Note: Descriptions are shown in the official language in which they were submitted.
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QUADRATURE IMBALANCE MITIGATION USING UNBIASED
TRAINING SEQUENCES
[0001] This application is a divisional of Canadian Patent Application
No. 2,678,126.
BACKGROUND
Field
[0002] This invention relates generally to communication channel estimation
and, more
particularly, to systems and methods for using a quadrature modulation
unbiased training
sequence in the training of receiver channel estimates.
Background
[0003] 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).
[0004] There are a number of errors that can be introduced into the
receiver that
detrimentally affect channel estimations and the recovery of
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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
Division Multiplexing (OFDM) system for example, the same IQ
constellation point may be transmitted repeatedly for each subcarrier.
[0005] 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 (e.g., the I channel) with 1 symbol
values does not rotate the constellation point, and provides no stimulation
for the quadrature channel.
[0006] 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.
[0007] 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+ 2Aco). 2Aw and 2e are hardware imbalances, respectively a
=
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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
2Ayo and 2e. Note: these two filters are real and affect both +w and ¨w in an
identical manner.
[0008] Assuming the errors are small:
(1+2e)cos(wt+24) (1+2e)cos(wt) ¨ 2Ago.sin(wt)
The first component on the right hand side, cos(wt), is the ideal
I path slightly scaled. The second component, ¨ 2AqLsin(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).
[0009] The errors result in the misinterpretation of symbol positions in the
quadrature modulation constellation, which in turn, results in incorrectly
demodulated data.
SUMMARY
[0010] 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, resulting in improperly
processed data.
[0011] A training signal can be used to calibrate receiver channels.
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.
[0012] Accordingly, a method is provided for transmitting an unbiased
communications training sequence. The method generates an unbiased
training sequence in a quadrature modulation transmitter. The unbiased
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training sequence represents a uniform accumulated power evenly distributed in
the
complex plane. More explicitly, training information in the time domain is
sent via an
in-phase (I) modulation path having an accumulated power. Training information
in
the time domain is sent via a quadrature (Q) modulation path having an
accumulated
power equal to the I modulation path power.
[0013] In one aspect, the unbiased training sequence is generated as
a signal
pair including a complex value reference signal (p) at frequency +f and a
complex
value mirror signal (pm) at frequency ¨f. The method nullifies the product
(p=pm).
[0014] A method is also provided for calculating an unbiased channel
estimate.
The method accepts an unbiased training sequence in a quadrature demodulation
receiver. The unbiased training sequence includes predetermined reference
signals
(p) representing a uniform accumulated power evenly distributed in the complex
plane. The method processes the unbiased training sequence and generates
processed symbols (y) representing complex plane information in the unbiased
training sequence. The processed symbols (y) are multiplied by the conjugate
of the
corresponding reference signal (p*), and an unbiased channel estimate (hi,) is
obtained.
[0014a] According to one aspect of the present invention, there is
provided a
method for transmitting a training sequence, the method comprising: generating
a
training sequence in a quadrature modulation transmitter, the training
sequence
representing at least three symbols, symbols A, B, and C, each symbol
representing
a complex value having an in-phase component value and a quadrature component
value, the at least three symbols having uniform power accumulation in a
complex
plane and being arranged at varying positions in the complex plane such that
the
symbols A, B, and C are located at varying angular locations in the complex
plane,
wherein one of the symbols A, B, and C has a zero value for the in-phase
component
value or the quadrature component value and wherein the sum of the squares of
the
in-phase component values of the at least three symbols is equal to the sum of
the
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squares of the quadrature component values of the at least three symbols; and
transmitting the training sequence.
[0014b] According to another aspect of the present invention, there is
provided
a method for calculating a channel estimate, the method comprising: receiving
a
training sequence in a quadrature demodulation receiver, the training sequence
representing of at least three symbols, symbols A, B, and C, each symbol
representing a complex value having an in-phase component value and a
quadrature
component value, the at least three symbols being arranged at varying
positions in
the complex plane such that symbols A, B, and C are located at different
angular
positions in the complex plane, wherein one of the symbols A, B, and C has a
zero
value for the in-phase component value or the quadrature component value, and
wherein the sum of the squares of the in-phase component values of the at
least
three symbols is equal to the sum of the squares of the quadrature component
values
of the at least three symbols; and obtaining a channel estimate based on the
received
training sequence.
[0014c] According to still another aspect of the present invention,
there is
provided a system for transmitting a training sequence, the system comprising:
a
processor configured to generate a training sequence representing at least
three
symbols, symbols A, B, and C, each symbol representing a complex value having
an
in-phase component value and a quadrature component value, the at least three
symbols being arranged at varying positions in the complex plane such that
symbols
A, B, and C are located at different angular positions in the complex plane,
wherein
one of the symbols A, B, and C has a zero value for the in-phase component
value or
the quadrature component value, and wherein the sum of the squares of the in-
phase
component values of the at least three symbols is equal to the sum of the
squares of
the quadrature component values of the at least three symbols; and a
transmitter
configured to transmit the training sequence.
[0014d] According to yet another aspect of the present invention,
there is
provided a system for calculating a channel estimate, the system comprising: a
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quadrature demodulation receiver configured to receive a training sequence
representing at least three symbols, symbols A, B, and C, each symbol
representing
a complex value having an in-phase component value and a quadrature component
value, the at least three symbols being arranged at varying positions in the
complex
plane such that symbols A, B, and C are located at different angular positions
in the
complex plane, wherein one of the symbols A, B, and C has a zero value for the
in-phase component value or the quadrature component value, and wherein the
sum
of the squares of the in-phase component values of the at least three symbols
is
equal to the sum of the squares of the quadrature component values of the at
least
three symbols; and a processor configured to obtain a channel estimate based
on the
received training sequence.
[0014e] According to a further aspect of the present invention, there
is provided
a machine-readable medium having stored thereon instructions for transmitting
a
communications training sequence, the instructions comprising: generating a
training
sequence in a quadrature modulation transmitter, the training sequence
representing
at least three symbols, symbols A, B, and C, each symbol representing a
complex
value having an in-phase component value and a quadrature component value, the
at least three symbols being arranged at varying positions in the complex
plane such
that symbols A, B, and C are located at different angular positions in the
complex
plane, wherein one of the symbols A, B, and C has a zero value for the in-
phase
component value or the quadrature component value, and wherein the sum of the
squares of the in-phase component values of the at least three symbols is
equal to
the sum of the squares of the quadrature component values of the at least
three
symbols; and transmitting the training sequence.
[0014f] According to yet a further aspect of the present invention, there
is
provided a machine-readable medium having stored thereon instructions for
calculating an unbiased channel estimate, the instructions comprising:
receiving a
training sequence in a quadrature modulation transmitter, the training
sequence
representing at least three symbols, symbols A, B, and C, each symbol
representing
a complex value having an in-phase component value and a quadrature component
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value, the at least three symbols being arranged at varying positions in the
complex
plane such that symbols A, B, and C are located at different angular positions
in the
complex plane, wherein one of the symbols A, B, and C has a zero value for the
in-
phase component value or the quadrature component value, and wherein the sum
of
the squares of the in-phase component values of the at least three symbols is
equal
to the sum of the squares of the quadrature component values of the at least
three
symbols; and obtaining a channel estimate based on the received training
sequence.
[0014g] According to still a further aspect of the present invention,
there is
provided a device for transmitting an unbiased communications training
sequence,
the device comprising: generating means for generating a training sequence in
a
quadrature modulation transmitter, the training sequence representing at least
three
symbols, symbols A, B, and C, each symbol representing a complex value having
an
in-phase component value and a quadrature component value, the at least three
symbols being arranged at varying positions in the complex plane such that
symbols
A, B, and C are located at different angular positions in the complex plane,
wherein
one of the symbols A, B, and C has a zero value for the in-phase component
value or
the quadrature component value, and wherein the sum of the squares of the in-
phase
component values of the at least three symbols is equal to the sum of the
squares of
the quadrature component values of the at least three symbols; and
transmitting
means for transmitting the training sequence.
[0014h] According to another aspect of the present invention, there is
provided
a device for calculating a channel estimate, the device comprising: receiving
means
for receiving a training sequence representing at least three symbols, symbol
A, B,
and C, each symbol representing a complex value having an in-phase component
value and a quadrature component value, the at least three symbols being
arranged
at varying positions in the complex plane such that symbols A, B, and C are
located
at different angular positions in the complex plane, wherein one of the
symbols A, B,
and C has a zero value for the in-phase component value or the quadrature
component value, and wherein the sum of the squares of the in-phase component
values of the at least three symbols is equal to the sum of the squares of the
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quadrature component values of the at least three symbols; and obtaining means
for
obtaining a channel estimate based on the received training sequence.
[0014i] According to yet another aspect of the present invention,
there is
provided a processing device for transmitting a training sequence, the
processing
device comprising: a generating module configured to generate a training
sequence
in a quadrature modulation transmitter, the training sequence representing at
least
three symbols, symbols A, B, and C, each symbol representing a complex value
having an in-phase component value and a quadrature component value, the at
least
three symbols being arranged at varying positions in the complex plane such
that
symbols A, B, and C are located at different angular positions in the complex
plane,
wherein one of the symbols A, B, and C has a zero value for the in-phase
component
value or the quadrature component value, and wherein the sum of the squares of
the
in-phase component values of the at least three symbols is equal to the sum of
the
squares of the quadrature component values of the at least three symbols.
[0014j] According to yet another aspect of the present invention, there is
provided a processing device for calculating a channel estimate, the
processing
device comprising: a receiver module configured to receive a training sequence
in a
quadrature modulation transmitter, the training sequence representing at least
three
symbols, symbols A, B, and C, each symbol representing a complex value having
an
in-phase component value and a quadrature component value, the at least three
symbols being arranged at varying positions in the complex plane such that
symbols
A, B, and C are located at different angular positions in the complex plane,
wherein
one of the symbols A, B, and C has a zero value for the in-phase component
value or
the quadrature component value, and wherein the sum of the squares of the in-
phase
component values of the at least three symbols is equal to the sum of the
squares of
the quadrature component values of the at least three symbols; and an
obtaining
module configured to obtain a channel estimate based on the received training
sequence.
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[0014k] According to one aspect of the present invention, there is
provided a method
for calculating an unbiased channel estimate, the method comprising: accepting
an unbiased
training sequence in a quadrature demodulation receiver, the unbiased training
sequence
including predetermined reference signals (p) representing a uniform
accumulated power
evenly distributed in a complex plane; processing the unbiased training
sequence, generating a
sequence of processed symbols (y) representing complex plane information in
the unbiased
training sequence; multiplying each processed symbol (y) by a conjugate of a
corresponding
reference signal (p*); and obtaining an unbiased channel estimate (hn),
wherein accepting the
unbiased training sequence includes accepting an unbiased training sequence
with a plurality
of simultaneously accepted predetermined reference signals (pn); wherein
generating the
processed symbol (y) includes generating a plurality of processed symbols (yn)
from the
corresponding plurality of reference signals; wherein multiplying the
processed symbol (y) by
the conjugate of the reference signal (p*) includes multiplying each processed
symbol by its
corresponding reference signal conjugate; and wherein obtaining the channel
estimate
includes: obtaining a plurality of channel estimates (hun); and averaging the
channel estimate
(hnn) for each value of n.
1001411 According to another aspect of the present invention, there is
provided a
system for calculating an unbiased channel estimate, the system comprising: a
receiving
configured to accept an unbiased training sequence, the unbiased training
sequence including
predetermined reference signals (p) representing a uniform accumulated power
evenly
distributed in a complex plane; a processor configured to process the unbiased
training
sequence, generating a sequence of processed symbols (y) representing complex
plane
information in the unbiased training sequence; a multiplier configured to
multiply each
processed symbol (y) by a conjugate of a corresponding reference signal (p*);
and an obtainer
configured to obtain an unbiased channel estimate (hu), wherein the receiver
is configured to
accept the unbiased training sequence by accepting an unbiased training
sequence with a
plurality of simultaneously accepted predetermined reference signals (pn);
wherein the
processor is configured to generate the processed symbol (y) by generating a
plurality of
processed symbols (yn) from the corresponding plurality of reference signals;
wherein the
multiplier is configured to multiply the processed symbol (y) by the conjugate
of the reference
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signal (p*) by multiplying each processed symbol by its corresponding
reference signal
conjugate; and wherein the obtainer is configured to obtaining the channel
estimate by:
obtaining a plurality of channel estimates (hun); and averaging the channel
estimate (hun) for
each value of n.
10014m1 According to still another aspect of the present invention, there
is provided a
machine-readable medium having stored thereon instructions for transmitting a
communications training sequence, the instructions for execution by a computer
and
comprising: accepting an unbiased training sequence in a quadrature
demodulation receiver,
the unbiased training sequence including predetermined reference signals (p)
representing a
uniform accumulated power evenly distributed in a complex plane; processing
the unbiased
training sequence, generating a sequence of processed symbols (y) representing
complex
plane information in the unbiased training sequence; multiplying each
processed symbol (y)
by a conjugate of a corresponding reference signal (p*); and obtaining an
unbiased channel
estimate (hu), wherein accepting the unbiased training sequence includes
accepting an
unbiased training sequence with a plurality of simultaneously accepted
predetermined
reference signals (pn); wherein generating the processed symbol (y) includes
generating a
plurality of processed symbols (yn) from the corresponding plurality of
reference signals;
wherein multiplying the processed symbol (y) by the conjugate of the reference
signal (p*)
includes multiplying each processed symbol by its corresponding reference
signal conjugate;
and wherein obtaining the channel estimate includes: obtaining a plurality of
channel
estimates (hun); and averaging the channel estimate (hun) for each value of n.
[0014n] According to yet another aspect of the present invention,
there is provided a
system for calculating an unbiased channel estimate, the system comprising:
means for
accepting an unbiased training sequence, the unbiased training sequence
including
predetermined reference signals (p) representing a uniform accumulated power
evenly
distributed in a complex plane; means for processing the unbiased training
sequence,
generating a sequence of processed symbols (y) representing complex plane
information in
the unbiased training sequence; means for multiplying each processed symbol
(y) by a
conjugate of a corresponding reference signal (p*); and means for obtaining an
unbiased
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channel estimate (hõ), wherein the means for accepting comprises means for
accepting an
unbiased training sequence with a plurality of simultaneously accepted
predetermined
reference signals (pn) wherein the means for processing comprises means for
generating a
plurality of processed symbols (yn) from the corresponding plurality of
reference signals;
wherein the means for multiplying comprises means for multiplying the
processed symbol (y)
by the conjugate of the reference signal (p*) by multiplying each processed
symbol by its
corresponding reference signal conjugate; and wherein the means for obtaining
comprises:
means for obtaining a plurality of channel estimates (h.); and means for
averaging the
channel estimate (km) for each value of n.
[0015] Additional details of the above-described methods, systems for
generating
unbiased training sequences and calculating unbiased channel estimates, and
variations of
these system and methods are presented below.
BRIEF DESCRIPTION OF THE DRAWINGS
[0016] FIG. 1 is a schematic block diagram of a conventional receiver
front end (prior
art).
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[0017] FIG. 2 is a schematic diagram illustrating quadrature imbalance at
the receiver side (prior art).
[0018] FIG. 3 is a schematic block diagram depicting an exemplary data
transmission system.
[0019] FIG. 4 is a schematic block diagram of a system or device for
transmitting an unbiased communications training sequence.
[0020] Fig. 5A is a diagram depicting an unbiased training sequence
represented in both the time and frequency domains.
[0021] FIGS. 5B and 5C are diagrams depicting the uniform accumulation
of power evenly distributed in a complex plane.
[0022] FIG. 6 is a diagram depicting an unbiased training sequence enabled
as a sequence of pilot tones in the time domain.
[0023] FIG. 7 is a diagram depicting an unbiased training sequence enabled
as a preamble preceding non-predetermined communication data.
[0024] FIG. 8 is a diagram depicting an unbiased training sequence enabled
by averaging symbols over a plurality of messages.
[0025] FIG. 9 is a schematic block diagram depicting a processing device for
transmitting an unbiased communications training sequence.
[0026] FIG. 10 is a schematic block diagram of a system for calculating an
unbiased channel estimate.
[0027] FIG. 11 is a schematic block diagram depicting a processing device
for calculating an unbiased channel estimate.
[0028] Fig. 12 depicts the performance achieved by applying the above-
described algorithms to the WiMedia UWB standard.
[0029] Fig. 13 is a flowchart illustrating a method for transmitting an
unbiased communications training sequence.
[0030] Fig. 14 is a flowchart illustrating a method for calculating an
unbiased channel estimate.
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DETAILED DESCRIPTION
[0031] 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.
[0032] As used in this application, the terms "processor", "processing
device", "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, generation, 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 system, distributed system, and/or across
a network such as the Internet with other systems by way of the signal).
[0033] Various embodiments will be presented in terms of systems that
may include a number of components, modules, and the like. It is to be
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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.
[0034] The various illustrative logical blocks, modules, and circuits that
have been described may be implemented or performed with a general
purpose processor, a digital signal processor (DSP), an application specific
integrated circuit (ASIC), a field programmable gate array (FPGA) or other
programmable logic device, discrete gate or transistor logic, discrete
hardware components, or any combination thereof designed to perform the
functions described herein. A general-purpose processor may be a
microprocessor, but in the alternative, the processor may be any
conventional processor, controller, microcontroller, or state machine. A
processor may also be implemented as a combination of computing devices,
e.g., a combination of a DSP and a microprocessor, a plurality of
microprocessors, one or more microprocessors in conjunction with a DSP
core, or any other such configuration.
[0035] The methods or algorithms described in connection with the
embodiments disclosed herein may be embodied directly in hardware, in a
software module executed by a processor, or in a combination of the two. A
software module may reside in RAM memory, flash memory, ROM memory,
EPROM memory, EEPROM memory, registers, hard disk, a removable disk,
a CD-ROM, or any other form of storage medium known in the art. A
storage medium may be coupled to the processor such that the processor can
read information from, and write information to, the storage medium. In the
alternative, the storage medium may be integral to the processor. The
processor and the storage medium may reside in an ASIC. The ASIC may
reside in the node, or elsewhere. In the alternative, the processor and the
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storage medium may reside as discrete components in the node, or
elsewhere in an access network.
[0036] FIG. 3 is a schematic block diagram depicting an exemplary data
transmission system 300. A baseband processor 302 has an input on line
304 to accept digital information form the Media Access Control (MAC)
level. In one aspect, the baseband processor 302 includes an encoder 306
having an input on line 304 to accept digital (MAC) information and an
output on line 308 to supply encoded digital information in the frequency
domain. An interleaver 310 may be used to interleave the encoded digital
information, supplying interleaved information in the frequency domain on
line 312. The interleaver 310 is a device that converts the single high speed
input signal into a plurality of parallel lower rate streams, where each lower
rate stream is associated with a particular subcarrier. An inverse fast
Fourier transform (IFFT) 314 accepts information in the frequency domain,
performs an IFFT operation on the input information, and supplies a digital
time domain signal on line 316. A digital-to-analog converter 318 converts
the digital signal on line 316 to an analog baseband signal on line 320. As
described in more detail below, a transmitter 322 modulates the baseband
signal, and supplies a modulated carrier signal as an output on line 324.
Note: alternate circuitry configurations capable of performing the same
functions as described above would be known by those with skill in the art.
Although not explicitly shown, a receiver system would be composed of a
similar set of components for reverse processing information accepted from a
transmitter.
[0037] FIG. 4 is a schematic block diagram of a system or device for
transmitting an unbiased communications training sequence. The system
400 comprises a transmitter or transmission means 402 having an input on
line 404 to accept digital information. For example, the information may be
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supplied from the MAC level. The transmitter 402 has an output on line
406 to supply a quadrature modulation unbiased training sequence
representing a uniform accumulated a power evenly distributed in a
complex plane.
[0038] The transmitter 402 may include a transmitter subsystem 407, such
as a radio frequency (RF) transmitter subsystem that uses an antenna 408
to communicate via an air or vacuum media. However, 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 transmitter subsystem 407 includes an in-phase (I)
modulation path 410, or a means for generating I modulation training
information in the time domain having an accumulated power. The
transmitter subsystem 407 also includes a quadrature (Q) modulation path
412, or a means for generating Q modulation training information in the
time domain having an accumulated power equal to the I modulation path
power. I path information on line 404a is upconverted at mixer 414 with
carrier fc, while Q path information on line 404b is upconverted at mixer
416 with a phase shifted version of the carrier (fc + 90 ). The I path 410 and
Q path 412 are summed at combiner 418 and supplied on line 420. In some
aspects, the signal is amplified at amplifier 422 and supplied to antenna 408
on line 406, where the unbiased training sequences are radiated. The I and
Q paths may alternately be referred to as I and Q channels. A unbiased
training sequence may also be referred to as a rotating training signal, a
quadrature balanced training sequence, balanced training sequence,
balanced training sequence, or unbiased training signal.
[0039] For example, the unbiased training sequence may be initially sent
via the I modulation path 410, with training information subsequently sent
via the Q modulation path 412. That is, the training signal may include
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information, such as a symbol or a repeated series of symbols sent only via
the I modulation path, followed by the transmission of a symbol or repeated
series of symbols sent only via the Q modulation path. Alternately, training
information may be sent initially via the Q modulation path, and
subsequently via the I modulation path. In the case of single symbols being
sent alternately through the I and Q paths, the transmitter sends a rotating
training signal. For example, the first symbol may always be (1,0), the
second symbol may always be (0,1), the third symbol (-1,0), and the fourth
symbol (0-1).
[0040] However, it is not necessary to simply alternate the transmission of
symbols through the I and Q modulations paths to obtain symbol rotation,
as described above. For example, the transmitter may send training
information simultaneously through both the I and Q modulation paths, and
combine I and Q modulated signals.
[0041] The above-mentioned rotating type of unbiased training sequence,
which initially sends training signal via (just) the I modulation path, may be
accomplished by energizing the I modulation path, but not energizing the Q
modulation path. Then, the transmitter sends a training signal via the Q
modulation path by energizing the Q modulation path, subsequent to
sending training information via the I modulation path. The training
symbols can also be rotated by supplying symbols, each with both I and Q
components, as is conventionally associated with quadrature modulation.
[0042] Typically, the transmitter 402 also sends quadrature modulated
(non-predetermined) communication data. The unbiased training sequence
is used by a receiver (not shown) to create unbiased channel estimates,
which permit the non-predetermined communication data to be recovered
more accurately. In one aspect, the quadrature modulated communication
data is sent subsequent to sending the unbiased training sequence. In
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another aspect, the unbiased training sequence 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.
[00431 To be unbiased, the symbol values associated with any particular
subcarrier may periodically vary. The simplest means of evenly distributing
information in the complex plane when there are an even number of
symbols per message, is to rotate the symbol value 90 degrees every period.
As used herein, a message is a grouping of symbols in a predetermined
format. A message has a duration of several symbols periods. One or more
symbols may be transmitted every symbol period. Some messages include a
preamble preceding the main body of the message. For example, a message
may be formed as a long packet containing many OFDM symbols. Each
OFDM symbol contains many subcarriers. In some aspects, the message
preamble includes the unbiased training sequence. In other aspects, the
unbiased training sequence is a sequence of pilot signals that are
transmitted simultaneously with the non-predetermined communication
data.
[00441 If an uneven number of symbols are used in the training sequence
of a message, a methodology that rotates the phase of the symbol by 90
degrees every period is not always useful. For a sequence of 3 symbols, a 60-
degree or 120-degree rotation may be used to evenly distribute the symbol
itrii values in the complex plane. For 5 symbols, a 180/5-degree or 360/5-
degree rotation may be used. If the number of symbols in a training
sequence is a prime number, combination solutions can be used. For
example, if there are a total of 7 symbols in a message, then a rotation of 90
degrees may be used for the first 4 symbols, and a rotation of 120 (or 60)
degrees for the next three symbols. In another aspect, the unbiased training
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sequence may be averaged over more than one message. For example, if a
message includes 3 training symbols, then the combination of 2 messages
includes 6 symbols. In the context of a 6-symbol training signal, a rotation
of 90 degrees may be used between symbols.
[0045] Since power is a measurement responsive to the squaring of a
complex symbol value, the power associated with a symbol vector at angle 0
in complex space may also be considered to be the power at (0 + 180).
Hence, the accumulated power at an angle of 60 degrees is the same as the
power at 240 degrees. Alternately stated, the power associated with a
symbol at angle 0 may be summed with the power at angle (0 + 180). By
summing the power at angles 0 and (0 + 180), complex space, as considered
from the perspective of power, only spans 180 degrees. For this reason, a
uniform accumulation of power is evenly distributed in complex space when
the unbiased training sequence consists of only 2 orthogonal symbols, or 3
symbols separated by 60 degrees.
[0046] Fig. 5A is a diagram depicting an unbiased training sequence
represented in both the time and frequency domains. In one aspect the
transmitter generates a signal pair including a complex value reference
signal (p) at frequency +f and a complex value mirror signal (pm) at
frequency ¨f, with a nullified product (ppm). For example, at time i-= 1, the
product (prpim) = 0. As noted above, p and pm are complex values with
amplitude and phase components. In another aspect, the transmitter
generates i occurrences of the reference signal (p) and mirror signal (pm),
and nullifies the sum of the products (pi-pim). Alternately stated, the sum
of (pi=pim) = 0, for i = 1 to N. Note: the "dot" between the Pi and Pim
symbols is intended to represent a conventional multiplication operation
between scalar numbers.
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[0047] Likewise, when the transmitter generates i occurrences of the
reference signal and mirror signal, the signal pair values p and pm may, but
need not, vary for every occurrence. For example, the transmitter may
nullify the sum of the products (pi=pim) by generating information as a
complex value that remains constant for every occurrence, to represent p.
To represent pm, the transmitter may generate information as a complex
value that rotates 180 degrees every occurrence. However, there are almost
an infinite number of other ways that the products (pi-pim) may be nulled.
[0048] In another aspect, the transmitter generates i occurrences of
reference signal (p) and mirror signal (pm), and a product (pipim) for each
occurrence. The transmitter pairs occurrences and nullifies the sum of the
products from each paired occurrence.
100491 For example, one or more messages may contain a temporal
sequence of N pilot tones, for a given subcarrier f, with N pilot tones for
the
mirror subcarrier ¨f. As noted above in the discussion of FIG. 5A, to create
an unbiased training sequence using this pilot tone, the general solution is
the sum of (pi=pim) = 0, for i = 1 to N. For one particular solution, the
pilot
tones are paired for i = 1 and 2. Thus, prpim + p2=p2m = 0. Likewise, the
pilot tones for i = 3 and 4 may be paired as follows: p3.p3m + p4p4m = 0.
This pairing may be continued out to i = N. If each pair has a sum of zero,
then the total sum is also zero, i.e., sum pi=pim = 0. Pairing simplifies the
nulling issue. Instead of searching for N pilots that verify sum pipim = 0, it
is enough that 2 pair of pilots can be nulled.
[0050] As described above, simple examples of creating an unbiased
training sequence include either the rotation of symbols by 90 degrees in the
time domain, or in the frequency domain, maintaining the symbol reference
on +f, but flipping the sign the mirror on ¨f. Both these examples used 2
pair of tones and satisfy the equation prpim + p2-p2m = 0.
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[0051] Alternately expressed, the unbiased training sequence may include:
Time 1: 131 for +f and pim for ¨f;
Time 2: p2 for +f and p2m for ¨f;
Time 3: p3 for +f and p3m for ¨f; and,
Time 4: p4 for +f and p4m for ¨f.
[0052] The unbiased training sequence can be obtained by averaging. The
principle of unbiased training sequence dictates that the pilot must satisfy:
P1'131m 4. P2*P2m + P3*P3m + P4*P4m = (1-
[0053] As a variation, the unbiased training sequence can be organized as
follows:
P1*P1m P2*p2m = 0 and p3-p3m + P4'P4m = 0-
[0054] FIGS. 5B and 5C are diagrams depicting the uniform accumulation
of power evenly distributed in a complex plane. The complex plane can be
used to represent real axis (R) and imaginary axis (I) information. The
circle represents the boundary of uniform power or energy with a
normalized value of 1. In FIG. 5B, the unbiased training sequence is formed
from 3 symbols: a first symbol (A) at 0 degrees; a second symbol (B) at 120
degrees; and a third symbol (C) at 240 degrees. The exact same power
distribution is obtained when the first symbol (A) remains at 0 degrees, the
second symbol (B') is at 60 degrees, and the third symbol (C') is at 120
degrees. The power associated with each symbol is 1.
[0055] In FIG. 5C, the unbiased training sequence is formed from 5
symbols: 2 symbols at 0 degrees, each with a power of 0.5, so that the
accumulated power is 1; a symbol at 90 degrees with a power of 1: a symbol
at 180 degrees with a power of 1; and a symbol at 270 degrees with a power
of 1.
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[00561 As used herein, the above-mentioned "uniform accumulation of
power" may be exactly equal accumulations in each complex plane direction,
as in many circumstances it is possible to transmit and receive an unbiased
training sequence with an error of zero. That is, the training sequence is
100% biased. Alternately stated, the sum of pi-pim = 0, as described above.
In a worst case analysis, L pilot symbols are averaged, each having a
uniform accumulated power as follows:
I sum PiTim I = sum I pi l2 = L.
If L is 100%, and if a I sum pi=pim I = L/4, then the (uniform
accumulated power) error is 25%. An unbiased training sequence with a
25% error still yields excellent results. If L/2 is used (a 50% error), good
results are obtained as the IQ interference from the channel estimate still
decreases by 6dB.
100571 FIG. 6 is a diagram depicting an unbiased training sequence enabled
as a sequence of pilot tones in the time domain. The transmitter may
generate the unbiased training sequence by supplying P pilot symbols per
symbol period, in a plurality of symbol periods. Each pulse in the figure
represents a symbol. The transmitter generates (N ¨ P) quadrature
modulated communication data symbols per symbol period, and
simultaneously supplies N symbols per symbol period, in the plurality of
symbol periods. Many communications systems, such as those compliant
with IEEE 802.11 and UWB using pilot tones for channel training purposes.
[0058] FIG. 7 is a diagram depicting an unbiased training sequence enabled
as a preamble preceding non-predetermined communication data. The
transmitter generates quadrature modulated communication data and
supplies the unbiased training sequence in a first plurality of symbol
periods (e.g., at times 1-4), followed by the quadrature modulated
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communication data in a second plurality of symbol periods (e.g., at times 5
through N). Again, the pulses in the figure represent symbols.
[0059] 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 the I
modulation path followed by 3 consecutive on the Q modulation path. Using
this process, the Q channel need only be activated briefly, for 3 symbols,
before returning to sleep. However, there are many other combinations of
symbols that may be used to generate an unbiased training sequence.
[0060] Viewing either FIG. 5B or 5C, it can be seen that the transmitter
generates a temporal sequence of complex plane symbols with equal
accumulated power in a plurality of directions (in the complex plane). As
used herein, "direction" refers to the summation of vectors at each angle 0
and (0 +180). For example, the power associated with a symbol at 0 degrees
is accumulated with the power from a symbol at 180 degrees, as 0 and 180
degrees are the same direction. As a consequence of this relationship, the
temporal sequence of symbols in the unbiased training sequence have a
cumulative power associated with real axis information in the time domain,
and an equal cumulative power associated with imaginary axis information
in the time domain, as supplied in a plurality of symbols periods by the
transmitter. In another aspect, the unbiased training sequence
representing the uniform accumulated power evenly distributed in the
complex plane may be expressed as a temporal sequence of i complex
symbols (a) in the time domain, as follows:
sum ai(k).ai(k) = 0;
where k is a number of samples per symbol period. Note: the "dot"
between the ai and ai symbols is intended to represent a conventional
multiplication operation between scalar numbers.
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[0061] Since the symbol ai is typically a subcarrier with a periodic
waveform, there is no one particular value for a. That is, ai varies with
time, and could be represented as ai(t). However, if t samples are obtained,
the symbol may be expressed as ai(kT), or ai(k), assuming T is normalized to
1. For time domain systems, the summation over k disappears. With only
one sample per symbol, the symbol and sample become the same and the
equation could be written as:
sum ai:ai = 0.
[0062] To illustrate with a simple 2-symbol orthogonal unbiased training
sequence, if the first symbol ( i = 1) has an angle of 0 degree, an equal
amount of power must exist at an angle of 180 degrees in order to satisfy the
equation. Likewise, if the second symbol is at 90 degrees, and equal amount
of power must exist at an angle of 270 degrees. Other more complication
examples may require that the symbols be summed over the index of i to
obtain the nulled final result.
[0063] Alternately considered, the formula sum ai-ai = 0 refers to the fact
that if a projection is made in any direction in the complex plane and the
power calculated, the power is always the same, regardless of the angle.
The power in direction cp is:
sum l Re ai(i(P) l 2 = 0.5 sum I ai 2 0.5 Re (23P) sum ai = 0.
I
This power is constant for all p if and only if sum ai=ai = 0.
[00641 It can be shown that the frequency domain formula (sum pipim = 0)
is equivalent to sum ai=ai = 0. The time domain signal corresponding to pi
and pim is:
ai = pi exp(j2nft) + pim exp(-j2nft);
since pi modulates +f and pi. modulates ¨f.
Within one symbol i, the integral over time of ai=ai is:
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integral ai-ai = integral {pi.pi exp(jThaft)
+ pim.pim exp(j4lift) + pi-pim} = pi-pim;
since the exp(j4uft) rotates several times and vanishes when
integrated in one symbol.
So ai-ai cumulated in one symbol is equal to pi-pim.
If all the symbols are added up:
sum integral ai-ai = sum pi-pim = O.
[0065] FIG. 8 is a diagram depicting an unbiased training sequence enabled
by averaging symbols over a plurality of messages. A symbol (or more than
one, not shown) is generated in a first symbol period in a first message. A
symbol is generated in a second symbol period in a second message,
subsequent to the first message. More generally, a training information
symbols are generated in a plurality (n) messages. The transmitter
generates the unbiased training sequence by creating equal power in a
plurality of complex plane directions, as accumulated over the plurality of
messages. Although a preamble type training sequence is shown, similar to
FIG. 7, the same type of analysis applied to pilot-type unbiased training
sequence.
[0066] FIG. 9 is a schematic block diagram depicting a processing device for
transmitting an unbiased communications training sequence. The
processing device 900 includes a transmitter module 902 for accepting
digital information on line 904 and supplying a quadrature modulation
unbiased training sequence on line 906. The unbiased training sequence
represents a uniform accumulation of power evenly distributed in the
complex plane. The functionality associated with the processing device 900
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is similar to the transmitter described in FIGS. 3 through 8 above, and will
not be repeated here in the interest of brevity.
[0067] FIG. 10 is a schematic block diagram of a system for calculating an
unbiased channel estimate. The system 1000 comprises a quadrature
demodulation receiver or receiving means 1002 having an input on line 1004
to accept an unbiased training sequence. As with the transmitter of FIG. 4,
the receiver 1002 may be an RF device connected to an antenna 1005 to
receive radiated information. However, the receiver may alternately receive
the unbiased training sequence via a wired or optical medium (not shown).
The unbiased training sequence includes predetermined reference signals
(p) representing a uniform accumulated power evenly distributed in the
complex plane, as defined above.
[0068] The receiver 1002 generates processed symbols (y) on line 1006
representing complex plane information in the unbiased training sequence,
which is sent to multiplier 1008. Since the value of p is predetermined, a
multiplier 1008 is able to multiply each processed symbol (y) by the
(predetermined) conjugate of the corresponding reference signal (p*), and
supply an unbiased channel estimate (hu) at an output on line 1010. The
conjugate information may, for example, be stored in memory 1012 and
supplied to the multiplier 1008 on line 1014.
[0069] In one aspect, the receiver 1002 accepts an unbiased training
sequence with a plurality of simultaneously accepted predetermined
reference signals (pn). For example, the receiver may accept a message with
P pilot symbols (per symbol period), see FIG. 6. The receiver 1002 generates
a plurality of processed symbols (yn) from the corresponding plurality of
reference signals, multiplies each processed symbol by its corresponding
reference signal conjugate, obtains a plurality of channel estimates (hun),
and averages the channel estimate (hun) for each value of n. Using the
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example of FIG. 6, P unbiased channels estimates are obtained. The
methodology for determining channel estimates is well known in the art.
The present invention receiver however, is able to calculate extremely
accurate unbiased type of channel estimate using predetermined data.
[0070] In another aspect, a receiver subsystem 1016 has an in-phase (I)
demodulation path 1018 or a means for accepting I demodulation training
information in the time domain having an accumulated power. A
quadrature (Q) demodulation path 1020 or a means for accepting Q
demodulation training information in the time domain has an accumulated
power equal to the I modulation path power.
[0071] Contrasting FIG. 10 with FIG. 6, the receiver 1002 accepts an
unbiased training sequence with temporal sequence of n predetermined
reference signals (pn). The receiver 1002 generates a temporal sequence of
n processed symbols (yn) from the temporal sequence of reference signals
and multiplies each processed symbol in the temporal sequence by its
corresponding reference signal conjugate. In FIG. 6, P processed symbols (y)
are generated each symbol period. The receiver 1002 obtains a temporal
sequence of n channel estimates (him), and averages the n channel
estimates.
[0072] In one aspect, the receiver 1002 accepts the unbiased training
sequence as a signal pair including a complex value reference signal (p) at
frequency +f and a complex value mirror signal (pm) at frequency ¨f, where
the product (p.pm) is null, see FIG. 5. Further, the receiver may accept the
unbiased training sequence as i occurrences of the reference signal (p) and
the mirror signal (pm), where the sum of the products (pi=pim) is null. In
one variation, the receiver 1002 accepts i occurrences of the reference signal
and mirror signal, where the signal pair values p and pm vary for every
occurrence. In another variation, the receiver accepts the unbiased training
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sequence as i occurrences of the reference signal (p) and mirror signal (pm),
and generates a product (pi=pim) for each occurrence. The receiver pairs
occurrences and generates a processed symbol by nullifying the sum of the
products from each paired occurrence. For example, the receiver may accept
a signal pair, where the sum of the products (pi-pim) is nulled, as follows.
Information is accepted as a complex value that remains constant for every
occurrence, representing p. Information representing pm is accepted as a
complex value that rotates 180 degrees every occurrence.
[0073] Contrasting FIGS. 10 and 6, in one aspect the receiver accepts the
unbiased training sequence as P pilot symbols per symbol period, in a
plurality of symbol periods, and obtains P unbiased pilot channel estimates.
The receiver simultaneously accepts (N ¨ P) quadrature modulated
communication data symbols in each symbol period, generating a processed
symbol (ye) for communication data in each symbol period. That is, (N-P)
processed symbols are generated. The receiver extrapolates channels
estimates for each processed symbol (ye), derived from the unbiased pilot
channel estimates, and multiplies each processed symbol by the
extrapolated channel estimate to derive a transmitted symbol (x). The
symbol x is the unknown symbol value that is transmitted as
communication data. The extrapolation of channels estimates for data
channels, based upon the unbiased channels estimates of adjacent pilot
channels would be understood by a person with skill in the art.
[0074] Contrasting FIGS. 10 and 7, the receiver 1002 accepts quadrature
modulated communication data in symbol periods, subsequent to accepting
the unbiased training sequence. The receiver generates a processed symbol
(ye) for each communication data symbol and multiplies each processed
symbol by the unbiased channel estimate to derive a transmitted symbol (x).
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[0075] As noted above in the description of the transmitted unbiased
training sequence, the receiver accepts a temporal sequence of complex
plane symbols with equal accumulated power (as defined above) in a
plurality of directions in the complex plane. As such, the temporal sequence
of unbiased training sequence symbols has a cumulative power associated
with real axis information in the time domain, and an equal cumulative
power associated with imaginary axis information in the time domain.
[0076] In another aspect, the unbiased training sequence accepted by the
receiver may be expressed as a temporal sequence of i complex symbols (a)
in the time domain, as follows:
sum ai(k).ai(k) = 0;
where k is a number of samples per symbol period.
[0077] Contrasting FIGS. 10 and 8, the receiver may accept the unbiased
training sequence as symbols in a plurality of messages, having an equal
power in a plurality of complex plane directions, as accumulated over the
plurality of messages.
[0078] FIG. 11 is a schematic block diagram depicting a processing device
for calculating an unbiased channel estimate. The processing device 1100
comprises a quadrature demodulation receiving module 1102 having an
input on line 1104 to accept an unbiased training sequence having
predetermined reference signals (p) representing a uniform accumulated
power evenly distributed in the complex plane. The receiver module 1102
generates processed symbols (y) representing complex plane information in -
the unbiased training sequence supplied on line 1106. A multiplication
module 1108 multiplies the processed symbols (y) by the conjugate of the
corresponding reference signals (p*), and supplies an unbiased channel
estimate (hu) at an output on line 1110. Many features of the process device
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1100 are shared in common with the receiver of FIG. 10, and will not be
repeated here in the interest of brevity.
[0079] Training sequences, whether enabled in a preamble or as 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.
[0080] 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.
[0081] Although not specifically shown, the transmitter of FIG. 3 and the
receiver of FIG. 10 may be combined to form a transceiver. In fact, the
transmitter and receiver of such a transceiver may share elements such as
an antenna, baseband processor, and MAC level circuitry. The explanations
made above are intended to describe a transceiver that both transmits
unbiased training sequences and calculates unbiased channel estimates
based upon the receipt of unbiased training sequences from other
transceivers in a network of devices.
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Functional Description
[0082] Modern high data rate communication systems transmit signals on
two distinct channels, the in-phase and quadrature-phase channels (I and
Q). The two channels form a 2D constellation in a complex plane. QPSK
and QAM are examples of constellations. The I and Q channels may be
carried by RF hardware that cannot be perfectly balanced due to variations
in RF components, which results in IQ imbalance. In the increasingly
common direct conversion systems, the imbalance issued are even greater.
IQ imbalance distorts the constellation and results in crosstalk between the
I and Q channels: the signal interferes with itself. Increasing transmission
power does not help, since self-generated interference increases with the
signal power. The signal-to-noise ratio (SINR) reaches an upper bound that
puts a limit on the highest data rate attainable with a given RF hardware.
In order to increase the data rate, a costly solution is to use fancier, more
expensive hardware. A possibly less costly solution is to digitally estimate
IQ imbalance and compensate for it. The concepts of digital estimation and
compensation algorithms have been previously advanced in the art.
However, the solutions tend to be expensive because they do not rely on a
special type of training sequence. These solutions often only consider
imbalance at one side, usually at the receiver.
[0083] Examples are given below that focus on Orthogonal Frequency
Division Multiplexing (OFDM), with insights for time domain systems,
which study end-to-end imbalance, from transmitter to receiver. Moreover,
in OFDM the imbalance is modeled as a function of frequency, taking into
account variations in the frequency response of the filters.
[0084] Two kinds of enhancements are presented: one with zero cost that
eliminates the interference from the channel estimate by using an unbiased
training sequence. Substantial gains are achieved because the error of the
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channel estimate is often more detrimental to performance than the error in
the data itself. A second, relatively low cost, enhancement compensates for
data distortion, if more gain is needed.
[0085] A model of the IQ imbalance is provided below. Analysis is provided
to show how conventional channel estimation using unbiased training
sequences can mitigate part of the IQ imbalance. Then, a straightforward
extension is provided to calculate the IQ imbalance parameters, proving
that the algorithms are effective. Using the estimated parameters, a simple
compensation algorithm is presented to mitigate data distortion.
Simulation results for WiMedia's UWB are also given, as well as
suggestions to amend the standard.
IQ Imbalance Model
[0086] IQ imbalance arises when the power (amplitude) balance or the
orthogonality (phase) between the in-phase (I) and quadrature-phase (Q)
channels is not maintained. IQ imbalance is therefore characterized by an
amplitude imbalance 2e and a phase imbalance 2Acp.
Time Domain Signals
[0087] A complex symbol x is transmitted and received via the I and Q
channels. In an ideal noiseless channel, the symbol x is received intact. But
in the presence of IQ imbalance, a noisy or distorted version is likely
received.
y = ax + 8x*, (1)
where
a = cos(Acp) + jesin(Acp),
ecos(Acp) - j sin(Acp) (2)
are complex quantities modeling the imbalance, a 1 and 8 O. Nonlinear
model W is linearized via the vector form
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(et fct 0 f x .
X
= v 1 _
-- Y = BX. (3)
B is the imbalance matrix. The second row is obsolete since it is a duplicate
version of the first row. But it gives a same size and type input and output
so imbalance blocks at transmitter and receiver can be concatenated, as
described below. The imbalance matrix at the transmitter is defined by Bt,
and at the receiver it is defined by Br.
One-Tap Channel
100881 A one-tap channel is considered, suitable for OFDM. A one-tap
channel h in appropriate matrix form is
µ
p 1 4
H=
With imbalance at transmitter and receiver, and in average while Gaussian
,
(AWGN) noise n, vector form N = tn "4'ft, the received signal is expressed
as a concatenation of linear blocks
Y = BrilBtX + N
-A H'X + N
I x ) tm
(
-- y = h'x + 8'x* + n. (5)
The overall result is that IQ imbalance and channel combine to create a
global channel h', plus an undesired distortion or interference characterized
by a global imbalance parameter 8'. The global imbalance parameter 8'
changes when the channel changes, and may need to be estimated regularly.
[00891 Next, the condition is considered where the symbol x, rather than
spanning the entire complex plane, is restricted to a given (1D) axis. For
example, the axis may be associated with BPSK modulation, the real axis,
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the imaginary axis, or any axis in between. In this case, x* = kx may be
written, where k is a complex constant (a rotation), and
y = (h' + B'k)x + n
h"x + n. (6)
If x is restricted to a unique axis, IQ imbalance vanishes, becoming an
integral part of an overall channel response.
Frequency Domain Signals
[0090] While the previous model applies to time domain signals, a
modification is now considered where the signal of interest x is given in
frequency domain, at frequency f. In time domain, this signal is carried by a
complex tone, xei2.ft. Replacing terms in equation (1), the following is
obtained
axei21ft + 13x*e-j2nft. (7)
In OFDM, the interference created by IQ imbalance does not show up at the
same frequency f, but rather at the mirror frequency ¨f, and vice versa.
What is transmitted at -f creates interference on frequency +f. If signal xm
is the signal transmitted at frequency -f, where index m denotes a quantity
at mirror frequency ¨f, then at frequency ¨f the following is obtained
anaxme-j2nft 8 mxm*ej2nft. (8)
A generalization of the time domain equations has been used. The IQ
imbalance parameters a and 6 are here a function of frequency. This models
an imbalance due to different low-pass (base-band) or band-pass (IF) filters
in the system. The I and Q paths cannot have the exact same filters and,
hence, the imbalance varies with frequency. In time domain systems, this
kind of imbalance exists but it is very expensive to compensate. An
equalizer and an extension of the model to deal with different convolutions
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on different channels are required. So in the time domain, bulk or average
imbalance is used. Frequency domain systems are able to take advantage of
the plain equalizer structure and model the imbalance on a per frequency
basis.
[0091] If the output of equations (1) and (8_) are combined per subcarrier,
the following is observed
Y = (ax + Bmxm*)epat
ym = (amxm + Bx*)e-i2nft. (9)
Omitting the subcarriers (automatically handled by the FFT), a linear
model function of signals at +f and ¨f can be written as
(= k13* 't14:41
---* Y = BX. (10)
In the frequency domain model, the second row is no longer obsolete. The
model deals, in one shot, with a pair of mirror frequencies. A one-tap
channel h at frequency f, and hm at frequency -f is modeled by the matrix
(11)
H=
(
AWGN noise n at frequency f, and nm at frequency -f form the noise vector N
= (it 11,1jr. The end to end model is
Y = BrFIBtX + N
A H'X + N
(3t,satte, 0,,,,,,t,i= y .4, i it v., 1
¨> y = h'x +13m'xm* + n
ym = hmrxm + ii'x* + n m (12)
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h', hõ,' are the global channel taps, and 6', 6m' are the global imbalance
parameters. The imbalance parameters change when the channels change
and may need to be estimated regularly.
[0092] Since IQ imbalance generates interference exclusively from the
mirror frequency, two interesting cases are noteworthy. If at the mirror
frequency no signal is transmitted, or the channel is in a fade, no
interference is created. If on the other hand, the signal or channel is
strong,
the interference can be strong. Hence, in OFDM, the effect of IQ imbalance
is more problematic.
Conventional Channel Estimation
[0093] Before examining the compensation algorithms, it is shown how half
of the problem can be solved at no cost, simply by using an unbiased
training sequence. An unbiased training sequence fully eliminates the
interference from the channel estimate, noticeably improving performance.
In fact, the error in the channel estimate is often more detrimental than the
error in the data, because the channel estimate tends to create a bias in the
constellation.
[0094] The model (12) is stimulated with pilot tones. At frequency +f, the
pilot p is transmitted, and at frequency ¨f, the pilot pm. Assuming, without
loss of generality, that the pilots have a unit norm (the channel carries the
effective power), the conventional channel estimate at frequency f is
obtained by de-rotating by p*
= h'pp* + 6' mpm*p* + n
h' + 61õipm*p* + n (13)
By averaging several channel observations, the noise is automatically
reduced (for clarity, noise de-rotation is omitted). With regard to the term
6'mpm*p*, many OFDM systems (e.g., WiMedia's UWB) use a training
sequence that is simply a repeated symbol. Therefore, this term does not
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decay with averaging. Applying a scrambling of +1 or -1 to the entire
OFDM symbol does not help, as nothing changes when the sign of both p*
and p.* are inverted. Rather, the following is accomplished: after
cumulating a number of observations, the sum of the products is nullified
E ipipi. 0. (14)
Often the training sequence consists of an even number of symbols, and it is
enough to ensure each pair adds up to zero
pipi. + p2p2. = 0. (15)
Table 1: Examples of unbiased training sequences
Second training symbol is a 90 degrees rotation of first training
P2 = jpi symbol.
P2 = p1, p2. = - For positive frequencies maintain fixed pilot, for negative
pim frequencies constantly invert the sign.
[00951 Examples of simple sequences that satisfy the condition are given in
Table 1. These types of training sequences are denoted as unbiased training
sequences because, on one hand, unbiased channel estimates are produced,
and on the other, the training signals equally spans the I and Q dimensions
of the complex plane in time domain. For example, an unbiased training
sequence is not concentrated along just the real axis.
100961 As a proof: consider the unit norm complex scalar ai = piej = pi.e-je,
half way between pi and pi.. In time domain, the pilots add up to 2ai
cos(2fift + 0). In time domain and in a given OFDM symbol, the 2 mirror
pilots span a unique direction determined by the complex constant a. If L
symbols are transmitted, the total (or average, or cumulated) power in a
direction p is E I Rai exp(¨jp) I 2 = 0.5 L + 0.5 21, exp(-2jp) aiai. This
power
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is constant in any direction p if and only if X iaiai EX ipipi. = O. Uniform
spanning of the complex plane is achieved.
IQ Imbalance Estimation
[0097] After estimating the global channel h', the estimation of the global
imbalance parameter B.' is considered. Careful analysis of equation (12)
reveals that this parameter can be obtained in manner very similar way to
the conventional channel estimation. That is, B.' can be treated like a
"channel" carrying the pilot pm*. Hence, by de-rotating by p., an estimate of
the imbalance may be obtained. The condition for unbiased estimation of
the imbalance is identical to equation (14).
[0098] In summary, using unbiased training sequences and two
conventional channel estimations, good estimates of the end-to-end channel
and imbalance parameter are obtained (Table 2).
Table 2: Estimation algorithm
H'
Derotate by p*Derotate by p.
Smoothing over Adjacent Subcarriers
[0099] In addition to averaging over adjacent OFDM symbols, the channel
estimate may be smoothed over adjacent subcarriers within one symbol. In
OFDM, the cyclic prefix is designed to be short, and the channel is supposed
to vary slowly from tone to tone. Likewise, the filters in the RF chain
should have short temporal response and their frequency response also
varies slowly, i.e., the IQ imbalance varies slowly across subcarriers. The
same channel smoothing techniques can be used to smooth and improve the
imbalance parameter estimate. By using unbiased training sequences,
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there is no interaction between the channel estimate and the imbalance
estimate. Each estimated can be independently smoothed.
[00100] If a unique OFDM symbol is used for estimation, it is impossible to
find an unbiased training sequence that satisfies equation (14). In this case,
a nearly unbiased training sequence can be obtained by applying the
summation from equation (14) over groups of 2 or more adjacent
subcarriers. Then smoothing automatically cancels all or part of the
interference from mirror frequencies. One solution is to rotate the pilot by
90 degrees on the adjacent subcarrier (moving in mirror directions on the
positive and negative frequencies).
Optimal Estimator
[00101] The use of unbiased training sequences and the above-mentioned
conventional channel estimation results is a Least Squares (LS) estimator.
Of all the LS estimators, the Minimum Mean Squared Error (MMSE) sense
shows significant value.
Least Squares Estimator
[00102] L transmissions Xi, L noise terms Ni and L observations Y i, may be
respectively concatenated into the 2 by L matrices
J =x
==
= Xij
=
F= (16)
Then, equation (12) becomes
S= ELY + N. (17)
The unknown is H'. The LS estimator is
= 2,..I'll(xõ111)-1. (18)
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When condition (14) is satisfied, it is easy to verify that 2xH is diagonal
(the
cross terms vanish). It is proportional to an identity matrix since the pilots
are normalized to unit norm. Then
= ,2.1:11/L = 1/LZ iYiXiH (19)
is precisely four conventional channel estimations with de-rotations
respectively by pi*, Pim, pi.* and pi as described in the previous section.
Two
estimations are obtained for frequency f, and two estimations for mirror
frequency -f.
Optimal Estimator
[00103] Unbiased training sequences and conventional channel estimations
are an LS estimator. But any estimator = .V.TH(.T.TH)-1 is also an LS
estimator. Below, it is shown that the use of unbiased training sequences
results in an excellent estimator. Model (17) can be viewed as unknown
information H' sent via 2 consecutive transmissions over 2 vectors (rows of
A) in an L dimension space. We denote by xi, IV; and 21) respectively row j of
Nand Y, where j ::{1,2}. Models (12) and (17) can be written
= + 6'm.I'2 +
Y2=13'xi + + N2. (20)
There are 2 transmissions, each involving the 2 vectors Xi, X2, and where
each vector is carrying complex amplitude information to be estimated. The
LS estimator consists of projecting onto each vector, in a parallel way to the
other vector in order to cancel interference. A very good result is obtained
when the 2 vectors are orthogonal, i.e., when dot product (14) is zero.
Unbiased training sequences are by definition, training sequences that
verify this condition. Other sequences use non-orthogonal vectors and suffer
a loss of performance function of the angle between the vectors x1 and .1'2.
Many OFDM systems currently use a very poor kind of training sequences
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where .1.1,x2 are collinear, and it is impossible to properly estimate the 4
entries in H'. These training sequences tend to estimate noisier versions of
the channels h' and h'n,.
[00104] To calculate the Mean Squared Errors (MSE), the estimation error is
fr-H' = M.0(.-)-1. This is a 2 by 2 matrix, i.e., 4 error values. Each value
can be isolated by multiplying left and right with combinations of the
vectors tOft and (43 tYr. Assuming E.A4WH is an identity matrix, or more
generally a diagonal matrix with elements 02 and 0m2, it can be shown that
the MSE of 1^i' and are, respectively, the first and second diagonal
elements of 02(x.-0)-1. And for .1?" and the MSE are,
respectively, the first
and second diagonal element of 0,õ2(.1"..0)-1.
[00105] The total MSE is 2(a2 + cr.2)tr(.1:-.0)-1. Now the problem is to find
x
that minimizes tr(s.11)-1 subject to the constraint that total pilot power is
constant, i.e., tr(X.VH) = 2L. Using an Eigen decomposition, the problem can
be written as minimize y Ilk subject to E A; is constant. The problem is
solved with the Lagrange multipliers, and is typically optimum when all
Eigen values are equal. This means .1'.0 = Li is proportional to an identity
matrix.
[00106] The total MSE has been minimized, and the resulting MSE per
element is either 02/L or 0.2/L. But this MSE per element is likely to be the
best that can be obtained, even if a unique vector transmission is used. The
MSE is unlikely to be improved for a 2 vector transmissions, and therefore
the MSE per element has been minimized. The unbiased training sequences
plus conventional channel estimator are the MMSE of all LS estimators.
IQ Imbalance Compensation
[00107] If the gain from the unbiased channel estimate is not enough, the IQ
imbalance parameters may be estimated (as described previously) and
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applied to compensate for data distortion. H' is estimated in model (12), Y =
H'X + N. Now the focus turns to the unknown data X. The model is the
same as any 2-tap channel with cross-correlations. Any channel
equalization algorithm can be fitted. A simple equalization algorithm is
presented suitable for the ubiquitous bit-interleaved coded QAM and fading
channels.
[00108j One concern with the Zero-Forcing (ZF) approach
= X + 11`1N
is that it enhances noise when the mirror channel is weak, unless an
accounting is made for the complicated colored noise. The present solution
uses ZF, but only when the mirror channel is not weak. In equation (12),
replacing xm by its value, the following is obtained
y = (h'- 603'*/h m'*)x + (6 mAimly m*- (6 m'Aim'*)n m* + n
h'x + (13m'Aim'*)y m* + n' + n, (21)
where n'.--(13m7linr)nm* is noise enhancement. Note: it is assumed the
second order imbalance term 613. Whnr. When this approximation
is
invalid, the corrected channel h'- 6m'6'*/hm'*is considered,
which entails
precise estimation of the channel and imbalance parameters.
Basically, the ZF technique consists of computing
Z = y - (6mYlinr)y m h'x + n' + n. (22)
By subtracting the mirror frequency quantity (13m?hm)ym from the received
signal y, the simple channel model with no IQ imbalance is obtained. The
rest of the decoding chain is unchanged.
[00109] This solution works well as long as the noise enhancement is weaker
than the original interference from IQ imbalance, i.e., I n' I 2 < I f3m'xm*I
2. If
not, then the original y is used rather than the imbalance corrected z. It is
unnecessary to estimate n' in order to make a decision. A robust average-
wise improvement may be elected. So, considering the expected values
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E In'12=(1 m' 124 h m'12)E In.12< 113.'12Elx.*1 2
ENX12 (23)
¨> I h.' I 2rPe.:x SNRm > 1.
When the mirror frequency's signal to noise ratio SNRm is greater than 1,
the imbalance corrected term z is used. Otherwise, the original signal y is
kept. Due to channel and imbalance estimation imprecision, it is safer to
use a larger SNR, for example, SNRm > 2 works well for WiMedia UWB.
Note that SNRm can usually be obtained from the global SNR via the
formula SNR. = I hm' I 2SNR.
[001101 Table 3 summarizes the ZF algorithm with noise enhancement
avoidance.
Table 3: Compensation algorithm
SNRm < 1 + 6 SNR. > 1 + 6
Z = y z = y - (6mr/hOym
Simulation Results
[001111 Fig. 12 depicts the performance achieved by applying the above-
described algorithms to the WiMedia UWB standard. The highest data rate,
480 Mbps, is simulated in IEEE 802.15.3's channel model CM2 (indoor pico-
environment of about 4 meters). Shadowing and band hopping are turned
off. The IQ imbalance is constant and equal to 2e = 10% (0.8 dB) in
amplitude and 26,cp = 10 degrees in phase. The same amount of imbalance
is present at the transmitter and receiver. The figure shows the Packet
Error Rate (PER) as a function of Eb/No. The performance degrades quickly
without any form of compensation. Table 4 lists the loss of various
algorithms with respect to ideal case.
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. . .. . .
Table 4: WiMedia UWB: loss from IQ imbalance at PER of 10-2
Current StandardUnbiased TrainingCompensation
3.1 dB 1.1 dB 0.35 dB
[00112] End-to-end IQ imbalance and channel combine to form a global 2 by
2 channel matrix. The use of unbiased training sequences achieves
considerable gains at no cost. The unbiased training sequences
automatically cancel end-to-end self-generated interference from the
channel estimate. Moreover, such training sequences are ideal for
estimating IQ imbalance parameters, and a simple algorithm is given to
compensate for data distortion: Zero-Forcing with noise enhancement
avoidance.
[00113] WiMedia UWB, in particular, benefits from the following
enhancement: the conventional biased training sequence that consists of 6
symbols exclusively transmitted on the I channel can be divided in 2 halves
to create an unbiased sequence. The first 3 symbols are sent on the I
channel, and the last 3 symbols are sent on the Q channel. By uniformly
spanning the complex plane, an unbiased training sequence is created with
large gains for high data rates. For backward compatibility, this scheme
may be reserved for high data rate modes and signaled via the beacons, or
the training sequence type may be blindly detected.
[00114] In OFDMA (e.g., WiMAX), the subcarriers f and -f can be assigned to
different users. Considerable interference can arise if power control drives
one user to high power level. It is therefore a good idea to locate the pilots
of
different users on mirror subcarriers. The pilots should satisfy the unbiased
training sequence criterion. Each user automatically benefits without any
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extra effort. The pilots may hop to different locations while maintaining
mirror positions.
[00115] The time domain formulas can be extended to Code Division
Multiple Access (CDMA) with a Rake equalizer combining several one-tap
channels. Unbiased training sequences automatically improve the channel
estimate per tap. A simple unbiased training sequence for CDMA consists
of constantly rotating the complex symbols by 90 degrees.
[00116] Fig. 13 is a flowchart illustrating a method for transmitting an
unbiased 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 requirement of maintaining a strict order of sequence. The
method starts at Step 1300.
[00117] Step 1302 generates an unbiased training sequence in a quadrature
modulation transmitter, with the unbiased training sequence representing a
uniform accumulation of power evenly distributed in the complex plane, as
defined above. Step 1304 transmits the unbiased training sequence. The
terms "generating", "deriving", and "multiplying" refer to processes that may
be enabled through the use of machine-readable software instructions,
hardware, or a combination of software and hardware.
[00118] In one aspect, generating the unbiased training sequence in Step
1302 includes substeps. Step 1302a generates training information in the
time domain sent via an in-phase (I) modulation path having an
accumulated power. Step 1302b generates training information in the time
domain sent via a quadrature (Q) modulation path having an accumulated
power equal to the I modulation path power.
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[00119] In another aspect, generating the unbiased training sequence in
Step 1302 includes the following substeps. Step 1302c generates a signal
pair including a complex value reference signal (p) at frequency +f and a
complex value mirror signal (pm) at frequency ¨f. Step 1302d nullifies the
product (ppm).
[00120] For example, i occurrences of the reference signal (p) and mirror
signal (pm) may be generated, and the sum of the products (pipim) is
nullified. The generation of i occurrences of the reference signal and mirror
signal may include generating signal pair values p and pm that vary for
every occurrence. In one aspect, the sum of the products (pi=pim) may be
nullified by generating information as a complex value that remains
constant for every occurrence, to represent p. To represent pm, information
may be generated as a complex value that rotates 180 degrees every
occurrence.
[00121] As another example, i occurrences of reference signal (p) and mirror
signal (pm) may be generated, and a product (pi=pim) may be generated for
each occurrence. The occurrences may then be paired, and the sum of the
products nullified from each paired occurrence.
[00122] In one aspect, generating the unbiased training sequence in Step
1302 includes generating P pilot symbols per symbol period, in a plurality of
symbol periods. Then, Step 1303 generates (N ¨ P) quadrature modulated
communication data symbols per symbol period. Transmitting the unbiased
training sequence in Step 1304 includes simultaneously transmitting N
symbols per symbol period, in the plurality of symbol periods.
[00123] In another aspect, Step 1303 generates quadrature modulated
communication data. Step 1304 transmits the unbiased training sequence
in a first plurality of symbol periods, followed by the quadrature modulated
communication data in a second plurality of symbol periods.
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[00124j In a different aspect, Step 1302 generates a temporal sequence of
complex plane symbols with equal accumulated power in a plurality of
directions in the complex plane. That is, the temporal sequence of symbols
has a cumulative power associated with real axis information in the time
domain, and an equal cumulative power associated with imaginary axis
information in the time domain. Then, Step 1304 transmits the temporal
sequence of symbols in a plurality of symbol periods. In another aspect,
Step 1302 transmits the unbiased training sequence expressed as a
temporal sequence of i complex symbols (a) in the time domain, as follows:
sum ai(k).ai(k) = 0;
[00125] where k is a number of samples per symbol period. In one aspect,
Step 1302 generates symbols in a plurality of messages having an equal
power in a plurality of complex plane directions, as accumulated over the
plurality of messages.
[00126] The above-described flowchart may also be interpreted as an
expression of a machine-readable medium having stored thereon
instructions for transmitting an unbiased communications training
sequence. The instructions for transmitting a rotating training signal would
correspond to Steps 1300 through 1304, as explained above.
[00127] Fig. 14 is a flowchart illustrating a method for calculating an
unbiased channel estimate. The method starts at Step 1400. Step 1402
accepts an unbiased training sequence in a quadrature demodulation
receiver, the unbiased training sequence having predetermined reference
signals (p) representing a uniform accumulated power evenly distributed in
the complex plane. Step 1404 processes the unbiased training sequence,
generating processed symbols (y) representing complex plane information in
the unbiased training sequence. Step 1406 multiplies the processed symbols
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(y) by the conjugate of the corresponding reference signals (p*). Step 1408
obtains an unbiased channel estimate (hu).
[00128] In one aspect, accepting the unbiased training sequence in Step
1402 includes accepting an unbiased training sequence with a plurality of
simultaneously accepted predetermined reference signals (pn). Generating
the processed symbol (y) in Step 1404 includes generating a plurality of
processed symbols (yn) from the corresponding plurality of reference signals.
Multiplying the processed symbol (y) by the conjugate of the reference signal
(p*) in Step 1406 includes multiplying each processed symbol by its
corresponding reference signal conjugate. Then, Step 1408 obtains the
channel estimate by obtaining a plurality of channel estimates (hull), and
averages the channel estimate (hun) for each value of n.
[00129] In another aspect, Step 1402 accepts the unbiased training sequence
by accepting training information in the time domain via an in-phase (I)
modulation path having an accumulated power, as well as accepting
training information in the time domain via a quadrature (Q) modulation
path having an accumulated power equal (as defined above) to the I
modulation path power.
[00130] In a different aspect, Step 1402 accepts an unbiased training
sequence with temporal sequence of n predetermined reference signals (pn)
having a cumulative power associated with real axis information in the time
domain, and with an equal amount of cumulative power associated with
imaginary axis information in the time domain. Step 1404 generates a
temporal sequence of n processed symbols (yn) from the temporal sequence
of reference signals. Step 1406 multiplies each processed symbol in the
temporal sequence by its corresponding reference signal conjugate. Then,
obtaining the channel estimate h in Step 1408 includes: obtaining a
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temporal sequence of n channel estimates (hun); and, averaging the n
channel estimates.
[00131] In one aspect, Step 1402 accepts the unbiased training sequence as a
signal pair including a complex value reference signal (p) at frequency +f
and a complex value mirror signal (pm) at frequency ¨f, where the product
(p=pm) is null. For example, i occurrences of the reference signal (p) and the
mirror signal (pm) may be accepted, where the sum of the products (pi=pim)
is null. Further, the signal pair values p and pm that vary for every
occurrence. In another variation the sum of the products (pi-pim) is nulled
by accepting information as a complex value that remains constant for every
occurrence, representing p; and, accepting information as a complex value
that rotates 180 degrees every occurrence, representing pm.
[00132] As another example, i occurrences of the reference signal (p) and
mirror signal (pm) may be accepted and a product (pi=pim) generated for
each occurrence. The occurrences are then paired, and the sum of the
products from each paired occurrence is nullified.
[00133] In one aspect, Step 1402 accepts the unbiased training sequence as
P pilot symbols per symbol period, in a plurality of symbol periods, and Step
1408 obtains P unbiased pilot channel estimates. Step 1403 simultaneously
accepts (N ¨ P) quadrature modulated communication data symbols in each
symbol period. Step 1405 generates a processed symbol (ye) for
communication data in each symbol period. Step 1410 extrapolates
channels estimates for each processed symbol (ye,), derived from the
unbiased pilot channel estimates. Step 1412 multiplies each processed
symbol (yc) by the extrapolated channel estimate to derive a transmitted
symbol (x).
[00134] In another aspect, Step 1403 accepts quadrature modulated
communication data in symbol periods, subsequent to accepting the
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unbiased training sequence. Step 1405 generates a processed symbol (yc)
for each communication data symbol, and Step 1414 multiplies each
processed symbol by the unbiased channel estimate to derive a transmitted
symbol (x).
[00135] In a different aspect, Step 1402 accepts a temporal sequence of
complex plane with equal accumulated power in a plurality of directions in
the complex plane. Alternately stated, the unbiased training sequence may
be expressed as a temporal sequence of i complex symbols (a) in the time
domain, as follows:
sum ai(k)-ai(k) = 0;
where k is a number of samples per symbol period.
[00136] In one aspect, accepting the unbiased training sequence in Step
1402 includes accepting symbols in a plurality of messages, having an equal
power in a plurality of complex plane directions, as accumulated over the
plurality of messages.
[00137] The above-described flowchart may also be interpreted as an
expression of a machine-readable medium having stored thereon
instructions for calculating an unbiased channel estimate. The instructions
for calculating the unbiased channel estimate would correspond to Steps
1400 through 1414, as explained above.
[00138] Systems, methods, devices, and processors have been presented to
enable the transmission and reception of quadrature modulated unbiased
training sequences in a communications device, and the calculation of
unbiased channel estimates. Examples of particular 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.
