Note: Descriptions are shown in the official language in which they were submitted.
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QUADRATURE MODULATION ROTATING TRAINING SEQUENCE
BACKGROUND
Field
[0001] This invention relates generally to the modulation of
communications and, more particularly, to systems and methods for
generating a quadrature modulation rotating training signal for use in the
training of receiver channel estimates.
Background
[0002] FIG. 1 is a schematic block diagram of a conventional receiver front
end (prior art). A conventional wireless communications receiver includes
an antenna that converts a radiated signal into a conducted signal. After
some initial filtering, the conducted signal is amplified. Given a sufficient
power level, the carrier frequency of the signal may be converted by mixing
the signal (down-converting) with a local oscillator signal. Since the
received signal is quadrature modulated, the signal is demodulated through
separate I and Q paths before being combined. After frequency conversion,
the analog signal may be converted to a digital signal, using an analog-to-
digital converter (ADC), for baseband processing. The processing may
include a fast Fourier transform (FFT).
[0003] There are a number of errors that can be introduced into the
receiver that detrimentally affect channel estimations and the recovery of
the intended signal. Errors can be introduced from the mixers, filters, and
passive components, such as capacitors. The errors are exacerbated if they
cause imbalance between the I and Q paths. In an effort to estimate the
channel and, thus, zero-out some of these errors, communication systems
may use a message format that includes a training sequence, which may be
a repeated or predetermined data symbol. Using an Orthogonal Frequency
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Division Multiplexing (OFDM) system for example, the same IQ
constellation point may be transmitted repeatedly for each subcarrier.
[0004] In an effort to save power in portable battery-operated devices, some
OFDM systems use only a single modulation symbol for training. For
example, a unique direction in the constellation (e.g., the I path) is
stimulated, while the other direction (e.g., the Q path) is not. The same type
of unidirectional training may also be used with pilot tones. Note:
scrambling a single modulation channel with 1 does not rotate the
constellation point, and provides no stimulation for the quadrature channel.
[0005] In the presence of quadrature path imbalance, which is prevalent in
large bandwidth systems, the above-mentioned power-saving training
sequence results in a biased channel estimate. A biased channel estimate
may align the IQ constellation well in one direction (i.e., the I path), but
provide quadrature imbalance in the orthogonal direction. It is preferable
that any imbalance be equally distributed among the two channels.
[0006] FIG. 2 is a schematic diagram illustrating quadrature imbalance at
the receiver side (prior art). Although not shown, transmitter side
imbalance is analogous. Suppose that the Q path is the reference. The
impinging waveform is cos(wt + 0), where 0 is the phase of the channel. The
Q path is down-converted with ¨sin(wt). The I path is down-converted with
(1+2e)cos(wt+ 240. 2466. and 2e are hardware imbalances, respectively a
phase error and an amplitude error. The low pass filters HI and HQ are
different for each path. The filters introduce additional amplitude and
phase distortion. However, these additional distortions are lumped inside
246o and 2e. Note: these two filters are real and affect both +w and ¨w in an
identical manner.
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[0007] Assuming the errors are small:
(1+2e)cos(wt+24) (1+2e)cos(wt) ¨ 24.sin(wt)
The first component on the right hand side, cos(wt), is the ideal I path
slightly
scaled. The second component, ¨ 2Av.sin(wt), is a small leakage from the Q
path. After down-
conversion of the impinging waveform:
in the I path: (1+2e)cos(0) + 2e.sin(0).
in the Q path: sin(0).
[0008] The errors result in the misinterpretation of symbol positions in the
quadrature
modulation constellation, which in turn, results in incorrectly demodulated
data.
SUMMARY
[0009] Wireless communication receivers are prone to errors caused by a lack
of tolerance
in the hardware components associated with mixers, amplifiers, and filters. In
quadrature
demodulators, these errors can also lead to imbalance between the I and Q
paths.
[0010] A training signal can be used to calibrate receiver channel errors.
However, a
training signal that does not stimulate both the I and Q paths does not
address the issue of
imbalance between the two paths.
[0011] Accordingly to one embodiment, a method is provided for transmitting a
quadrature
modulated rotating training sequence. A rotating training signal is generated
by a quadrature
modulation transmitter. The rotating training signal includes training
information sent via an in-
phase (I) modulation path, as well as training information sent via a
quadrature (Q) modulation
path. Quadrature modulated communication data is generated either simultaneous
with, or
subsequent to the training signal. The rotating training signal and quadrature
modulated
communication data are transmitted.
[0012] For example, the rotating training signal may be generated by
initially sending
training information via the I modulation path, and subsequently sending
training information
via the Q modulation path. More explicitly, the training information sent via
the I modulation
path may include a first symbol having a reference phase (e.g., 0 degrees or
180 degrees).
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Then, the training information sent via the Q modulation path would include a
second symbol
having a phase that is 90 from the reference phase.
10012a1 According to another aspect of the present invention, there is
provided a method for
transmitting a communications training sequence, the method comprising:
generating a training
sequence in a quadrature modulation transmitter, the training sequence
representing at least a
first symbol representing a first complex value immediately followed by a
second symbol
representing a second complex value immediately followed by a third symbol
representing a
third complex value, wherein the first complex value and the second complex
value define a
first angle, wherein the second complex value and the third complex value
define a second
angle, and wherein the first angle and second angle are equal and less than
180 degrees; and
transmitting the training sequence.
10012b1 According to another aspect of the present invention, there is
provided a processing
device for transmitting a communications training sequence, the processing
device comprising:
a generating module configured to generate a training sequence representing at
least a first
symbol representing a first complex value immediately followed by a second
symbol
representing a second complex value immediately followed by a third symbol
representing a
third complex value, wherein the first complex value and the second complex
value define a
first angle, wherein the second complex value and the third complex value
define a second
angle, and wherein the first angle and second angle are equal and less than
180 degrees.
[0012c] According to a further aspect of the present invention, there is
provided a system for
transmitting a communications training sequence, the system comprising: a
processor
configured to generate a training sequence representing at least a first
symbol representing a
first complex value immediately followed by a second symbol representing a
second complex
value immediately followed by a third symbol representing a third complex
value, wherein the
first complex value and the second complex value define a first angle and the
second complex
value and the third complex value define a second angle, wherein the first
angle and second
angle are equal and less than 180 degrees; and a transmitter configured to
transmit the training
sequence.
[0012d] According to a further aspect of the present invention, there is
provided a non-
transitory machine-readable medium having stored thereon instructions for
transmitting a
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communications training sequence, the instructions comprising: generating a
training sequence
in a quadrature modulation transmitter, the training sequence representing at
least a first symbol
representing a first complex value immediately followed by a second symbol
representing a
second complex value immediately followed by a third symbol representing a
third complex
value, wherein the first complex value and the second complex value define a
first angle,
wherein the second complex value and the third complex value define a second
angle, and
wherein the first angle and second angle are equal and less than 1 80 degrees;
and transmitting
the training sequence.
[0012e] According to another aspect of the present invention, there is
provided a
communications device for transmitting a communications training sequence, the
device
comprising: means for generating a training sequence representing at least a
first symbol
representing a first complex value immediately followed by a second symbol
representing a
second complex value immediately followed by a third symbol representing a
third complex
value, wherein the first complex value and the second complex value define a
first angle,
wherein the second complex value and the third complex value define a second
angle, and
wherein the first angle and second angle are equal and less than 180 degrees;
and means for
transmitting the training sequence.
[0013] Additional details of the above-described method, a system for
generating a rotating
training signal, and other variations of the invention are presented below.
BRIEF DESCRIPTION OF THE DRAWINGS
[0014] FIG. 1 is a schematic block diagram of a conventional receiver front
end (prior art).
[0015] FIG. 2 is a schematic diagram illustrating quadrature imbalance at the
receiver side
(prior art).
[0016] FIG. 3 is a schematic block diagram of a wireless communications
device, with a
system for transmitting a rotating training sequence.
[0017] FIGS. 4A through 4D are diagrams depicting a training signal with
quadrature
modulated communication data.
[0018] FIGS. 5A and 5B are diagrams of the rotating training symbols as
represented in a
quadrature constellation.
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[0019] FIG. 6 is a diagram depicting an exemplary framework for carrying a
message with
a rotating training signal.
[0020] FIG. 7 is a schematic block diagram depicting a processing device for
transmitting a
quadrature modulation rotating training sequence.
[0021] FIG. 8 is a diagram depicting ideal and imbalanced constellations for 2
different
phases 0 of the impinging waveform of FIG 2.
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[0022] FIG. 9 is a graph depicting phase imbalance as a function of the
phase on the impinging waveform.
[0023] Fig. 10 is a flowchart illustrating a method for transmitting a
communications training sequence.
DETAILED DESCRIPTION
[0024] Various embodiments are now described with reference to the
drawings. In the following description, for purposes of explanation,
numerous specific details are set forth in order to provide a thorough
understanding of one or more aspects. It may be evident, however, that
such embodiment(s) may be practiced without these specific details. In
other instances, well-known structures and devices are shown in block
diagram form in order to facilitate describing these embodiments.
[0025] As used in this application, the terms "component," "module,"
.`system," and the like are intended to refer to a computer-related entity,
either hardware, firmware, a combination of hardware and software,
software, or software in execution. For example, a component may be, but is
not limited to being, a process running on a processor, a processor, an
object,
an executable, a thread of execution, a program, and/or a computer. By way
of illustration, both an application running on a computing device and the
computing device can be a component. One or more components can reside
within a process and/or thread of execution and a component may be
localized on one computer and/or distributed between two or more
computers. In addition, these components can execute from various
computer readable media having various data structures stored thereon.
The components may communicate by way of local and/or remote processes
such as in accordance with a signal having one or more data packets (e.g.,
data from one component interacting with another component in a local
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system, distributed system, and/or across a network such as the Internet
with other systems by way of the signal).
[0026] Various embodiments will be presented in terms of systems that
may include a number of components, modules, and the like. It is to be
understood and appreciated that the various systems may include
additional components, modules, etc. and/or may not include all of the
components, modules etc. discussed in connection with the figures. A
combination of these approaches may also be used.
[0027] FIG. 3 is a schematic block diagram of a wireless communications
device 300, with a system for transmitting a rotating training sequence.
The system 302 comprises a radio frequency (RF) transmitter 304 having an
input on lines 306a and 306b to accept information, an in-phase (I)
modulation path 308, a quadrature (Q) modulation path 310, and a
combiner 312 for combining signals from the I and Q modulation paths, 308
and 310, respectively. Although an RF transmitter is used as an example to
illustrate the invention, it should be understood that the invention is
applicable to any communication medium (e.g., wireless, wired, optical)
capable of carrying quadrature modulated information. The I and Q paths
may alternately be referred to as I and Q channels. The combined signals
are supplied on line 318 to amplifier 320, and finally to antenna 322, where
the signals are radiated. The transmitter 304 can be enabled to send a
message with a rotating training signal. A rotating training signal, which
may also be referred to as an quadrature balanced training signal, balanced
training signal, balanced training sequence, or unbiased training signal
includes training information sent via the I modulation path 308 and
training information sent via the Q modulation path 310. The transmitter
304 also sends quadrature modulated (non-predetermined) communication
data. In one aspect, the quadrature modulated communication data is sent
subsequent to sending the rotating training signal. In another aspect, the
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training signal is sent concurrently with the communication data in the
form of pilot signals. The system is not limited to any particular temporal
relationship between the training signal and the quadrature modulated
communication data.
[0028] FIGS. 4A through 4D are diagrams depicting a training signal with
quadrature modulated communication data. Considering both FIGS. 3 and
4A, in one aspect the transmitter 304 sends the rotating training signal by
initially sending training information via the I modulation path 308 and
subsequently sending training information via the Q modulation path 310.
That is, the training signal includes information, such as a symbol or a
repeated series of symbols sent only via the I modulation path 308, followed
by the transmission of a symbol or repeated series of symbols sent only via
the Q modulation path 310. Alternately but not shown, training
information may be sent initially via the Q modulation path 310, and
subsequently via the I modulation 308.
[0029] In the case of single symbols being sent alternately through the I
and Q paths, it is more likely that transmitter sends a rotating training
signal with predetermined training information via the I and Q modulation
paths. For example, the first symbol may always be (1,0) and the second
symbol may always be (0,1).
[0030] The above-mentioned rotating training signal, which initially sends
rotating training signal via (just) the I modulation path, may be
accomplished by energizing the I modulation path 308, but not energizing
the Q modulation path 310. Then, the transmitter sends the rotating
training signal via the Q modulation path by energizing the Q modulation
path 310, subsequent to sending training information via the I modulation
path.
[0031] FIGS. 5A and 5B are diagrams of the rotating training symbols as
represented in a quadrature constellation. Considering FIGS. 3, 4A, and
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5A, the transmitter 304 generates the rotating training signal by sending a
first symbol having a reference phase via the I modulation path 308, and
sending a second symbol having a phase that is either (reference phase + 90
degrees) or the (reference phase ¨ 90 degrees), via the Q modulation path
310. For example, the reference phase of the first symbol may be 0 degrees,
in which case the phase of the second symbol might be 90 degrees (as
shown) or -90 degrees (not shown).
[0032] However, it is not necessary to simply alternate the transmission of
symbols through the modulations paths 308/310 to obtain symbol rotation,
as described above. For example, the first symbol may be sent through
(just) the I (or Q) modulation path, and the transmitter may send training
information simultaneously through both the I and Q modulation paths, and
combine I and Q modulated signals to supply the second symbol. As another
example, the transmitter may send the training information simultaneously
through both the I and Q modulation paths, and combine I and Q modulated
signals to supply the first symbol, while the second symbol is obtained by
using just the Q (or I) modulation path.
[0033] The training symbols can also be rotated by supplying symbols, each
with both I and Q components, as is conventionally associated with
quadrature modulation, see FIG. 4B. That is, the transmitter 304 may send
training information simultaneously through both the I and Q modulation
paths 308/310, and combine I and Q modulated signals to supply the first
symbol on line 318. For example, the first symbol may occupy a position at
45 degrees in the constellation, see FIG. 5B. Likewise, the transmitter
would send training information simultaneously through both the I and Q
modulation paths 308/310, and combine I and Q modulated signals to supply
the second symbol. For example, the second symbol may be rotated to a
position of -45 degrees, which is orthogonal to the first symbol (45 degrees).
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[0034] Thus, in one aspect a rotating training symbol minimally includes a
sequence of two symbols with a phase difference of 90 degrees. However,
the system is not limited to a system that uses only two symbols. Generally,
an even number of symbols is preferred so that half the symbols may be
generated by using the I modulation path, and the other half generated
using the Q modulation path. However, in sequences of longer than two
symbols, a 90 degree rotation need not be performed between every symbol.
That is, there is no particular order of phase between symbols. In one
aspect, half the symbols are different from the other half by 90 degrees, on
average. For example, an Ultra Wideband (UWB) system uses 6 symbols
transmitted prior to the transmission of communication data or a beacon
signal. Therefore, 3 consecutive symbols may be generated on I modulation
path followed by 3 consecutive on Q modulation path. Using this process,
the Q channel need only be activated briefly, for 3 symbols, before returning
to sleep.
[0035] FIG. 6 is a diagram depicting an exemplary framework for carrying
a message with a rotating training signal. Considering FIGS. 3 and 6, in
one aspect the transmitter 304 is operated in accordance with the OSI
model. In this typically 7-layer model, the transmitter is associated with
the physical (PHY) layer. As shown, the transmitter 304 sends a physical
layer (PHY) signal 600 including a preamble 602, header 604, and payload
606. The transmitter sends the rotating training signal in the PHY header
604, and sends the quadrature modulated communication data in the PHY
payload 606.
[0036] Many communication systems transmit beacon information at
relatively slow quadrature modulated communication data rates, while
reserving higher data rates for the transfer of (non-predetermined)
information. Networks operating in accordance with IEEE 802.11 protocols
are an example of these systems. Since many wireless communication
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devices are battery-operated, it is desirable that these units operate in a
"sleep" mode when they are not actually transferring information. For
example, master units or access points may broadcast relatively simple, low
data rate beacon signals until a sleeping unit responds.
[0037] Pilot signals may be considered as a special case of training signals.
While training signals are transmitted before the data, typically using every
subcarrier (all N frequencies in the communication bandwidth), pilot tones
are transmitted together with the quadrature modulated communication
data on a subset of (reserved) frequencies. In system using OFDM, such as
UWB, this reserved set is comprised of pilot tones. That is, the pilot tones
are associated with P frequencies, and the data is associated with the
remaining N-P frequencies.
[0038] Training signals and pilot signals are similar in that the information
content of transmitted data is typically predetermined or "known" data that
permits the receiver to calibrate and make channel measurements. When
receiving communication (non-predetermined) data, there are 3 unknowns:
the data itself, the channel, and noise. The receiver is unable to calibrate
for noise, since noise changes randomly. Channel is a measurement
commonly associated with delay and multipath. For relatively short periods
of time, the errors resulting from multipath can be measured if
predetermined data is used, such as training or pilot signals. Once the
channel is known, this measurement can be used to remove errors in
received communication (non-predetermined) data. Therefore, some
systems supply a training signal to measure a channel before data decoding
begins.
[0039] However, the channel can change, for example, as either the
transmitter or receiver moves in space, or the clocks drift. Hence, many
systems continue to send more "known" data along with the "unknown" data
in order to track the slow changes in the channel. For the purpose of
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describing the present system, it will be assumed that pilot signals are a
subset of a more general class of training signals. That is, as used herein,
training signals refer to both an initial training sequence, as well as the
tracking training sequence referred to pilot tones in a UWB or 802.11
system. Alternately stated, the terms "initial training" and "tracking
training" or "pilot tones", are all types of training signals.
[0040] In one aspect then, the transmitter 304 sends a message where the
quadrature modulated communication data is a beacon signal, sent at a
beacon data rate, following the rotating training signal. That is, the beacon
signals used by many communication systems can be transmitted with a
rotating training signal. Further, the transmitter 304 may alternately, or in
addition, send a message with quadrature modulated communication data
at a communication data rate, greater than the beacon data rate, following a
rotating training signal.
[0041] In one aspect, the transmitter may send a combination of messages
with rotating and non-rotating training signals. For example, the
transmitter 304 may send multi-burst messages that include a balanced
message, following an unbalanced message. For the sake of brevity, the
phase "balanced message" is used to describe a message that includes both a
rotating training signal and quadrature modulated communication data.
An unbalanced message is a message comprising a non-rotating training
signal where training information is sent via the I modulation path, for
example, but not sent via the Q modulation path. In this aspect, the
unbalanced message also includes a message format signal, embedded in the
header for example, indicating that a balanced message (with a rotating
training signal) is sent subsequent to the unbalanced message. The
unbalanced message includes quadrature modulated communication data,
which may be sent subsequent to the message format signal, in the payload.
However, the system is not limited to any particular temporal relationship
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between training signal, message format signal, and quadrature modulated
data. For example, the unbalanced message may be a beacon signal or
initial training message. Alternately, the unbalanced message may be sent
subsequent to the balanced message, or unbalanced messages may be
interspersed with balanced messages.
[0042] Considering FIG. 4C, many communications systems, such as those
compliant with IEEE 802.11 and UWB, use a plurality of subcarriers that
are simultaneously transmitted. In this aspect the rotating training signal
may be enabled in the form of pilot signals. For example, P rotating pilot
symbols may be generated with (N ¨ P) quadrature modulated
communication data symbols. Each rotating pilot symbol includes training
information that changes by 90 degrees every symbol. Thus, a balanced
message, with a rotating training signal, is sent by simultaneously
transmitting N symbols. In other aspects, less than P rotating pilot symbols
are used, as some of the pilot symbols are non-rotating symbols.
[0043] Considering FIG. 4D, in a different aspect of a multi-subcarrier
system, the rotating training signal includes symbols simultaneously
generated for a plurality of subcarriers using training information sent via
the I modulation path, but not the Q modulation path, for i subcarriers.
Further, the training signal uses training information sent via the Q
modulation path, but not the I modulation path, for j subcarriers. Then, IQ
modulated communication data is generated for the i and j subcarriers
subsequent to the generation of the training information. In one aspect the
subset of i subcarriers includes "paired subcarriers" or "paired tones", which
is a pair of tones at frequency ¨f and frequency +f. Likewise, tones in the
subset j can be paired. The pairing of tones at ¨f and +f aids in the
achievement of I channel training, Q channel training, and rotation
training.
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[0044] If the sequence of training symbols through any particular
subcarrier does not rotate by 90 degrees, this system may still be considered
as generating a rotating training signal, since a channel estimation
averaging technique may be used at the receiver to average adjacent
subcarriers. Then, the overall effect of using adjacent non-rotating I and Q
training symbols is a rotating training signal. In one aspect, the training
signal is designed so that the odd-numbered subcarriers use non-rotating
training symbols sent through the I modulation path (channel X), and the
even-numbered subcarriers use the Q modulation path (channel X + 90
degrees).
[0045] In another aspect of the invention, the wireless communications
device 300 of FIG. 3 can be considered as comprising a means 308/310 for
rotating a training signal using the I and Q modulation paths, and a means
308/310 for generating quadrature modulated communication data. As
above, the training signal may be pilot symbols sent simultaneously with
communication data, or the communication data may be sent subsequent to
the rotating training signal. Further, the device 300 includes a means
320/322 for transmitting as an RF communication.
[0046] Likewise, an unbalanced message may be generated, with
quadrature modulation means 308/310 being used to generate the following:
a non-rotating training signal with training information sent via the I
modulation path, but no training information sent via the Q modulation
path; a message format signal indicating that a balanced message (with a
rotating training signal) is to be sent subsequent to the unbalanced
message; and, quadrature modulating communication data.
[0047] FIG. 7 is a schematic block diagram depicting a processing device for
transmitting a quadrature modulation rotating training sequence. The
processing device 700 comprises an I path modulation module 702 having an
input on line 704 to accept information and an input on line 706 to accept I
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control signals. The I path modulation module 702 has an output on line
708 to supply I modulated information. A Q path modulation module 710
has an input on line 712 to accept information and an input on line 714 to
accept Q control signals. The Q path modulation module 710 has an output
on line 716 to supply Q modulated information.
[0048] A combiner module 718 has inputs on lines 708 and 716 to accept
the I and Q modulated information, respectively, and an output on line 720
to supply a quadrature modulated RF signal. A controller module 722 has
outputs on lines 706 and 714 to supply the I and Q control signals,
respectively. The controller module 722 uses the I and Q control signals to
generate a message with a rotating training signal including training
information sent via the I modulation path and training information sent
via the Q modulation path, as well as quadrature modulated communication
data. The functions performed by the above-mentioned modules are similar
to those performed by the device of FIG. 3, and will not be repeated here in
the interest of brevity.
Functional Description
[0049] As described above, the present invention rotating training signal
may be used to modify conventional systems that use only the I modulation
path for training in an effort to save power. Such a system can be modified
by momentarily enabling the Q modulation path during the second part of
the training sequence. This solution uses only slightly more power, while
stimulating both I and Q channels during the training sequence.
[0050] Alternately, the unbalanced message with the non-rotating training
signal can be used for a beacon, while balanced messages, with rotating
training signals are used for high data rates. This solution may require that
a receiver be programmed to associate rotating training signal messages
with high data rates and unbalanced messages with beacons. To eliminate
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the need for a receiver to "guess" the type of training signal to be received,
information can be embedded in the preamble to inform the receiver of the
type of training sequence that is to follow.
[0051] In another variation, a conventional unbalanced message can be
used as the first burst in a multi-burst transmission. With multi-burst
transmissions, the receiver can easily be informed, in each burst, of the type
of training sequence that is to appear in the following burst. Typically then,
the first burst can be an unbalanced message, with all the subsequent
bursts being balanced messages. These messages may be optionally
enabled, used only for example, if they are supported by both the
transmitter and receiver. In this manner, the invention can be made
backward compatible with existing devices.
[0052] Another solution, which is not backward compatible, is to modify all
training sequences, including the beacon's training sequence, such that
training sequences are always balanced. In this variation the receiver does
not have to operate on two different types of training signals.
[0053] By way of illustration, an analysis is presented below of the
improvements that can be obtained in a conventional UWB-OFDM system,
by adding balanced messages with rotating training signals.
Conventionally, the training sequence is a repeated OFDM symbol. This
means that the same constellation point is transmitted repeatedly for each
subcarrier. A unique direction in the constellation (e.g., I path) is
stimulated while the other direction (e.g., Q path) is not. The errors
associated with such a system have been presented above in the
BACKGROUND Section, above.
[0054] FIG. 8 is a diagram depicting ideal and imbalanced constellations
for 2 different phases 0 of the impinging waveform of FIG 2. The phase
imbalance is 246o = 10 degrees (with no amplitude imbalance). Note: the
imbalance is strongest when the angles are 0 and 90 degrees but is nearly
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absent when the angles are 45 and 135 degrees. This is because the
imbalance self compensates around 45 degrees when the phase of the
impinging wave is halfway between the I and Q paths. The angle of the
impinging waveform depends on the both the data and the channel and can
take any value between 0 and 360 degrees.
[0055] Assuming that the impinging waveform has an angle such that all
the training symbols are aligned with the I direction (0 = 0), for instance,
then the I direction will be precisely estimated, with 0 degrees of error.
But,
the Q direction will be off by 10 degrees. In average while Gaussian noise
(AWGN), this results in excessive errors for the constellation points lying in
the Q direction. If, on the other hand, the impinging waveform has an angle
of 0 = 45 degrees (halfway between I and Q), then the imbalance is near
absent.
[0056] FIG. 9 is a graph depicting phase imbalance as a function of the
phase on the impinging waveform. The solid line on the figure below shows
the phase imbalance in the case of a repeated training sequence. The dotted
line shows the case of the rotating training sequence. In AWGN and for
uncoded QPSK at a BER of 10-5, the loss is between 0 dB and 1.5 dB for an
imbalance varying between 0 and 10 degrees (depending on the phase of the
impinging waveform).
[0057] Analysis can begin with the simpler problem of time domain
modulations such as Time Division Multiple Access (TDMA) or Code
Division Multiple Access (CDMA) in AWGN. A training sequence is
assumed with all the symbols lying on the I axis (I channel). After
transmission through an AWGN channel, the axis can rotate to a direction X
in the quadrature 2D plane (depending on the channel phase). By having
all the training symbols aligned with a direction X, then direction X is
properly estimated and any data symbol in that direction lies on the proper
axis (after rotation). However, the symbols in the orthogonal direction Y will
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be off by 246o degrees from the ideal position. They will incur significantly
more errors.
[0058] Since all training symbols lie on the X axis, the channel estimate is
H = angle(X).
The error in the direction of X is angle(X) ¨ H = O.
The error in the direction of Y is angle(Y) ¨ 900 ¨ H = 246o.
[0059] This analysis assumes that the training sequence constantly rotates,
such that the I and Q channels are equally stimulated. In this case, the
average channel has a phase that is no longer exclusively aligned with the X
direction. It will also be aligned with the Y direction, half of the time.
The channel estimate is now H = [angle(X) + angle(Y) ¨ 901 / 2.
The error in the direction of X is angle(X) ¨ H = ¨2466. / 2.
The error in the direction of Y is angle(Y) ¨ 90 ¨ H = 2466. / 2.
The dotted line curve in the figure shows the phase imbalance in each
direction. The dotted line curve is essentially 0.5 times the solid line
curve.
[0060] Each direction X and Y now shares half of the quadrature imbalance
burden. The loss is 0 to 0.5 dB corresponding to 5 degrees maximum
imbalance on each axis. The gain varies between 0 and 1 dB. Note: in the
presence of a LOS channel (AWGN), most carriers can be aligned at the
same phase and degraded by 1.5 dB for the repeated training sequence case.
In the same scenario, the degradation is only 0.5 dB for the rotating training
sequence, which is a 1 dB gain. However, as the phase noise and/or the
frequency offset residual changes the phase of the impinging waveform, the
phase imbalance varies between 0 and 10 degrees. The error is partly
smoothed. But for high data rates, diversity may not be enough to
compensate for the excessive error that regularly hits the subcarriers. The
effect on high data rates is more important.
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[0061] An implementation of a rotating training sequence does not
necessarily imply any greater hardware complexity in a receiver or
transmitter. At the receiver, rotation by 90 degrees before accumulation is
performed by swapping the I and Q channels, and sign-inverting one of
them. This operation can be done either in the time domain (if all
frequencies are rotated the same way) or in the Fourier domain, which is the
more general case.
[0062] Using the notation of the 2003 IEEE publication, Compensation of
IQ imbalance in OFDM systems, by Jan Tubbax et al., the authors reference
the imbalance halfway between the I and Q channel, so that rather than
having an imbalance of 246o and 2e on the I channel, an imbalance of No and
e is obtained on each of I and Q.
[0063] The quadrature imbalance distorted received signal, in the absence
of any channel and noise, can be expressed in terms of the transmitted
signal by
y=ax+f3x*
where x is the complex transmitted signal, x* its complex conjugate, y the
complex received signal, and a,,--- 1 and ,6 --z 0 are complex quantities that
characterize the quadrature imbalance distortion. They are given by
a = cosA6o +je.sinNo
,6 = e.cosNo ¨ jsinNo
When they are equal to 1 and 0 respectively, the received signal is identical
to the transmitted signal.
[0064] The time domain modulation case in AWGN will be revisited using
this more formal description. In the absence of noise, but in the presence of
an AWGN channel with coefficient c, the received signal before the
imbalance is cx, and after the imbalance it is
y=acx+f3c*x*
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Biased Training Sequence
[0065] If a training sequence is sent consisting of the symbols u, i.e.,
always aligned with the unique direction of u in the 2D plane, then 2
possible received symbols are obtained
y=acu+13c*u*
y = ¨a c u ¨ /3 c* u*
Assuming for the sake of simplicity, but without loss of generality, that the
vector u is unitary, to estimate the channel a digital de-rotation of +u* and
¨
u* are respectively applied to obtain the channel estimate
a c + /3 c*u*2
[0066] On the left hand side of the addition operator, the channel (or
nearly) is obtained, but on the right hand side a noise or bias occurs. This
noise does not vanish as more and more training symbols are averaged: it
remains as only the white noise vanishes. Hence, the estimate of the
channel is biased if a training sequence is transmitted that is exclusively
aligned with the symbol u.
[0067] When transmission of the data x is started, the metric that goes into
a Viterbi decoder for example, is obtained by multiplying the complex
conjugate of the channel (channel's match filter) to the received signal.
Hence
Metric = [a c + /3 c*u*21*y = [a c + /3 c*u*2]*[a cx + /3 c* x*]
And after eliminating some of the second order quantities
Metric= lapici2x a 13 Ic12x* + fla *ou2x
[0068] The first component in the metric formula above is ideally a positive
real scalar, proportional to the channel energy, which multiplies the original
constellation point. But the second and third components of that formula
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are undesired noises created by the bias. Their noise variance is identical
and equal to
al21/3121epix12
And the signal-to-noise ratio (SNR) in the absence of other source of noise is
SNR = I al4lepix12/21a12 L612104142
= I al2 21)612
0.5 [e2 Aq)2[
[0069] This noise does not have the distribution of white Gaussian noise,
but if various symbols are arriving from different independent channels ci
(multi-paths in CDMA, or interleaving, etc), after the symbols are combined,
a slow convergence to white Gaussian noise is obtained. This SNR can be of
the order of 10 to 20 dB. For data rates running at low SNRs this additional
noise may not be an issue. But for high data rates running at high SNR,
this additional noise has a significant impact.
Unbiased Training Sequence
[0070] If, rather than sending the entire training sequence aligned with the
unique direction of u, half of the symbols are transmitted aligned with an
orthogonal direction to u, denoted by u, then an average the channel
estimate is obtained of:
a c + /3 c*(u*2 + u*2) = a c
The right-hand side bias vanishes because u*2 + u*2 = 0 when these two
unitary vectors are orthogonal. Now the metric is
Metric= icti2m2x a/3 IcI2x*
Half of the quadrature imbalance noise is gone. The SNR (in the absence of
noise) is improved by 3dB.
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SNR = 1a12/ 1 12
z 1 i [e2 + 466.2]
OFDM
[0071] In OFDM, the formula for the received symbol is a little changed,
except that the entire OFDM symbol must be considered as a vector of
symbols,
y = FFT { a IFFT(c = x) + ,6 [IFFT(c = x)]*}
where vectors are denoted in boldface and where the (.) operation is the
element-wise product between two vectors. The channel c is the Fourier
domain version of the channel. This equation can be rewritten as
y=ac =x+ 13 (c = x)in*
=ac =x+ 13 (c in* = x in')
where index m denotes the vector mirrored over the sub-carriers. The only
contributors to the received symbol at frequency +f are the channels and
symbols at the symmetric frequencies +f and ¨f. The two symmetric sub-
carriers, +f and ¨f can be isolated and the received symbol for sub-carrier +f
written as
y=ac.x+13cin*.xin*
where the index m denotes the channel or symbol at frequency ¨f. The main
difference between this formula and the formula for TDMA or CDMA is that
the distortion is now created by the channel and signal at a different
frequency, namely frequency ¨f. This can have significant impact on a
particular received symbol if the symmetric frequency has a much stronger
channel, or much stronger signal. Hence, things can be more problematic in
OFDM.
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Biased Training Sequence
[0072] Assuming that the pilot tone transmitted at frequency +f is u and
the pilot tone transmitted at frequency ¨f is um, a biased training sequence
does not properly rotate the pilot tones, thereby introducing a bias in the
channel estimate
a c + /3 cm*um*u*
Then, the received metric at frequency +f can be written as
Metric(+f) = la121cl2x+ a*,(3 c*cm*xm* + a fl*c u cm um x + I/31 2 I Cm I 2Um
u xm*
The 4th (noisy) term in the formula above can no longer be neglected, since
the channel I cm I 2 can be very strong. The noisy terms now depend on the
strength of the channel at frequency ¨f and can be significant. The
frequency ¨f acts as an interferer that can confuse the Viterbi decoder,
which may sometimes interpret a weak metric with plenty of interference as
a good metric.
Unbiased Training Sequence
[0073] For the unbiased training sequence, the channel estimate is a c and
the 2 noisy terms are eliminated from the equation to obtain
MetricH) = lal2lcI2x+ a*,(3 c*cm*xm*
The improvement is clear. However, it is difficult to assess the benefit for
the 480 megabytes per second (Mbps) data rate in UWB-OFDM without
simulation in a realistic channel model. Note that for such high data rates,
the devices are expected to have an LOS or a near LOS and hence the
variations of the channel at frequencies +f and ¨f are not expected to be too
large. But a 3dB or more difference in channel strength is very likely.
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Transmitter's Quadrature Imbalance
[0074] Quadrature imbalance is also present at the transmitter side and
adds to the distortion. If a' and ,6' are denoted as the imbalance
coefficients
at the transmitter side, then the output of the transmitter can be written as
z = a'x + x*
and the receiver obtains after the channel c and the distortion a, ,G,
y=acz+13c*z*
= (aa'c + /3/3'*c*) x + (af3'c + a'*13 c*) x*
= a(c, c*) x + b(c, c*) x*
The above analysis applies to TDMA/CDMA, but also to OFDM if c* is
replaced with cm*, and x* with xm* (i.e., the values at frequency ¨f).
[0075] The problem of quadrature imbalance at both transmitter and
receiver remains the same as previously studied but with different values
for the imbalance coefficients that are function of the channel. If second
order quantities are neglected, and assuming cm* is not excessively stronger
or weaker than c, then
y z aa'c x + ( 'c + /3 c*) x*
The noise from distortion is increased. Using the unbiased training
sequence helps eliminate some of the terms contributing to the noise on the
metrics, as explained above.
[0076] Transmitting an unbiased training sequence can be achieved in a
conventional UWB system by transmitting the first part of the training
sequence using the I path and the second part on the Q path. Even if an
unbiased (non-rotating training signal) is used for beaconing, to save power
by turning off the Q channel, a special signal embedded in the preamble can
inform the receiver of the type of training sequence. Alternately, the
receiver can automatically detect the training sequence that is transmitted.
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This is not a difficult task, as it is enough to look at a few strong sub-
carriers to decide if the transmission was identical or rotated by 90 degrees.
[0077] As noted earlier, pilot tones are considered to be a special case of
training signals, since many conventional systems use pilots that are
transmitted in a unique direction in the complex plane. As the pilot tones
are tracked, a bias is constantly introduced along that direction. Better
pilots are obtained by changing them every OFDM symbol by 90 degrees, or
within the same OFDM symbol, rotating some paired ( f) subcarriers by 90
degrees with respect to other paired subcarriers (on different frequencies).
This change in pilot tones is simple and has almost a zero cost. As the
clocks between transmitters and receivers drift, the pilot tones may have
the potential of compensating for some of the bias introduced with the initial
biased training sequence when an unbalanced training signal is used. In
other words, generating just rotating pilot tones, while keeping a biased
(non-rotating) training sequence, reduces bias in most circumstances.
[0078] Simulations have been run to measure the effect of quadrature
imbalance with, and without a balanced training sequence. For an
imbalance on the TX side of 10% in amplitude (0.4 dB) and 10 degrees in
phase, and for the same amount of imbalance on the receiver side, the gain
for the highest data rate (480 Mbps) is nearly 1 dB. Even larger gains can
be expected if more types of loss are introduced that result in a requirement
for higher SNR. The higher the SNR, the more gain that can be obtained
using a balanced training sequence.
[0079] Fig. 10 is a flowchart illustrating a method for transmitting a
communications training sequence. Although the method is depicted as a
sequence of numbered steps for clarity, the numbering does not necessarily
dictate the order of the steps. It should be understood that some of these
steps may be skipped, performed in parallel, or performed without the
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requirement of maintaining a strict order of sequence. The method starts at
Step 1000.
[0080] Step 1002 generates a rotating training signal in an quadrature
modulation transmitter. Typically, predetermined or known information is
sent as the training signal. Step 1002a sends training information via an I
modulation path, and Step 1002b sends training information via a Q
modulation path. Step 1004 generates quadrature modulated
communication data. Step 1004 may be performed subsequent to Step 1002,
or simultaneous with the performance of Step 1002. In one aspect, Step
1004 generates a beacon signal at a beacon data rate. Alternately, Step
1004 generates information at a communication data rate, greater than the
beacon data rate. Step 1006 transmits the rotating training signal and
quadrature modulated communication data. Typically, the generation and
transmission of symbols or information occurs almost simultaneously.
[0081] In one aspect, transmitting the rotating training signal in Step 1006
includes initially sending training information via the I modulation path,
and subsequently sending training information via the Q modulation path.
For example, initially generating training information via the I modulation
path (Step 1002a) may include energizing the I modulation path, but not
energizing the Q modulation path. Then, generating training information
via the Q modulation path, subsequent to generating training information
via the I modulation path, includes energizing the Q modulation path.
Alternately, the training information may be sent in the opposite order.
More explicitly, generating training information via the I modulation path
in Step 1002a may include generating a first symbol having a reference
phase. Then, generating training information via the Q modulation path in
Step 1002b includes generating a second symbol having a phase of the
reference phase + 90 degrees, or the reference phase ¨ 90 degrees.
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[0082] In another aspect, Step 1002b generates training information via the
Q modulation path using the following substeps (not shown). Step 1002b1
generates training information simultaneously through both the I and Q
modulation paths, and Step 1002b2 combines I and Q modulated signals to
supply the second symbol. Alternately or in addition, generating training
information via the I modulation path may include substeps (not shown).
Step 1002a1 generates training information simultaneously through both
the I and Q modulation paths, and Step 1002a2 combines I and Q modulated
signals to supply the first symbol.
[0083] In a different aspect, transmitting (Step 1006) includes substeps.
Step 1006a organizes a physical layer (PHY) signal including a preamble,
header, and payload. Note, this organization typically occurs as a response
to receiving the information to be transmitted in a corresponding MAC
format. Step 1006b transmits the rotating training signal in the PHY
header, and Step 1006c transmits the IQ modulated communication data in
the PHY payload.
[0084] In another aspect, Step 1001a sends a multi-burst transmission with
an unbalanced message (Step 1001b) followed by the rotating training signal
(Step 1006). The unbalanced, or imbalanced message includes a non-
rotating training signal with training information sent via the I modulation
path (Step 1001b1), but no training information sent via the Q modulation
path (Step 1001b2). The unbalanced message includes a generated message
format signal (Step 1001b3) indicating that a rotating training signal is sent
subsequent to the unbalanced message. Quadrature modulated
communication data is generated in Step 1001b4. In a different aspect,
generating a rotating training signal in Step 1002 includes generating P
rotating pilot symbols, and generating quadrature modulated
communication data in Step 1004 includes generating (N ¨ P)
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communication data symbols. Then, transmitting in Step 1006 includes
simultaneously transmitting N symbols.
[0085] In another variation, generating a rotating training signal in Step
1002 includes simultaneously generating symbols for a plurality of
subcarriers. More explicitly, Step 1002a uses training information sent via
the I modulation path, but not the Q modulation path, for i subcarriers.
Step 1002b uses training information sent via the Q modulation path, but
not the I modulation path, for j subcarriers. Then, generating quadrature
modulated communication data in Step 1004 includes generating
quadrature modulated communication data for the i and j subcarriers
subsequent to the generation of the training information. In one aspect,
each i subcarrier is adjacent a j subcarrier.
[0086] More formally, the channel estimated by subcarrier i is
a c + /3 cm*um*u* (1)
Nearly the same channel is estimated by the adjacent subcarrierj with a 90
degrees rotated pilot as
a c + / 3 cm*jum*ju* = a c ¨ / 3 cm*um*u* (2)
Note: the symbol for complex numbers j in the equation should not be
confused with the subset j. Then, after averaging over the subcarriers, i.e.,
after averaging the results of (1) and (2), the bias is automatically
canceled.
[0087] The above-described flowchart may also be interpreted as an
expression of a machine-readable medium having stored thereon
instructions for transmitting a quadrature modulation rotating training
sequence. The instructions for transmitting a rotating training signal would
correspond to Steps 1000 through 1006, as explained above.
[0088] Systems, methods, devices, and processors have been presented to
enable the transmission of quadrature modulated rotating training signals
in a wireless communications device transmitter. Examples of particular
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communications protocols and formats have been given to illustrate the
invention. However, the invention is not limited to merely these examples.
Other variations and embodiments of the invention will occur to those
skilled in the art.
