U.S. patent application number 11/492414 was filed with the patent office on 2006-11-23 for vector calibration system.
Invention is credited to Richard C. Anderson-Sprecher, David C. Farden, Roger A. Green, John W. Pierre, Edwin A. Suominen.
Application Number | 20060262872 11/492414 |
Document ID | / |
Family ID | 36942051 |
Filed Date | 2006-11-23 |
United States Patent
Application |
20060262872 |
Kind Code |
A1 |
Green; Roger A. ; et
al. |
November 23, 2006 |
Vector calibration system
Abstract
Among other things, calibration of a signal processing system is
disclosed to minimize vector mismatch between signals
frequency-translated from an RF signal and conveyed along a
plurality of signal paths of the signal processing system. A
calibration signal having a plurality of tones is coupled to the
signal processing system such that it is frequency translated. The
frequency-translated calibration signal is sampled along a first
signal path of the signal processing system to obtain a first set
of observed samples. It is also sampled along a second signal path
of the system to obtain a second set of observed samples. The first
set of observed samples is filtered with an adaptive filter having
a set of adaptable coefficients to obtain a set of filtered
samples. The coefficients are adapted to minimize undesired
deviations between the set of filtered samples and the second set
of observed samples.
Inventors: |
Green; Roger A.; (Fargo,
ND) ; Farden; David C.; (Fargo, ND) ; Pierre;
John W.; (Laramie, WY) ; Anderson-Sprecher; Richard
C.; (Laramie, WY) ; Suominen; Edwin A.;
(Phoenix, AZ) |
Correspondence
Address: |
LOUIS J. HOFFMAN, P.C.
14614 NORTH KIERLAND BOULEVARD, SUITE 300
SCOTTSDALE
AZ
85254
US
|
Family ID: |
36942051 |
Appl. No.: |
11/492414 |
Filed: |
July 24, 2006 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
09730681 |
Dec 6, 2000 |
7088765 |
|
|
11492414 |
Jul 24, 2006 |
|
|
|
60190226 |
Mar 15, 2000 |
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Current U.S.
Class: |
375/260 ;
375/350 |
Current CPC
Class: |
H04L 27/364
20130101 |
Class at
Publication: |
375/260 ;
375/350 |
International
Class: |
H04K 1/10 20060101
H04K001/10; H04B 1/10 20060101 H04B001/10 |
Claims
1. A method for calibrating a signal processing system to minimize
vector mismatch between signals frequency translated from an RF
signal and conveyed along a plurality of signal paths of the signal
processing system, the method comprising: (a) applying a
calibration signal having a plurality of tones to the signal
processing system, such that the calibration signal is frequency
translated; (b) sampling the frequency-translated calibration
signal (1) along a first signal path of the signal processing
system to obtain a first set of observed samples and (2) along a
second signal path of the signal processing system to obtain a
second set of observed samples; (c) filtering the first set of
observed samples with an adaptive filter having adaptable
coefficients to obtain a set of filtered samples; and (d) adapting
the coefficients to minimize undesired deviations between the set
of filtered samples and the second set of observed samples.
2. The method of claim 1 further comprising using the filter with
the adapted coefficients to minimize vector mismatch between
signals frequency-translated by the signal processing system from
an RF input signal of interest and conveyed along the first and
second signal paths.
3. The method of claim 1 further comprising generating the
calibration signal.
4. The method of claim 3 wherein generating the calibration signal
comprises: (a) generating a local oscillator signal, which signal
the signal processing system uses to perform frequency translation;
(b) generating a baseband calibration signal; and (c) mixing the
local oscillator signal with the baseband calibration signal,
thereby obtaining a radio frequency calibration signal.
5. The method of claim 1 wherein: (a) the signal paths include an
in-phase signal path and a quadrature signal path; and (b) the
filter coefficients are adapted to minimize deviations from a
quadrature relationship between a signal on the in-phase signal
path and a signal on the quadrature signal path.
6. The method of claim 1 wherein: (a) the signal paths include a
plurality of signal paths coupled to respective elements of a
spatially selective array; and (b) the filter coefficients are
adapted to minimize deviations from a predetermined phase and
amplitude relationship between signals on each respective one of
the plurality of signal paths, such deviations degrading spatial
selectivity of the array.
7. The method of claim 6 further comprising generating the
calibration signal and transmitting it through an antenna placed at
a fixed position with respect to the array elements.
8. The method of claim 1 wherein adapting is performed by a least
mean squares algorithm.
9. The method of claim 8 wherein a plurality of values are
determined by least mean squares constrained to a predetermined
bounded region.
10. The method of claim 1 wherein: (a) the signal paths include an
in-phase signal path and a quadrature signal path; and (b) the
filter coefficients are adapted by a least mean squares algorithm
to minimize deviations from a quadrature relationship between a
signal on the in-phase signal path and a signal on the quadrature
signal path.
11. The method of claim 10 further comprising: (a) generating the
calibration signal; and (b) after adapting the filter coefficients,
using the filter with the adapted coefficients to minimize
deviations in a quadrature relationship between in-phase and
quadrature signals frequency-translated by the signal processing
system from an RF input signal of interest.
12. A signal processing system comprising: (a) a frequency
translation subsystem structured to produce a plurality of
frequency-translated signals responsive to a calibration signal
having a plurality of tones; (b) one or more converters coupled to
the frequency translation subsystem and structured to convert the
signals into a plurality of sets of observed samples; (c) an
adaptive filter having adaptable coefficients and structured to
produce a set of filtered samples responsive to one of the sets of
observed samples; and (d) control circuitry structured to adapt the
filter coefficients to minimize undesired deviations between the
set of filtered samples and a different one of the sets of observed
samples.
13. The system of claim 12 further comprising a calibration signal
subsystem coupled to the frequency translation subsystem and
structured to produce the calibration signal.
14. The system of claim 12 wherein: (a) the plurality of
frequency-translated signals consists of an in-phase signal and a
quadrature signal; (b) the plurality of sets of observed samples
consists of two sets of observed samples, one converted from the
in-phase signal and the other converted from the quadrature signal;
and (c) the undesired deviations are deviations from a quadrature
relationship between the in-phase signal and the quadrature
signal.
15. The system of claim 12 wherein: (a) the frequency-translated
signals are from respective elements of a spatially selective
array; and (b) the undesired deviations are deviations from a
predetermined phase and amplitude relationship between signals on
each respective one of the plurality of signal paths, such
deviations degrading spatial selectivity of the array.
16. The system of claim 12 further comprising: (a) a front-end
stage structured to produce a selectively amplified RF signal
responsive to RF input; (b) wherein the frequency translation
subsystem is further coupled to the front-end stage and structured
to produce frequency-translated in-phase and quadrature signals
responsive to the selectively amplified RF signal from the
front-end stage.
17. The system of claim 16 further comprising a switch coupled to
the calibration signal subsystem and the front-end stage, and
structured to convey a selected one of the calibration signal and
the selectively amplified RF signal to the frequency translation
subsystem for frequency translation into the in-phase and
quadrature signals.
18. The system of claim 12 wherein the control circuitry is
structured to adapt the filter coefficients by a least mean squares
algorithm that determines a plurality of values by least mean
squares constrained to a predetermined bounded region.
19. The system of claim 12 further comprising: (a) a switch; (b) a
calibration signal subsystem selectably coupled to the frequency
translation subsystem via the switch and structured to produce the
calibration signal; and (c) a front-end stage selectably coupled to
the frequency translation subsystem via the switch and structured
to produce a selectively amplified RF signal responsive to RF
input; (d) wherein the frequency translation subsystem is
structured to produce frequency-translated in-phase and quadrature
signals responsive to either one of (1) the calibration signal, and
(2) the selectively amplified RF signal from the front-end
stage.
20. The system of claim 19 wherein: (a) the plurality of
frequency-translated signals consists of an in-phase signal and a
quadrature signal; (b) the plurality of sets of observed samples
consists of two sets of observed samples, one converted from the
in-phase signal and the other converted from the quadrature signal;
and (c) the undesired deviations are deviations from a quadrature
relationship between the in-phase signal and the quadrature
signal.
21. The system of claim 20 wherein the control circuitry is
structured to adapt the filter coefficients by a least mean squares
algorithm that determines a plurality of values by least mean
squares constrained to a predetermined bounded region.
22. A signal processing system comprising: (a) means for generating
a calibration signal having a plurality of tones; (b) means for
producing a plurality of frequency-translated signals responsive to
the calibration signal; (c) means for producing filtered samples
from one of the frequency-translated signals, using a set of
adaptable coefficients; and (d) means for adapting the filter
coefficients to minimize undesired deviations between the filtered
samples and a different one of the frequency-translated
signals.
23. The system of claim 22 further comprising means for receiving
and frequency translating an RF input signal to the plurality of
frequency-translated signals with undesired deviations between the
signals minimized by the adaptation of the filter coefficients.
24. The system of claim 22 wherein the plurality of
frequency-translated signals consists of an in-phase signal and a
quadrature signal and the undesired deviations are deviations from
a quadrature relationship between the two signals.
25. The system of claim 22 wherein the calibration signal is
phase-synchronous with a local oscillator signal employed for
producing a plurality of frequency-translated signals responsive to
the calibration signal.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of U.S. application Ser.
No. 09/730,681, filed on Dec. 6, 2000, which claims benefit of U.S.
Provisional Application No. 60/190,226, filed Mar. 15, 2000. Both
of those applications are incorporated herein by reference, and all
U.S. patents or patent applications, published or appended
articles, and any other written materials incorporated by reference
therein are also specifically incorporated herein by reference.
BACKGROUND OF THE INVENTION
[0002] Communication systems frequently separate signals by using a
plurality of signal paths that have a predetermined vector
relationship. By suitably combining the signal paths, such systems
can cancel out undesired signals by mathematically exploiting
predetermined phase and amplitude relationships between respective
signal vectors of each signal path.
[0003] Quadrature image rejection receivers employ signal paths
having a quadrature relationship to discriminate between signals
having positive frequency (above DC) and negative frequency (below
DC). Quadrature direct conversion receivers separate points in a
two-dimensional signal space using the orthogonality of quadrature
signals to define axes of the signal space. Array processors couple
signal processing circuitry to array elements (e.g., antennas,
ultrasonic transducer elements, etc.) via signal paths having
particular phase and amplitude relationships to define a desired
beam pattern. For example, an array beamformer may provide signal
paths to antenna elements of an array with equal phase and a
windowed (i.e., tapered) distribution of amplitudes to define a
broadside beam having superior sidelobe rejection. The beamformer
may vary the gain and/or phase between elements to steer the beam
to a particular deviation from broadside.
[0004] Many communication systems require precise vector matching
between signal paths to achieve a high degree of separation between
desired and undesired signals. To obtain 50 dB of quadrature image
rejection, for example, an in-phase and quadrature signal are
required to have no more than about 0.6% amplitude mismatch and
about .+-.0.4 degrees of phase mismatch from quadrature. Comparable
levels of vector matching are required between elements of an array
having 50 dB of sidelobe rejection.
[0005] Conventional communication systems employ digital signal
processing to determine vector mismatch between signal paths and
correct the mismatch. The precision to which such systems can
correct mismatch is limited, however, because the mismatch often
varies with frequency and is difficult to determine with enough
precision to achieve high separation between desired and undesired
signals. Consequently, the need remains for determination of vector
mismatch across a range of frequencies and with greater
accuracy.
SUMMARY OF THE INVENTION
[0006] According to various aspects and methods of the present
invention, a signal processing system determines vector mismatch
between a plurality of signal paths. Advantageously, such a system
can determine mismatch across a range of frequencies. A signal
generator can provide a periodic calibration signal having a
plurality of frequency components. The system frequency translates
the calibration signal to provide a first set of observed samples.
The first sample set is compared to a second set of samples, which
are modeled by a function of parameters including an estimated
vector mismatch and a plurality of basis functions. A value of
vector mismatch is determined (at least to an estimate) that
minimizes the difference between the first sample set and the
second sample set.
[0007] According to one advantageous aspect of the invention, the
calibration signal comprises multiple tones having predetermined
gain, phase and frequency relationships to each other. By providing
a periodic calibration signal with a plurality of tones, the signal
processing system is able to concurrently determine vector mismatch
at the frequency of each tone. Consequently, the system can
determine mismatch across a range of frequencies simply and
efficiently.
[0008] By minimizing the difference between a set of observed
samples and a set of samples modeled by basis functions, the system
can determine vector mismatch using linear techniques. According to
various advantageous aspects of the invention, deterministic least
squares can be employed. Straightforward and efficient recursive
techniques such as least mean squares (LMS) and recursive (i.e.,
adaptive) least squares (RLS) can also be employed.
[0009] By continuously or periodically updating its determination
of vector mismatch, a system according to a further aspect of the
invention can accommodate nonstationary (i.e., time-varying)
errors.
[0010] A system according to another advantageous aspect of the
present invention provides a phase-synchronous calibration signal.
After frequency translation, components of a phase-synchronous
calibration signal are matched in frequency with components of
modeled signals, which are mathematically modeled by one or more
basis functions. In one such system, a baseband calibration signal
that is phase-synchronous with the basis functions is frequency
translated to RF with a first mixer and frequency translated again
to baseband or a low-IF frequency range with a second mixer or pair
of mixers. Advantageously, the first mixer and second mixer (or
mixer pair) can be fed by signals from the same local oscillator
output. Thus, the frequency-translated calibration signal remains
phase-synchronous with the basis functions even when the local
oscillator output is subject to phase variations.
[0011] A system according to still another advantageous aspect of
the present invention provides a plurality of first sample sets.
The system determines, at least to an estimate, a plurality of
vector mismatch values by comparing each respective first sample
set to a respective second sample set modeled by basis functions
and minimizing the difference between the compared sample sets. By
statistically combining the values of vector mismatch determined
for each one of the plurality of first sample sets, such a system
can improve accuracy of the mismatch determination while keeping
the interval of each sample set relatively short. Sample sets
having shorter intervals are less prone to problems caused by
local-oscillator induced phase variation between the
frequency-translated calibration signal and the basis
functions.
[0012] Quadrature receiver and array processor systems operating in
accordance with further aspects of the invention determine and
correct vector mismatch across a range of frequencies, thus
providing improved performance. Vector mismatch between in-phase
and quadrature signal paths can be more accurately and efficiently
determined and corrected across a range of frequencies to improve
demodulator performance or image rejection. Similarly, vector
mismatch between array elements can be better determined and
corrected to improve array efficiency and sidelobe rejection.
BRIEF DESCRIPTION OF THE DRAWING
[0013] Various embodiments of the present invention are described
below with reference to the drawing, wherein like designations
denote like elements.
[0014] FIG. 1 is a schematic block diagram of a radio receiver
implementing functions of a vector calibration system according to
various aspects of the present invention.
[0015] FIG. 2 is a schematic block diagram of a digital signal
processor of the receiver of FIG. 1.
[0016] FIG. 3 is a schematic block diagram of a baseband
calibration signal generator of the receiver of FIG. 1.
[0017] FIG. 4 is a functional block diagram illustrating functions
performed according to various aspects of the present invention by
the digital signal processor of FIG. 2.
[0018] FIG. 5 is a flow diagram of a method of the invention for
vector mismatch determination using deterministic least-squares
processing.
[0019] FIG. 6 is a flow diagram of a method of the invention for
vector mismatch determination using Least Mean Square (LMS)
processing.
[0020] FIG. 7 is a flow diagram of a method of the invention for
vector mismatch determination using Recursive Least Square (RLS)
processing with an exponential forgetting window.
[0021] FIGS. 8-10 are simulated time-domain plots illustrating
frequency-translated quadrature calibration signals suitable for
use in the receiver of FIG. 1, wherein the signals are mismatched
in phase from a quadrature relationship.
[0022] FIGS. 11-13 are simulated time-domain plots illustrating
frequency-translated quadrature calibration signals suitable for
use in the receiver of FIG. 1, wherein the signals are mismatched
in amplitude from a quadrature relationship.
[0023] FIGS. 14-16 are simulated time-domain plots illustrating
frequency-translated quadrature calibration signals suitable for
use in the receiver of FIG. 1, wherein the signals are mismatched
in both phase and amplitude from a quadrature relationship.
[0024] FIGS. 17 and 18 are simulated plots of a residual signal
envelope and smoothed envelope, respectively, illustrating
reduction of the difference between an observed calibration signal
and a modeled calibration signal during simulated operation of
vector mismatch calibration according to various aspects of the
present invention.
[0025] FIGS. 19-21 are simulated plots of relative amplitude (in
dB) of an undesired image signal, illustrating improvement in image
rejection during simulated operation of vector mismatch calibration
according to various aspects of the present invention.
[0026] FIG. 22 is a simulated frequency-domain plot illustrating
frequency response of an exemplary noise reduction filter that may
be used during vector mismatch calibration according to various
aspects of the present invention.
[0027] FIG. 23 is a simulated frequency-domain plot illustrating
frequency response of the filter of FIG. 22 when implemented at a
360 kHz sample rate.
[0028] FIG. 24 is a simulated frequency domain plot illustrating
frequency response of an exemplary anti-aliasing filter of the
receiver of FIG. 1 and the filter of FIG. 22 when implemented at a
360 kHz sample rate.
[0029] FIG. 25 is a simulated frequency-domain plot illustrating a
cascaded frequency response of the filters of FIG. 15.
[0030] FIG. 26 is a schematic block diagram of an array processor
implementing functions of a vector calibration system according to
various aspects of the present invention.
DESCRIPTION OF PREFERRED EXEMPLARY EMBODIMENTS
[0031] A vector calibration system according to various aspects of
the present invention provides numerous benefits, including
concurrently determining vector mismatch between a plurality of
signal paths across a range of frequencies. Such a system can be
advantageously implemented in any communication system that
separates signals using a plurality of signal paths having a
predetermined vector relationship. As may be better understood with
reference to FIG. 1, for example, a low-IF receiver 100 employs
quadrature signal paths to separate desired signals from image
signals having opposite frequencies. Conventional low-IF (low
intermediate frequency) receivers reduce the complexity of IF
processing by performing the processing at frequencies that are
much closer to the baseband frequency range of a signal of interest
than the RF frequency of the signal. In a receiver variation having
circuitry similar to that of receiver 100, quadrature signal paths
are employed to separate frequency components of a signal that is
directly converted to baseband frequencies. In accordance with the
invention, receiver 100 includes hardware and software for
correcting mismatch from a quadrature relationship across its
low-IF frequency range.
[0032] As discussed in detail below, receiver 100 includes, inter
alia, a calibration signal subsystem 150 for implementing an
exemplary vector calibration system. Receiver 100 also includes
circuitry that conventionally converts a selected radio frequency
(RF) signal to baseband information. This circuitry includes an RF
input port 102 (e.g., a suitable type of coaxial connector), a
front-end stage 104, a frequency translation subsystem 110, a
digital subsystem 130, a control subsystem 140, and a clock
generator 145.
[0033] Front-end stage 104 receives RF signals from input port 102
and amplifies the signals using a conventional low-noise amplifier.
Preferably, front-end stage 104 selectively amplifies signals from
a frequency band of interest (e.g., one of the frequency bands for
cellular telephone downlink signals) while at least partially
rejecting signals outside the band of interest. Front-end stage 104
couples the amplified signals to frequency translation subsystem
110 through a switching device 106, the purpose of which is
discussed below. Frequency translation subsystem 110 conveys the
selected RF signal to digital subsystem 130 in a frequency
translated, filtered form. Digital subsystem 130 samples and
digitizes the selected frequency-translated signal and subjects the
signal to further signal processing in the digital domain. Clock
generator 145 provides synchronized clock signals to various
portions of receiver 100, preferably by dividing down the high
frequency output of a high-stability master oscillator (e.g., a
temperature-compensated crystal oscillator) by various divide
ratios. (Even-numbered divide ratios are preferred, with powers of
two being particularly efficient to implement.)
[0034] Frequency translation subsystem 110 includes a pair of
mixers 112 and 114, a local oscillator 116, and bandpass filters
118 and 119. Local oscillator 116 provides in-phase and quadrature
outputs to mixers 112 and 114, respectively. Responsive to the RF
input from front-end stage 104 and respective inputs from local
oscillator 116, mixers 112 and 114 translate RF signals of interest
into in-phase and quadrature signals, respectively, within a low-IF
frequency range. The in-phase and quadrature signals are filtered
by respective bandpass filters 118 and 119 to perform an initial
selection of a relatively narrow frequency range of interest (e.g.,
one signal channel) within the low-IF frequency range.
[0035] Digital subsystem 130 includes A/D converters 120 and 122
and a digital signal processor (DSP) 132. A/D converters 120 and
122 sample the in-phase and quadrature signals, respectively, from
frequency translation subsystem 110 and convert the signals into
digital data. Bandpass filters 118 and 119 of frequency translation
subsystem 110 are preferably configured to substantially reject
signals at frequencies above the low-IF frequency range that would
alias into the frequency range after sampling. (As set forth in
Appendix D, lowpass filters can also be employed.) A/D converters
120 and 122 convey the digital data to DSP 132 in any suitable
format, serial or parallel. DSP 132 performs digital signal
processing. Preferably, this processing includes (1) selecting a
signal of interest from within the low-IF frequency range of the
signals represented by the digital data, (2) rejecting signals
within an undesired image frequency range opposite the frequency of
interest, and (3) translating the signal of interest into a
baseband output signal. The baseband output signal can be a
spectral copy of the signal of interest that has been frequency
translated to baseband frequencies. Alternatively, the baseband
output signal can be a representation of baseband information
demodulated from the signal of interest.
[0036] Functions of frequency translation subsystem 110 and digital
subsystem 130 can be implemented by any suitable hardware and/or
software. For example, U.S. Pat. No. 5,937,341 issued Aug. 10, 1999
to Suominen discloses suitable hardware and software that provides
particular advantages including simplified tuning of local
oscillator 116 and reduced computational burden in DSP 132. This
aforementioned patent is referred to herein as the '341 patent. The
detailed description portion of the '341 patent (and referenced
drawing figures) is incorporated herein by reference. The detailed
description portions of any patents or patent applications
referenced in the '341 patent are also specifically incorporated
herein by reference.
[0037] As discussed above, receiver 100 employs in-phase and
quadrature signal paths to separate signals of interest from image
signals having frequencies of equal magnitude but opposite sign
(i.e., inverse or mirror frequencies). Circuitry in the in-phase
signal path includes mixer 112, bandpass filter 118, and A/D
converter 120. Circuitry in the quadrature signal path includes
mixer 114, bandpass filter 119, and A/D converter 122. The
separation between signals of interest and image signals in
receiver 100 is degraded by vector mismatch between the in-phase
and quadrature signal paths. (In a variation, a single A/D
converter samples both the in-phase and quadrature signals.)
[0038] Vector mismatch between the in-phase and quadrature signal
paths can arise from a number of sources including deviations from
a quadrature relationship between 0 degree and 90 degree output
signals of local oscillator 116, variations in mixers 112 and 114,
variations in the transfer functions of filters 118 and 119,
varying sensitivity of A/D converters 120 and 122, and variations
in propagation delay between these components. Frequently, the
vector mismatch caused by these sources various as a function of
frequency. For example, varying transfer functions of bandpass
filters 118 and 119 can cause frequency-dependent vector mismatch
across the low-IF frequency range of receiver 100.
[0039] Receiver 100 implements functions of a vector calibration
system to correct vector mismatch and thus improves separation
between signals of interest and image signals. A vector calibration
system according to various aspects of the present invention can be
implemented by any suitable combination of analog circuitry,
digital circuitry, and/or software that controls execution of
software-based digital circuitry to perform computations and
digital signal processing functions. For example, circuitry of
receiver 100 includes circuitry that is configured for implementing
an exemplary vector calibration system, including clock generator
145, a calibration signal subsystem 150, switching device 106, and
digital subsystem 130. Calibration signal subsystem 150 generates
an RF calibration signal S2 having frequency components within the
frequency band of interest. Clock generator 145 provides a time
base for the calibration signal. Frequency translation subsystem
110 translates the RF calibration signal back down in frequency,
(to the low-IF range of frequencies employed by receiver 100) to
provide an in-phase calibration signal S3a and a quadrature
calibration signal S3b.
[0040] Digital subsystem 130 digitizes calibration signals S3a and
S3b to provide a set of observed samples and implements functions
of a vector calibration system that determines vector mismatch
based on those samples. The vector calibration system also performs
suitable digital signal processing to at least partially correct
the vector mismatch. An exemplary multi-frequency vector
calibration system 400 that can be implemented by hardware and/or
software of digital subsystem 130 may be better understood with
reference to the functional block diagram of FIG. 4. Digital
subsystem 130 also implements functions of a conventional baseband
translator 440, for example in accordance with the disclosure of
the '341 patent. In a variation employing direct-conversion (e.g.,
frequency translation directly from RF to baseband) baseband
translator 440 can be a conventional quadrature direct-conversion
tuner (implemented digitally).
[0041] Functional blocks of exemplary system 400 include a sample
modeling and mismatch determination subsystem 410, a correction
coefficient generator 420, and a digital filter 430. In receiver
100, system 400 receives calibration signals S3a and S3b from
frequency translation subsystem 110 via in-phase and quadrature
inputs, labeled in FIG. 4 as I and Q. Based on the calibration
signals S3a and S3b, sample modeling and mismatch determination
subsystem 410 determines a mismatch parameter vector .beta. that is
representative of vector mismatch between the in-phase and
quadrature signal paths. Correction coefficient generator 420
converts the mismatch parameter vector .beta. into correction
coefficients that digital filter 430 employs to correct the vector
mismatch.
[0042] Sample modeling and mismatch determination subsystem 410
compares the observed samples from digitized calibration signals
S3a and S3b to a set of modeled samples, which it generates either
as actual samples or conceptually. Subsystem 410 models the modeled
samples as a function of parameters including an estimated vector
mismatch and a plurality of basis functions. Subsystem 410
determines a value of vector mismatch that minimizes the difference
between the observed samples and the modeled samples.
[0043] The modeling function can include other parameters, for
examples indicia of environmental conditions. A communication
system implementing vector mismatch calibration according to the
invention can include one or more environmental sensors for
providing indicia of one or more environmental conditions. One
example of an environmental conditions that can influence vector
mismatch is temperature of circuitry in the communication system.
Another environmental condition that can be determined by circuitry
controlling the local oscillator of a communication system is the
frequency of local oscillator. The local oscillator may have
quadrature signals whose phase relationship varies somewhat over a
frequency range. Incorporating the local oscillator frequency to
the model may help improve its accuracy.
[0044] Vector .beta. can consist of the amplitudes of each basis
function used to model samples matching the observed samples of
signals S3a and S3b. This exemplary form of parameter vector .beta.
is discussed in detail below with reference to FIGS. 5-7 and
Appendices A,B, and C, which are integral to the specification of
this application and incorporated by reference as discussed
below.
[0045] Correction coefficient generator 420 and digital filter 430
can cooperate in any suitable manner to correct vector mismatch
based on a mismatch parameter vector .beta.. When vector .beta.
represents amplitudes of modeling basis functions, for example,
correction coefficient generator 420 can compute amplitude and
phase mismatch between signal paths based on the basis function
amplitudes. Appendix A describes an example of such a computation,
particularly with reference to equations labeled (11) and (12).
[0046] Advantageously, calibration signals S3a and S3b have
multiple tones in exemplary receiver 100 and system 400. (Appendix
B discloses a two-tone calibration signal.) Using the values of
amplitude and phase mismatch that it computes at each tone of
calibration signals S3a and S3b, generator 420 can form complex
exponentials corresponding to frequency-dependent vector mismatch.
Generator 420 can then derive coefficients of an impulse response
that is inversely representative of the vector mismatch based on
the complex exponentials. Generator 420 can derive these
coefficients by applying the complex exponentials to appropriate
frequency bands of an inverse fast Fourier transform (IFFT).
Digital filter 430 realizes this impulse response, preferably as an
finite-impulse-response (FIR) filter.
[0047] In a variation of subsystem 400, a conventional adaptive FIR
is employed to correct vector mismatch without the need for the
vector mismatch to be determined. Since the desired relationship of
calibration signals S3a and S3b to baseband calibration signal S1
is known (or easily determined), an error signal (i.e., the
difference between observed and modeled samples) can be generated
that reflects the deviation(s) of S3a and S3b from the ideal. This
error signal can then be incorporated into a conventional LMS
algorithm for determining the adaptive FIR filter coefficients. In
this advantageous variation, the estimated parameter vector
directly contains the FIR filter coefficients. In this variation,
the difference between the first sample set (observed samples) and
the second sample set (actual or conceptual modeled samples) is
minimized not to determine a value of vector mismatch, but to
correct the mismatch without needing to know what it is.
[0048] Operation of exemplary receiver 100 and vector calibration
system 400 may be better understood with reference to simulation
plots of FIGS. 8-15. In the simulation, receiver 100 is a low-IF
receiver configured to select one of three frequency-translated
channels from a low-IF frequency range between 60 kHz and 120 kHz.
The three channels have 20 kHz bandwidth and are adjacent. If
desired, receiver 100 can be configured in accordance with the
disclosure of the '341 patent to obtain improved digital signal
processing efficiency and doubled local oscillator step size (e.g.,
120 kHz instead of 60 kHz). Calibration signal subsystem 150
provides RF calibration signal S2 with components at three offset
frequencies above and below the output frequency of local
oscillator 116. These offset frequencies are .+-.70 kHz, .+-.90
kHz, and .+-.110 kHz. Frequency translation subsystem 110 converts
signal S2 into in-phase and quadrature signals S3a and S3b using
the same output frequency of local oscillator 116. Thus, signals
S3a and S3b each contain three tones (at 70, 90, and 110 kHz),
which are matched to the offset frequencies of signal S2. (The
simulation assumes that frequency translation of signals S1, S2,
and S3a, S3b causes no gain or phase distortion of the calibration
signals.)
[0049] Vector mismatch between signal paths of frequency
translation subsystem 110 cause calibration signal S3a and S3b to
differ. FIGS. 8, 11, and 14 are time-domain plots illustrating
calibration signals S3a and S3b on the same axes with differences
caused by phase-only, amplitude-only, and phase/amplitude types of
vector mismatch. FIGS. 8-10 illustrate differences caused by phase
mismatch between signal paths, FIGS. 11-13 illustrate differences
caused by amplitude mismatch, and FIGS. 14-16 illustrate
differences caused by vector mismatch comprising both phase and
amplitude mismatch. In FIGS. 8-10, the 70, 90, and 110 kHz tones of
signals S3a and S3b have relative amplitudes (i.e., amplitude-type
vector mismatch) of -1, 0, and +1 dB, respectively. In FIGS. 11-13,
these tones have relative phases (i.e., phase-type vector mismatch)
of +1, 0, -2 degrees, respectively. In FIGS. 14-16, these tones
have the combined vector mismatches illustrated in FIGS. 8-10 and
FIGS. 11-13 (phase/amplitude-type vector mismatch).
[0050] Each plot of FIGS. 8-10 includes a respective dashed box
910, 1110, and 1410 highlighting a sub-interval within the interval
of the plots. In this time interval, differences between signals
S3a and S3b are particularly apparent. FIGS. 9, 12, and 15 are
time-domain plots illustrating calibration signals S3a and S3b
within the sub-interval of dashed boxes 910, 1110, and 1410. FIGS.
10, 13, and 16 are time-domain plots illustrating signals of the
difference between the calibration signals S3a and S3b (i.e., a
residual signal) illustrated in FIGS. 8, 11, and 14,
respectively.
[0051] A vector mismatch calibration system according to various
aspects of the present invention determines (at least to an
estimate) a value of vector mismatch that minimizes (at least down
to an acceptable local minimum or the system noise level) the
difference between samples of an observed calibration signal and
samples of a modeled calibration signal. The system compares the
observed samples are compared to the modeled samples without the
modeled samples necessarily needing to be stored in any separate
form. In other words, the modeled samples may exist only
mathematically in the equations used during comparison. The system
generates the modeled (again, not necessarily as actual data
values) by a mathematical function of parameters including (1) an
estimated vector mismatch (e.g., estimated phase and/or amplitude)
and (2) a plurality of basis functions. This modeling is discussed
in further detail below with reference to FIGS. 4-7. The parameters
can also include indicia of environmental conditions such as
temperature or local oscillator frequency.
[0052] An actual vector calibration system of the invention using
discrete-time processing compares samples of observed and modeled
signals rather than actual continuous-time signals. However, the
comparison process may better understood (with reference to the
plots of FIGS. 8-10) by viewing signal S3b as the observed signal
and signal S3a as the modeled calibration signal. The more the
system can minimize the difference between signals S3a and S3b, the
smaller the residual signal of FIGS. 10, 13, and 16 will become. To
minimize this difference and thus model the observed calibration
signal, the system seeks to minimize the amplitude of the residual
signal, either iteratively or deterministically.
[0053] Initially, the residual signal can be expected to have a
relatively high amplitude because the absolute phase of the
observed calibration signal is not known. In receiver 100, the
observed calibration signals S3a and S3b are filtered component
signals of a frequency-translated calibration signal S3, which is
derived from RF calibration signal S2, which is a
frequency-translated copy of baseband calibration signal S1. In
other words, the signal flow is as follows: S1 (baseband) to S2
(RF) to S3 (frequency-translated) to S3a and S3b (filtered,
quadrature split). Even though the modeled calibration signal can
be matched relatively closely in phase to the originating baseband
calibration signal S3, the intervening signal processing that
converts signal S3 to observed calibration signal S3a or S3b causes
unpredictable phase offsets. Fortunately, the absolute phase is
unimportant. The inventive vector mismatch calibration system only
needs to determine the relative phases between two or more signal
paths, not their absolute phase delay.
[0054] FIGS. 17 and 18 are simulated plots of a residual signal
envelope and smoothed envelope, respectively, illustrating
reduction of the residual signal during operation of the vector
calibration system. As the residual signal amplitude diminishes,
the modeled calibration signal more closely approximates the
observed calibration signal and the vector calibration system
converges to a more accurate determination of vector mismatch.
[0055] FIGS. 19-21 are simulated plots of the relative amplitude of
an undesired image signal (in dB), illustrating increasing image
rejection during operation of the vector calibration system. FIG.
19 illustrate undesired image signal amplitude at the center of the
70 kHz channel of exemplary receiver 100, while FIGS. 20 and 21
illustrate undesired image signal amplitude for the 90 and 110 kHz
channels, respectively. As the system converges to a more accurate
determination of vector mismatch, the mismatch can be corrected
more accurately. Image rejection improves as a result.
[0056] FIGS. 22-25 are simulated frequency-domain plots
illustrating frequency response of analog and digital filters of
exemplary receiver 100. Receiver 100 implements analog (i.e.,
continuous-time) filtering in bandpass filters 118 and 119, and
implements digital (i.e., discrete-time) filtering as part of
sample modeling and mismatch determination subsystem 410. Subsystem
410 performs digital filtering of the in-phase and quadrature
signals entering digital subsystem 130 before it performs sample
modeling and mismatch determination. Because exemplary calibration
signals S3a and S3b of receiver 100 contain tones only at desired
frequencies, filtering can be omitted for simplicity but at the
expense of increased overall noise levels. In variations where the
calibration signal(s) contain undesired tones, filtering is more
important to ensure convergence of sample modeling.
[0057] FIG. 22 illustrates the baseband frequency response of an
exemplary digital filter implemented in subsystem 410, across a
frequency range twice the Nyquist limit of the filter. FIG. 23
illustrates frequency response of the filter of FIG. 22 when
digital subsystem 130 processes signals entering the digital filter
at a 360 kHz sample rate. This frequency response has deep but
narrow spectral nulls, which provide particular advantages for
certain types of calibration signals, as discussed in further
detail below.
[0058] FIG. 24 is a simulated frequency domain plot illustrating an
exemplary frequency response of bandpass filters 118 and 119 in
dashed lines and the digital filter of subsystem 410 (when
implemented at a 360 kHz sample rate) in solid lines. The frequency
response of bandpass filters 118 and 119 reaches a significant
level of stop band attenuation by the time the frequency of
response of the digital filter reaches its first alias, at about
240 kHz.
[0059] FIG. 25 is a simulated frequency-domain plot illustrating a
cascaded frequency response of bandpass filters 118 and 119 and
digital filter of subsystem 410. The respective filters add several
dB of ripple to the passband of receiver 100.
[0060] A multi-tone calibration signal according to various aspects
of the present invention can be employed to correct passband ripple
without the need for adaptive equalization of a received signal.
The inventive calibration signal can be applied even in
communication systems where the benefits of vector mismatch
calibration are not required. For example, a conventional
superheterodyne receiver can benefit from ripple correction using a
phase-coherent calibration signal even though such a receiver may
not have multiple signal paths that could benefit from vector
mismatch calibration. A calibration signal subsystem according to
various aspects of the present invention (e.g., subsystem 150) can
be advantageously employed in such a receiver to quickly and
efficiently correct ripple across a range of frequencies. A sample
modeling and mismatch determination subsystem according to various
aspects of the invention can be suitably adapted for calibrating
mismatch between a known baseband calibration signal (e.g., S1 of
receiver 100) and an observed calibration signal (e.g., S3a, S3b).
Such calibration can also be performed in conjunction with vector
mismatch calibration. Passband ripple can also be conventionally
equalized.
[0061] A calibration signal subsystem according to various aspects
of the invention includes any suitable hardware and/or software for
generating an RF calibration signal having a frequency component at
the frequency of a potential RF signal of interest. Such hardware
and/or software can be integrated into the circuitry and/or
software of a vector calibration system according to the invention,
or into a device incorporating such circuitry. Alternatively,
separate hardware and/or software can implement functions of a
calibration signal subsystem during a one-time calibration process.
For example, manufacturing or maintenance test equipment can
implement a calibration signal subsystem to perform a one-time
calibration of a communication receiver that contains circuitry and
software of the inventive vector calibration system. Such a
receiver can include a nonvolatile memory device (e.g., flash
memory) to retain data resulting from the calibration.
[0062] According to a particularly advantageous aspect of the
invention, the calibration signal can include multiple RF frequency
components (i.e., tones) that the receiver can frequency translate
to a single IF frequency range. When the calibration signal
comprises multiple tones having predetermined phase and frequency
relationships to each other, a vector calibration system of the
invention can determine vector mismatch at the frequency of each
tone concurrently. As a result, the system can determine mismatch
across a range of frequencies simply and efficiently.
[0063] As may be better understood with reference to FIGS. 1-3,
exemplary calibration signal subsystem 150 includes a calibration
signal generator 152, a mixer 154, and a local oscillator phase
adjustor 156. Controlled by clock generator 145, calibration signal
generator 150 provides a baseband calibration signal S1 having
multiple tones, as is preferred, within the low-IF frequency range
of receiver 100. Mixer 154 translates calibration signal S1 to an
RF calibration signal S2 in the RF frequency range of several
potential signals of interest, e.g., adjacent channels of a
channelized frequency spectrum. Mixer 154 uses the same output
signal of local oscillator 116 that mixer 112 would use when
frequency translating one of the potential signals of interest.
[0064] According to a particularly advantageous aspect of the
present invention, a single local oscillator can provide a shared
phase-coherent signal for both translation of the calibration
signal from baseband to RF (S1 to S2) and translation of the RF
calibration signal back to baseband (S2 to S3a, S3b). For example,
the in-phase (0-degree) output of local oscillator 116 feeds both
mixer 154 and mixer 112. Phase-synchronous local oscillator signals
perform frequency translation of (1) the baseband components from
calibration signal generator 152 to RF and (2) the RF-translated
calibration signal to its original baseband frequency, within its
low-IF frequency range. When it reaches digital subsystem 130,
quadrature calibration signals S3a and S3b are phase-synchronous
(i.e., having matched frequencies) with basis functions that vector
calibration subsystem 400 (FIG. 4) models against the calibration
signal to determine vector mismatch. The frequency-translated
calibration signals remain phase-synchronous with the basis
functions even when the local oscillator output is subject to phase
variations.
[0065] A calibration signal generator of a calibration signal
subsystem (e.g., subsystem 150) can provide a baseband calibration
signal by any suitable technique, using analog and/or digital
signal processing. As may be better understood with reference to
FIG. 3, for example, calibration signal generator 152 generates a
three-tone calibration signal S1 primarily using digital signal
processing. (The tones of this exemplary signal are not necessarily
phase-optimized for minimum peak amplitude, but lack of such
optimization is not important for a signal having only three
tones.) Generator 152 includes a state machine 310 for generating
digital output values and a D/A converter 320. State machine 310
changes states at a 180 kHz rate, as controlled by a clock signal
(e.g., 360 kHz) from clock generator 145. Each time state machine
310 changes states, it provides a new digital output that D/A
converter 320 converts into an analog sample of the baseband
calibration signal S1. Lowpass filtering can follow D/A converter
320 to limit the bandwidth of the RF calibration signal provided by
mixer 154.
[0066] TABLE I below illustrates exemplary output values of signal
generator 152 for a baseband calibration signal having three
primary tones. When provided periodically at a sample rate of 180
kHz, these 18 output values form a periodic calibration signal with
tones at 70 kHz, 90 kHz, and 110 kHz. The 110 kHz frequency
component is the first alias of the 70 kHz component. State machine
310 can generate these values using five preset multipliers labeled
A,B,C,D, and zero with varying sign. Thus, state machine 310 needs
only to store four separate digital values. State machine 310 can
provide any desired one of the 18 repeated output values of TABLE I
by selecting the desired digital value and multiplying it by the
desired .+-.sign.
[0067] In a variation of baseband calibration signal generator 152,
the preset multipliers are integrated into D/ A converter 320. In
such a variation, D/A converter 320 is only capable of providing
nine distinct output values. (These are the four preset multipliers
with both possible signs plus zero.) Such a variation is
particularly inexpensive to implement on an integrated circuit that
already includes precision analog circuitry, for example circuitry
implementing functions of frequency translation subsystem 110.
TABLE-US-00001 TABLE I Sample Output Preset Multiplier 0
0.16666666666667 +A 1 -0.14067160479100 -B 2 0.07484979751855 +C 3
0.00000000000000 Zero 4 -0.04885473564288 -D 5 0.04885473564288 +D
6 0.00000000000000 Zero 7 -0.07484979751855 -C 8 0.14067160479100
+B 9 -0.16666666666667 -A 10 0.14067160479100 +B 11
-0.07484979751855 -C 12 0.00000000000000 Zero 13 0.04885473564288
+D 14 -0.04885473564288 -D 15 0.00000000000000 Zero 16
0.07484979751855 +C 17 -0.14067160479100 -B
[0068] In an advantageous variation of calibration signal subsystem
150, baseband calibration signal generator 152 generates a harmonic
rich baseband calibration signal S1 (e.g., a square wave) at a
desired fundamental frequency (e.g., 10 kHz). The fundamental
frequency is selected to produce harmonics at desired calibration
tone frequencies. For example, a 10 kHz fundamental square wave
modulating mixer 154 will produce harmonics at the offset
frequencies of .+-.70 kHz, .+-.90 kHz, and .+-.110 kHz that are
desired in receiver 100. The undesired harmonics (e.g., 30, 50, 130
kHz) can be filtered out in digital filtering of sample modeling
and mismatch determination subsystem 410. Such filtering may be
better understood with reference to exemplary frequency response
plots of FIGS. 22-25. This frequency response has deep but narrow
spectral nulls at the frequency of the undesired harmonics.
[0069] Calibration signal subsystem 150 includes a local oscillator
phase adjustor 156, which adjusts the phase of the signal from
local oscillator 116 by an amount controlled by control subsystem
140. (Control subsystem 140 can be implemented by software of DSP
132 or in a separate microcontroller IC, clocked by clock generator
145 as illustrated in FIG. 1.) A local oscillator phase adjustor
according to various aspects of the present invention can include
any structure for varying the propagation delay or phase of a local
oscillator signal. An example of a suitable phase adjustor is an
electronically variable capacitance device (i.e., a varactor)
controlled by an analog voltage from control subsystem 140. The
higher the capacitance of such a device, the more it delays local
oscillator phase.
[0070] Phase adjustor 156 can be controlled to maximize the
accuracy of vector mismatch calibration according to any suitable
technique. Accuracy can be expected to be optimal when the phase of
the local oscillator signal at the input of mixer 154 is midway the
phase of that signal at the input of mixers 112 and 114. In other
words, the local oscillator signal at the input of mixer 154 is
preferably (1) offset +45 from the local oscillator signal at the
input of mixer 112 and (2) offset -45 degrees from the local
oscillator signal at the input of mixer 114.
[0071] When local oscillator phase adjustor 156 has a known control
vs. phase shift transfer function (preferably linear over the range
of interest), an optimal phase offset can be determined by setting
the phase offset to a point midway between two phase offsets that
null out calibration signals S3a and S3b, respectively. An
exemplary technique for controlling phase adjustor 156 includes
steps of (1) adjusting phase adjustor 156 to a first phase setting
to minimize amplitude of calibration signal S3a, (2) adjusting
phase adjustor 156 to a second phase setting to minimize amplitude
of calibration signal S3b, (3) and setting phase adjustor 156 to a
third phase setting that is midway between the first phase setting
and the second phase setting. For example, if the first phase
setting is 10 degrees and the second phase setting is 100 degrees,
the third phase setting is determined as 55 degrees.
[0072] Appendix B provides disclosure of a method for dealing with
an undesired phase offset, which may be instructive in operation of
a local oscillator phase adjustor according to various aspects of
the present invention.
[0073] As may be better understood with reference to FIG. 2,
digital signal processor (DSP) 132 can include a high-rate
hardware-based DSP 210 and a lower-rate software-based DSP 220.
High-rate DSP 210 can be a suitable type of programmable logic
device or application-specific integrated circuit performing
high-rate digital signal processing for baseband translation of
receiver 100. For example, high-rate DSP 210 can implement signal
processing blocks 38, 40, 64, and 66 of receiver 10 of the '341
patent, as illustrated in FIG. 8 of that patent. Low-rate DSP 220
can be a suitable type of software-programmable DSP (e.g., of the
type available from Analog Devices, Texas Instruments, etc.) for
performing low-rate digital signal processing after decimation by
high-rate DSP 210. For example, low-rate DSP 220 can implement
signal processing blocks 70, 68, 72, 74, and 76 of receiver 10 of
the '341 patent.
[0074] During vector mismatch calibration according to various
aspects of the present invention, low-rate DSP 220 acquires
observed samples from the I and Q inputs of DSP 132. Although the
samples at these inputs are provided at a high sample rate (at the
non-decimated input of high-rate DSP 210), only a relatively
limited number of samples needs to be processed at a time during
vector mismatch calibration. Consequently, low-rate DSP 220 can
acquire a block of samples, perform vector mismatch calibration on
that block (e.g., using one of exemplary methods 500,600, and 700),
store the results of that particular calibration, and repeat the
process on another block of samples when available processing time
of DSP 220 permits. Repeated results of this block processing can
be statistically combined (e.g., averaged) to more accurately
determine and/or correct vector mismatch.
[0075] Baseband translation performed by DSP 220 can be interrupted
for vector mismatch calibration, or the two functions can be
performed concurrently. In receiver 100 of FIG. 1, for example,
translation of an RF signal of interest to baseband can be
interrupted (stopped momentarily), preferably for a short enough
time to be unobtrusive to a user or between packets of data
transmission. When receiver 100 is interrupted for vector mismatch
calibration, switch 106 can couple mixers 112 and 114 to
calibration signal subsystem 150 instead of front-end stage 104.
Switch 106 is conceptually a single pole-double, throw-switch,
preferably implemented as a solid-state alternating-conduction
device such as a suitable type of PIN diode. In a variation, a
weakly coupled link can be employed to couple calibration signal
subsystem 150 to mixers 112 and 114.
[0076] Three methods of sample modeling and mismatch determination
according to various aspects of the present invention to derive an
unknown parameter vector {circumflex over (.beta.)} may be better
understood with reference to flow diagrams of FIGS. 5-7 and
appendices A, B, and C of the '226 application. The various aspects
of the invention disclosed herein and set forth particularly by the
exemplary claims below are not limited in any way to the disclosure
set forth in the appendices. Further, some statements made in the
appendices only apply within a relatively narrow context of
communications systems toward which a particular appendix is
directed. Descriptions of the appendices are provided in TABLE II
below. TABLE-US-00002 TABLE II Appendix Description of Relevance to
the Application A From "An Optimized Multi-Tone Calibration Signal
for Quadrature Receiver Communication Systems," submitted by R. A.
Green for publication to the 10th IEEE Workshop on Statistical
Signal and Array Processing and now published as: IEEE Workshop on
Statistical Signal and Array Processing, Aug. 14-16, 2000, pp.
664-667. (Incorporated herein by reference.) This appendix
discloses a phase-optimized multi-tone calibration signal according
to various aspects of the present invention. A three-tone version
of this particularly advantageous type of calibration signal is
employed in the simulation of FIGS. 8-12. B From "A SDB-SC Signal
Model for Nonlinear Regression-Based Quadrature Receiver
Calibration," listing R. A. Green as author, Proceedings ICASSP
1999, Phoenix, AZ, Mar. 15, 1999, incorporated herein by reference.
This appendix presents a two-tone calibration signal consistent
with the nonlinear regression techniques presented in Appendix A.
This appendix illustrates some of the difficulties involved in
construction of alternate calibration signals such as multitone
calibration signals. In particular, the appendix details an
undesired phase parameter PSI that results from modulating a
baseband calibration signal with a carrier tone, and provides a
method to accommodate the undesired phase parameter. Phase adjuster
156 of receiver 100 addresses undesired phase offset introduced by
modulating a calibration signal with a carrier signal. C From
"Quadrature Receiver Mismatch Calibration," listing R. A. Green, R.
C. Anderson-Sprecher, and J. W. Pierre as coauthors, IEEE
Transactions on Signal Processing; Vol 47, No. 11, November 1999,
incorporated herein by reference. This appendix introduces
quadrature receiver calibration over multiple frequencies using
nonlinear regression techniques. In this reference, mismatch at
each frequency is estimated separately through repeated application
of a single-tone calibration signal. Some aspects of the present
invention are according to this disclosure, but other aspects offer
particular advantages including: simultaneous calibration over
multiple frequencies using multitone calibration signals; linear
regression models that admit closed-form, real time estimation; and
generalization to multiple signal path systems such as array
processors. D Matlab (RTM The Mathworks, Inc.) source code for the
simulations of FIGS. 8-25. This code provides a conceptual-level
context for the simulation plots. However, it does not carry out an
exhaustive simulation of an actual communications system during
operation of various aspects of the invention.
[0077] Subsystem 410 of exemplary vector calibration system 400
collects observation values and generates an estimate of the
unknown parameter vector, {circumflex over (.beta.)}. For
quadrature receiver 100 of FIG. 1, observations are taken from the
in-phase and quadrature branches, as sampled and digitized by A/D
converters 120 and 122. In variations such as multi-sensor array
processors, observations can be taken from other types of signal
paths. Typically data are collected simultaneously from each signal
path at a uniform sampling rate. However, a calibration system
according to various aspects of the present invention permits
non-uniform sampling as well as sampling of signal paths at
different times.
[0078] Subsystem 410 normally employs one of two general class of
algorithm. Recursive algorithms provide new parameter estimates
with each new observation set. Non-recursive algorithms provide
parameter estimates less frequently; typically estimates are
computed after a block of samples is collected. Deterministic least
squares, for example, is typically a non-recursive algorithm that
post-processes data. Adaptive techniques are often recursive and
permit real-time parameter estimation. Real-time operation is
important to accommodate systems that possess slow time variations
in the unknown parameters .beta..
[0079] Many methods exist to estimate the unknown parameters. When
observations are expressed as a linear combination of basis
functions and unknown parameters plus noise (Y=X.beta.+.epsilon.),
efficient parameter estimation is accomplished using techniques
such as deterministic least-squares or adaptive techniques such as
the Least Mean Square (LMS) algorithm and the Exponential
Forgetting Window Recursive Least Squares (EFW-RLS) algorithms.
Guidance as to implementation of such techniques may be found in
Simon Haykin, "Adaptive Filter Theory", 2nd edition, Prentice Hall
Inc., 1991, referred to herein as "Haykin" and incorporated herein
by reference. FIGS. 5, 6, and 7 illustrate methods 500, 600, and
700 of recursive parameter estimation (given a linear model) using
deterministic least-squares, LMS, and EFW-RLS, respectively.
Sometimes the calibration signal requires a nonlinear model. In
these cases, nonlinear regression techniques can be applied to
generate parameter estimates, as discussed in Appendix A.
[0080] Algorithm 500 illustrates a recursive implementation of
deterministic least squares. This approach is taken for consistency
with methods 600 and 700. However, the computational burden of this
implementation of deterministic least squares increases with the
amount of data collected, so it is not often used in practice.
Rather, deterministic least squares normally post-processes data to
estimate unknown parameters. In a variation of method 500 for
standard post-processing, step 540 is skipped until all data is
collected.
[0081] Method 500 begins at step 505. Step 510 is executed once to
initialize system parameters. Specifically, a sample index n is set
to zero, an observation vector Y.sub.n is cleared, and a basis
function matrix X.sub.n is also cleared. The types of elements of
X.sub.n depend on the particular calibration signal employed, as
well as the number of frequencies at which vector mismatch is to be
determined.
[0082] Step 515 begins the main loop of the algorithm by
incrementing the sample index n. Step 520 acquires and stores
samples of the observation y[n]. Method 500 can be applied to
signal paths separately or in combinations, e.g., with I and Q
samples interleaved. If method 500 is applied to each signal path
separately, y[n] is simply a sample of that signal path at time
index n. If method 500 is applied to the collection of signal
paths, samples from each signal path are typically stacked into
y[n]. Deterministic least squares requires all data points to be
saved, so the new sample is stored into a vector of observations
Y.sub.n that contains all samples from beginning step 515 to the
current time index n.
[0083] Step 525 computes the known basis functions X[n] for the
current index n. Computation can be avoided through the use of a
data look up table. The length of this row vector depends on the
number of signal paths being processed, the calibration signal, and
the number of frequency bins of interest. For example, calibration
of mismatch between quadrature signal paths using a calibration
signal with three tones requires that X[n] is a length-6 row
vector. In this example, X[n]=[cos({tilde over
(w)}.sub.1t+.theta..sub.1),sin({tilde over
(w)}.sub.1t+.theta..sub.1),cos({tilde over
(w)}.sub.2t+.theta..sub.2),sin({tilde over
(w)}.sub.2t+.theta..sub.2),cos({tilde over
(w)}.sub.3t+.theta..sub.3),sin({tilde over
(w)}.sub.3t+.theta..sub.3)] where {tilde over (w)} are the
calibration tone frequencies and .theta. are the optimized phases.
Simultaneous processing of both the I and Q branches using the same
calibration signal requires that X[n] is a length-12 vector. The
row vector X[n] is stored into the n.sup.th row of the matrix
X.sub.n.
[0084] Step 540 determines the parameter estimate using the
equation {circumflex over
(.beta.)}.sub.n=(X.sub.n.sup.HX.sub.n).sup.(-1)X.sub.n.sup.HY.sub.n.
Here, .sup.(-1) designates a matrix inverse operation and .sup.H
indicates the complex-conjugate transpose operation. As indicated
above, standard deterministic least-squares would skip step 540
until all data had been collected. By applying method 500 to
relatively short-length data sets, however, non-stationarities in
the parameters .beta. can be accommodated. The column vector .beta.
has the same length as X[n].
[0085] An exemplary implementation of vector calibration with the
LMS algorithm may be better understood with reference to FIG. 6.
The computational burden of the LMS algorithm remains constant with
the addition of data. The LMS algorithm is very simple to
implement, and thus it is relatively easy to achieve real-time
operation even with relatively modest DSP resources. LMS does not
converge as quickly as other adaptive algorithms, but the robust
nature of the algorithm has made it a popular choice in adaptive
signal processing applications.
[0086] A bounded version of the LMS algorithm has been shown to
have desirable convergence behavior. The bounded version simply
constrains the values attained by the algorithm to a pre-determined
bounded region. Further information instructive for implementing
the bounded version of the LMS algorithm is found in D. C. Farden,
"Tracking Properties of Adaptive Signal Processing Algorithms,"
IEEE Trans. Acoust., Speech, and Signal Processing, ASSP-29, June
1981, pp. 439-446, incorporated herein by reference. In a bounded
version of method 600, step 640 is suitably modified.
[0087] Method 600 of FIG. 6 begins at step 605. Step 610 is
executed once to initialize system parameters. Specifically, the
sample index n is set to zero, the initial parameter estimates
{circumflex over (.beta.)}.sub.0 are set to nominal values, and the
step-parameter .mu. is set according to particular conditions of
the communications system in which method 600 is implemented, e.g.,
receiver 100. The step parameter .mu. affects convergence rates as
well as the ability of the algorithm to track temporal variations
in the unknown parameters .beta.. Published references such as
Haykin provide basic rules for establishing .mu.. As a general
rule, .mu. is a small value. For systems with little or no
parameter variation, small .mu. can reduce estimate variance but
also slows convergence. Larger .mu. allows the algorithm to track
more rapid parameter variations but with less accuracy.
[0088] Step 615 begins the main loop of method 600 by incrementing
the sample index n. Step 620 acquires and stores the observation
y[n]. Method 600 can be applied to signal path separately or in
combination. If method 600 is applied to each signal path
separately, y[n] is simply a sample of that signal path at time
index n. If method 600 is applied to multiple signal paths, samples
from each signal path can be interleaved into y[n]. Only the
current set of observations needs to be stored in method 600.
[0089] Step 625 computes the known basis functions X[n] for the
current index n. Computation can be avoided through the use of a
data look-up table. The length of this column vector depends on the
number of signal paths being processed as well as the number of
frequency bins of interest. For example, quadrature mismatch
calibration of a quadrature receiver using a calibration signal
with three tones requires that X[n] is a length-6 column vector. In
this example, X .function. [ n ] = [ cos .function. ( .PI. 1
.times. t + .theta. 1 ) sin .function. ( .PI. 1 .times. t + .theta.
1 ) cos .function. ( .PI. 2 .times. t + .theta. 2 ) sin .function.
( .PI. 2 .times. t + .theta. 2 ) cos .function. ( .PI. 3 .times. t
+ .theta. 3 ) sin .function. ( .PI. 3 .times. t + .theta. 3 ) ]
##EQU1## where {tilde over (.OMEGA.)} are the calibration tone
frequencies and .theta. are optimized phases, selected to minimize
the peak amplitude of the signal. Simultaneous processing of two
signal paths (e.g., I and Q) using the same calibration signal
requires X[n] to be a length-12 vector. Only the basis functions
for the current index are required.
[0090] In a variation, basis functions can be complex exponentials
instead of sines and cosines. Conceptually, the two types of basis
functions are the same. However, with complex exponentials, a
single basis functions forms orthogonal basis for a single tone.
With sines and cosines, two basis functions for an orthogonal basis
for a single tone.
[0091] Step 630 computes a gain term k[n]=.mu.[n]. The gain term is
used to weight the error term e[n]=y[n]-.beta..sub.n-1.sup.HX[n]
computed in step 635. The unknown parameter vector is estimated in
step 630 according to {tilde over (.beta.)}.sub.n={tilde over
(.beta.)}.sub.n-1+k[n]e*[n]. Here, * represents complex
conjugation. The column vector .beta. has the same dimension as
X[n].
[0092] An exemplary implementation of vector calibration with an
"exponential forgetting window-recursive least squares" algorithm
according to various aspects of the present invention may be better
understood with reference to FIG. 7. The computational burden of
the LMS algorithm remains constant with the addition of data.
EFW-RLS converges more quickly than LMS, but performance is not as
robust to model deviations. The EFW-RLS algorithm is moderately
complex to implement, but real-time operation is still possible
using today's modern DSP technology.
[0093] Method 700 of FIG. 7 begins at step 705. Step 710 is
executed once to initialize system parameters. Specifically, a
sample index n is set to zero, an initial parameter estimates
{tilde over (.beta.)}.sub.0 are set to nominal values, and a
"forgetting factor" .lamda. is set according to particular
communication system conditions. The forgetting factor affects
convergence rates as well as the ability of the algorithm to track
temporal variations in the unknown parameters .beta.. Published
references such as Haykin provide basic rules for establishing
.lamda.. By setting the forgetting factor to one, there is no loss
and the results are similar to deterministic least squares. For
.lamda.<1, old data are given less weight. This approach allows
temporal variation of parameters, as is typical with component
drift in analog systems. A parameter P used in computations is
initialized to P[0]=.delta..sup.-1I. Here, .delta. is a small
positive constant (Haykin provides pertinent details) and I is an
identity matrix with dimension equal to the number of unknown
parameters. (The matrix "I" of this example is not to be confused
with the in-phase signal path labeled "I" in FIG. 4.)
[0094] Step 715 begins the main loop of method 700 by incrementing
the sample index n. Step 720 acquires and stores the observation
y[n]. Method 700 can be applied to signal path, separately or in
combination. If method 700 is applied to each signal path
separately, y[n] is simply a sample of that signal path at time
index n. If method 700 is applied to multiple signal paths, samples
from each signal path can be interleaved into y[n]. Only the
current set of observations needs to be stored in method 700.
[0095] Step 725 computes the known basis functions X[n] for the
current index n. Computation can be avoided through the use of a
data look up table. The length of this column vector depends on the
number of signal paths being processed as well as the number of
frequency bins of interest. For example, I-branch processing of a
quadrature receiver using a calibration signal with three tones
requires that X[n] is a length-6 column vector. In this example, X
.function. [ n ] = [ cos .function. ( .PI. 1 .times. t + .theta. 1
) sin .function. ( .PI. 1 .times. t + .theta. 1 ) cos .function. (
.PI. 2 .times. t + .theta. 2 ) sin .function. ( .PI. 2 .times. t +
.theta. 2 ) cos .function. ( .PI. 3 .times. t + .theta. 3 ) sin
.function. ( .PI. 3 .times. t + .theta. 3 ) ] ##EQU2## where {tilde
over (w)} are the calibration tone frequencies and .theta. are
optimized phases. Simultaneous processing of both the I and Q
branches using the same calibration signal requires that X[n] is a
length-12 vector. Only the basis functions for the current index
are required.
[0096] Step 730 computes a gain term
k[n]=.lamda..sup.-1P[n-1]X[n]/{1-.lamda..sup.-1X.sup.H[n]P[n-1]X[n]}.
In this expression, P is a variable defined simply for convenient
computation. The gain term is used to weight the error term
e[n]=y[n]-{tilde over (.beta.)}.sub.n-1.sup.HX[n] computed in step
635. The unknown parameter vector is estimated in step 730
according to {tilde over (.beta.)}.sub.n={tilde over
(.beta.)}.sub.n-1+k[n]e* [n]. Here, * represents complex
conjugation. Finally, step 745 computes the next value of P,
P[n]=.lamda..sup.-1P[n-1]-.lamda..sup.-1k[n]X.sup.H[n]P[n-1], which
is needed for the next recursion.
[0097] While the present invention has been described in terms of
preferred embodiments and generally associated methods, the
inventors contemplate that alterations and permutations of the
preferred embodiments and method will become apparent to those
skilled in the art upon a reading of the specification and a study
of the drawings. For example, vector mismatch between signal paths
of an array processor can be determined instead of mismatch between
quadrature signal paths of a quadrature receiver.
[0098] An exemplary array processor 2600 employing vector mismatch
calibration according to various aspects of the present invention
may be better understood with reference to FIG. 26. Array processor
2600 includes conventional circuitry for superheterodyne RF
frequency translation and digital array processor of translated
signals. The circuitry includes front-end stages 2622 and 2624
coupled to image-reject filters 2632 and 2634, which are in turn
coupled to mixers 2642 and 2644, which are coupled to IF stages
2652 and 2654. Digital subsystem 2660 digitizes signal that are
suitably selected and amplified by IF stages 2652 and 2654 and
performs array processing on the digitized signals. Mixers 2642 and
2644 are fed by local oscillator signals from local oscillator
2670.
[0099] Array processor 2600 further includes circuitry for
implementing vector mismatch calibration according various aspects
of the present invention. The circuitry includes calibration signal
subsystem 2680, amplifier 2685, RF transmission path 2687, another
amplifier 2610, an antenna 2612. Calibration signal subsystem 2680
generates a phase-coherent calibration signal (as is preferred) and
sends the signal to amplifier 2685, which amplifies the signal for
transmission through transmission path 2687. Amplifier 2610 further
amplifies the signal for transmission through antenna 2612. Antenna
2612 is suitably placed at a predetermined (or fixed) position with
respect to array elements coupled to amplifiers 2622 and 2624.
Because the position of 2612 with respect to the array elements is
fixed, desired or known calibration signals can be modeled against
signals received from IF stages 2652 and 2654. Thus, vector
mismatch can be determined and/or corrected between a signal path
for one array element (e.g., including front-end stage 2622,
image-reject filter 2632, mixer 2642, and IF stage 2652) and a
signal path for another array element (e.g., including front-end
stage 2624, image-image-reject filter 2634, mixer 2644, and IF
stage 2654).
[0100] Although a predetermined position for antenna 2612 is
preferred, antenna 2612 can be placed at an unknown but fixed
far-field location in an advantageous variation of array processor
2600. In such a variation, a predetermined phase relationship still
exists among the array elements coupled to amplifiers 2622 and
2624, but the relationship is dependent on an unknown angle of
arrival. Array processor 2600 can estimate this angle of arrival
using conventional techniques (e.g., beamforming, MVDR, MUSIC,
root-MUSIC, etc.) and then correct any mismatch. In a further
variation, array processor 2600 can update adaptive filtering
algorithms to correct mismatch without needing to provide an
estimate of the angle of arrival.
[0101] Accordingly, neither the above description of preferred
exemplary embodiments nor the abstract defines or constrains the
present invention. Rather, the issued claims variously define the
present invention. Each variation of the present invention is
limited only by the recited limitations of its respective claim,
and equivalents thereof, without limitation by other terms not
present in the claim. Further, aspects of the present invention are
particularly pointed out below using terminology that the inventors
regard as having its broadest reasonable interpretation; the more
specific interpretations of 35 U.S.C. .sctn.112(6) are only
intended in those instances where the term "means" is actually
recited.
[0102] In addition, the inventors contemplate that their inventions
include all methods that can be practiced from all suitable
combinations of the method claims filed with the application, as
well as all apparatus and systems that can be formed from all
suitable combinations of the apparatus and system claims filed with
the application.
* * * * *