY08].
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
5 [E5Y05, 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
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.
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).
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
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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.
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.
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.
Environmental parameters includes the range from the UE 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.
There are several kinds of access in cellular systems. Aloha random access
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].
"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.
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 11 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.
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
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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.
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].
A mixed macro/micro cellular network includes large cells for vehicles and
small cells for pedestrians [Cas04, pg. 45]. For a general perspective on
cellular system
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).
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.
Figure 24 is often thought of in the context of lossless sampling. If the
power spectrum of a signal A(f) is zero for If] >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.
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
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real or complex) values generated in sequence.
"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
-- other sources. The basic theory of detection of signals in noise is treated
in [3B99, Ch.
2.6].
"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.
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 (1:0) which are unrelated to the
basis, tlf,
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.
1. The overall cellular system continues to operate with full performance
even if a sampler stops working.
2. The remote samplers are widely distributed with a spacing of 30 to 300 m
in building/city environments.
3. The base station is not limited in its computing power.
4. The cellular system downlink is provided by a conventional cell tower,
with no unusual RF power limitation.
5. UE battery is to be conserved, the target payload data transmission power
level is 10 to 100 [tWatts.
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.
7. If possible, the remote sampler should operate on battery power. Using
line power (110 V, 60 Hz in US) is another possibility.
From the overall system characteristics, we infer the following traits of a
remote sampler.
1. The remote sampler is very inexpensive, almost disposable.
2. The remote sampler battery must last for 1-2 years.
3. The remote sampler power budget will not allow for execution of
receiver detection/demodulation/decoding algorithms.
4. The remote sampler will have an RF down conversion chain and some
scheme for sending digital samples to the base station.
5. The remote sampler will not have the computer intelligence to recognize
when a UE is signaling.
6. The remote sampler can receive instructions from the base station related
to down conversion and sampling.
Examples of modulation schemes are QAM and PSK and differential
varieties [Pro83, pp. 164, 188], coded modulation [BB99, Ch.12].
From those traits, these Design Rules emerge:
Rule A: Push all optional computing tasks from the sampler to the base
station.
Rule B: Drive down the sampler transmission rate on the fiber to the lowest
level harmonious with good system performance.
Rule C: In a tradeoff between overall system effort and sampler battery
saving, overpay in effort.
Rule D: Make the sampler robust to evolutionary physical layer changes
without relying on a cpu download.
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
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.
Please see Figure 26 for an illustration of the messages being sent in
cellular
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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, al, which is correlated
with a
frame of the input to obtain a correlation value. The correlation value is
called
)71 where i is the column of al used 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.
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 S2 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 1
to 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.
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.
The sampler is able to compute sensing measurements, y, by correlating
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with independently selected columns of the al matrix. Sensing parameters are
the
parameters which characterize the variables in the correlation of the received
signal g
with columns of the al matrix. These parameters include the number of elements
in y, i.e.
M, the values of the elements of al, and the number of chip samples
represented by g,
i.e., N. Selection of the columns of the al 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 al are used is independent of tP, but the number of columns
of al used
is dependent on an estimate of a property off. Or, the sparsity of f can be
controlled by
DL transmissions as shown at time t17 in Figure 26.
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
inform the base station as to its selections.
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.
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
tlf 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 tlf columns
which are to be
selected from.
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 iv0.
This
would act as a pilot. The remote sampler 2212 would operate, according to
Incoherent
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Sampling, and send samples y to the base station 2216. The base station 2216
would
then process this signal and detect the presence of iv0, 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 iv0 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).
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.
The remote sampler 2212 is unaware of this protocol progress, and simply
keeps sensing with columns from al 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
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, S3 , 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 M3
in the figure. In the figure these events occur at times tn , tn and t16 . At
t17 the base
station expects a message with sparsity S3 and that that message has probably
been
sensed with an adequate value of M, in particular the value called here M3. A
sequence
of events is illustrated, but the timing is not meant to be precise. In the
limit as M is
increased, if al is deterministic (for example, sinusoidal) and complex, when
M takes on
the limiting value N, al in the remote sampler has become a DEL 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.
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
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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, 381]. Our initial link budget calculations show
that a UE
may be able to operate at a transmission power of 10 to 100 [tWatts 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 off 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,
sometimes the noisy version off is referred to as g.
"Reuse" includes how many non-overlapping deployments are made of a
radio bandwidth resource before the same pattern occurs again geographically.
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.
Coming to a concrete example, then, we have fashioned the following
scenario.
1. The channel is static (no fading).
2. The noise is AWGN.
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 [3B99, Ch. 5.8, Ch. 9].
4. There is one UE.
5. The Incoherent Sampling scheme uses a random pair ( , (I)r ) or a
deterministic pair ('rd d (I)d ), in any case the solver knows everything
except the
signals x, f and noise.
6. The base station has instructed the sampler to use a specific set of M
columns of (I).
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7. The base station has instructed the UE and the sampler that transmission
waveforms consist of N intervals or chips.
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
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 Mxl
vector y
3215 (Equation 1). y 3215 is passed down a fiber optic to the base station
3216.
"Estimation" is a statistical term which includes attempting to select a
number, X, 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 [(2}. Statistical operations, such as Expectation, are covered in
- x)
[Pro83, Ch. 1]. In practice, numbers output from estimators are often
represented with
fixed-point values.
For reals, the correlation, or inner product, of g with (pp is computed as
Yp= (/,.\
L tppv )g (k), where the kth element of g is denoted g(k).
vN-i ,4,
For complex numbers the correlation would be yp = EiNc=1 (k)g * (k),
where g * denotes complex conjugation.
The 12 norm of a signal, g, is 119112 = EiNc=1 g (k)g * (k); the expression
for
reals is the same, the complex conjugation has no effect in that case.
The base station 3216 produces first an estimate of x, called X 3246, and
then a hard decision called X 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.
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
(Equation 5). is generally not equal to x, so a hard decision is made to
find the
nearest vector X to x consisting of S ones and N - S zeros.
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 x? do not appear
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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 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 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.
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 off 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.
The y* is notation from [CW08, page 24]. The is not notation from
[CW08], because that reference does not treat signals corrupted by noise. The
and
/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"].
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 ''if
Rando iid iid
Determi 1 if i=j, (rrij
cos Lii
nistic else 0
Table 1: Nature of the Matrices
The deterministic matrices are generated only once, and would not change if
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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 tlf matrix the UE 3206 uses at any time and what al matrix the
sampler
3212 uses. This does not mean the solver 3228 must dictate what matrices are
used. If
the UE is changing tlf 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 tlf 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.
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].
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.
SN S Pr{ Total Pr{j Pr{j
0 1 0.6 0.
10 1 0.2 0.
1 0.1 0.
0 2 0.4 0. 0.
10 2 0.2 0. 0.
20 2 0.1 0. 0.
20 Table 2: Detector Performance with M=5, N=10. AWGN. tlf and al with
iid
Gaussian entries. See Figure 27.
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%.
The data from Table 3 is plotted in Figure 14. S is the number of nonzero
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entries in x and is called "pulses" in Figure 14. The event "j = 1 hit" means
that the
detector detected exactly one nonzero entry in x correctly. In the case that S
= 1, that is
the best the detector can do. The event "j = 2 hit" means that the detector
detected
exactly two nonzero entries in x correctly.
I also did a simulation with M = 3, N = 10 and S = 1 (please see Figure 17
discussed below).
SN S Pr{ Total Pr{j Pr{j
0 1 0.6 0.
1 0.1 0.
1 0.0 0.
0 2 0.4 0. 0.
10 2 0.1 0. 0.
20 2 0.0 0. 0.
Table 3: Detector Performance with M=5, N=10. AWGN. tlf andOwith
deterministic entries.
10 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 11
minimizer and the
Quantizer (Figure 25).
For system design, the important probability is the probability that the
15 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
20 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.
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 1 for the deterministic case, Figure 17.
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 = 1.
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 andObe weakly related at most. This
means
that a great variety of sense matrices (Os) could be used for any 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 41:0 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
41:0 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 actual0 matrix on the performance. Another way
to put
this, is that there are "bad" 41:0 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
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 41:0
matrices. Constraining the matrices will also be beneficial, especially as S
increases.
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
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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.
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.
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
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.
1. Instructions, communication protocols and hardware interfaces between
the base station and the sensors
a. remote conversion instructions
b. oscillator retuning instructions
c. beam steering (phase sampling) instructions
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2. Communication protocols and hardware interfaces between the MS and
the BS or Central Brain
a. a high bandwidth MAC hybrid-ARQ link between an MS and the BS
which can support real-time services.
3. Communication protocols and processing techniques between the MS
and the central processor / Central Brain
a. presence-signaling codes which work without active cooperation from the
sensors
b. space time codes for this new topology and mixture of channel
knowledge c. fountain codes for mobile station registration and real time
transmission
d. large array signal processing techniques
e. signal processing techniques taking advantage of the higher frequency
transmission bands
4. The Base Stations support activities which include the following:
a. transmission of system overhead information
b. detection of the presence of mobile stations with range of one or more
sensors
c. two-way real-time communication between the base stations and mobile
station.
This memo addresses the sensor or sampler to be used in a cellular
telephony 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 Fl-T, 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
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or frames of du-ration 1 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 1 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 matrix,
number of
sensors in view of the mobile station) to determine link adaptation strategies
on a 1 ms
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 A/D path from a conventional base station, like pulling a corner
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
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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 m (building deployment) and possibly one every 300 m x 300 m (street
light
deployment).
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 of M 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 ("tr) 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
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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.
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
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 iid
Gaussian
matrix is used for the sensing matrix ("0") and a Walsh matrix is used for the
sparse
representation matrix ("tr). 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 al for each M. As shown by the graph, the
worst
bound (a),t1i) 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.
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 M may 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.
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.
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 of M 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.
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
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
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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.
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 f 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 operations0 for the analogue signals. The
output is the
signal y 3203 which is passed to optimizer 3204 which recovers an estimate of
2 3205.
Frequency domain sampling using filter banks is characterized by the following
points:
1. 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.
3213 is a diagram of a sparse signal sampler using frequency shifting. 3213
presents a method for recovering the signal f directly from the time domain
signal y for
a temporally stationary signal. The voltage controlled oscillator 3207 and
narrow band
filter 3208 perform the operations of 41:0 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 2 3211. Frequency domain sampling using frequency shifting is
characterized by the following points:
1. 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.
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3. The signal must be stationary or slowly time varying.
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).
An example of a low cost radio is given in Kaukovuori [KJR+06], another is
given in Enz lESY051.
Using fiber to connect a remote antenna to a base station was proposed and
tested by Chu [CG91].
Current Intel processors like the QX9775 execute at over 1 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
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/
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".
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."
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".
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, CISS
51
CA 02758937 2014-04-17
2008, pp. 545-550".
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 IP 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 T
matrix. The
probability of detecting the Presence signal with S = 1 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 samplers) downlink connection to
mobile stations.
Appendices A, B, C, D, E, F, and G, which are attached hereto, 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.
References:
[AAN081 K. Adachi, F. Adachi, and M. Nakagawa. Cellular mimo channel
capacities of mc-cdma and ofdm. IEEE, 2008.
[BB99] S. Benedetto and E. Biglieri. Principles of Digital Trans-mission with
Wireless Applications. Kluwer, New York, 1999.
[Cas04] J.P. Castro. All IP in 3G CDMA Networks. John Wiley & Sons, Ltd.,
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[CG91] T.S. Chu and M.J. Gans. Fiber optic microcellular radio. IEEE, pages
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[CR02] S. Cotter and B. Rao. Sparse channel estimation via matching pursuit
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[CW08] E. Candes and M. Wakin. An introduction to compressive sampling.
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[ESY05] C. Enz, N. Scolari, and U. Yodprasit. Ultra low-power radio design for
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IEEE Intl. Sym. Info. Theory, pages 2444¨ 2448, July 2008.
[KJR+06] J. Kaukovuori, J.A.M. Jarvinen, J. Ryynanen, J. Jussila, K. Kivekas,
and K.A.I. Halonen. Direct-conversion receiver for ubiquitous communications.
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[LKL+08] M. Lee, G. Ko, S. Lim, M. Song, and C. Kim. Dynamic spectrum
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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 of the invention and are not
necessarily required.
Accordingly, the scope of the present disclosure should be considered in terms
of the
following claims. As set forth above, the described disclosure includes the
aspects set forth
below.
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