U.S. patent number RE31,351 [Application Number 06/334,308] was granted by the patent office on 1983-08-16 for feedback nonlinear equalization of modulated data signals.
This patent grant is currently assigned to Bell Telephone Laboratories, Incorporated. Invention is credited to David D. Falconer.
United States Patent |
RE31,351 |
Falconer |
August 16, 1983 |
**Please see images for:
( Certificate of Correction ) ** |
Feedback nonlinear equalization of modulated data signals
Abstract
A receiver for a quadrature amplitude modulated data signal
impaired by linear and nonlinear distortion, phase jitter and
additive noise includes circuitry which compensates for these
impairments. In particular, the receiver includes a processor (FIG.
1 44; FIG. 2, 44') which subtracts a feedback nonlinear signal
(FIG. 1, D(n); FIG. 2, D'(n)) from each sample of the received
signal, either prior or subsequent to demodulation, providing
compensation for nonlinear intersymbol interference. The feedback
nonlinear signal subtracted from each sample is comprised of a
weighted sum of products of individual data decisions and/or the
complex conjugates of data decisions, each such product, in turn,
being multiplied by a predetermined harmonic of the carrier
frequency. In an illustrative embodiment, compensation for second-
and third-order intersymbol interference is provided by including
two- and three-multiplicand weighted products in the feedback
nonlinear signal. Weighting coefficients for each product are
adaptively updated in a decision-directed manner.
Inventors: |
Falconer; David D. (Nepean,
CA) |
Assignee: |
Bell Telephone Laboratories,
Incorporated (Murray Hill, NJ)
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Family
ID: |
26989142 |
Appl.
No.: |
06/334,308 |
Filed: |
December 24, 1981 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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Reissue of: |
931025 |
Aug 4, 1978 |
04181888 |
Jan 1, 1980 |
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Current U.S.
Class: |
375/235; 333/18;
375/232 |
Current CPC
Class: |
H04L
27/01 (20130101) |
Current International
Class: |
H04L
27/01 (20060101); H04B 001/16 () |
Field of
Search: |
;375/11,14,15,16
;333/18,17 ;328/155,162 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Lawless et al., "Binary Signalling Over Channels Containing
Quadratic Nonlinearities", Mar. 1974, IEEE Transaction on Comm.,
vol. Com-22, #3, pp. 288-298. .
Falconer et al., "Theory of Minimum Mean-Square-Error QAM Systems
Employing Decision Feedback Equalization", Bell System Technical
Journal, vol. 52, #10, Dec. 1973, pp. 1821-1849..
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Primary Examiner: Masinick; Michael A.
Attorney, Agent or Firm: Slusky; Ronald D.
Claims
I claim:
1. An arrangement for .[.equalizing.]. .Iadd.processing
.Iaddend.samples of a received modulated data signal having a
predetermined carrier frequency, said arrangement including means
operative in response to said samples for forming decisions as to
the values of data symbols represented thereby, each of said
decisions being represented by a complex number,
characterized in that said arrangement further includes means
(51-55, 61-65) for forming a plurality of signal products
associated with an individual one of said samples, each
multiplicand of each product being derived from a respective one of
said decisions, each said respective one of said decisions bearing
a predetermined temporal relationship to said one of said samples,
at least one multiplicand of individual ones of said signal
products being the complex conjugate of the decision from which
said one multiplicand is derived, and means (71-75) for multiplying
each of .Iadd.at least ones of .Iaddend.said products by an
associated coefficient and by a predetermined harmonic of said
carrier frequency to form a plurality of modulated weighted
products, .Iadd.and further characterized in that .Iaddend.said
decision forming means .[.including.]. .Iadd.includes .Iaddend.data
recovery means (14, 17) for forming a decision as to the value of
the data symbol represented by said one of said samples in response
to said modulated weighted products.
2. The invention of claim 1 wherein said modulated data signal is
of the type in which both the carrier phase and amplitude are
information-bearing.
3. The invention of claim 2 wherein said modulated data signal is a
quadrature amplitude modulated signal.
4. The invention of claims 2 or 3 wherein said decision forming
means includes means for applying to said data recovery means said
modulated weighted products and a demodulated version of said one
of said samples.
5. The invention of claim 4 wherein the harmonic by which each of
.Iadd.said at least ones of .Iaddend.said products is multiplied is
of the form
e.sup.j[2.pi.f.sbsp.c.sup.nT(x-y-1)+.PHI..sbsp.x,y.sup.], where
f.sub.c is said carrier frequency, n is the sample time index, T is
the sample interval, x is the number of decisions in said each of
said products, y is the number of complex conjugates of decisions
in said each of said products and .PHI..sub.x,y is a selected phase
angle.
6. The invention of claims 2 or 3 wherein said decision forming
means further includes means for combining said one of said samples
with said modulated weighted products to form a combined modulated
signal, means for demodulating said combined modulated signal and
means for applying the demodulated signal to said data recovery
means.
7. The invention of claim 6 wherein the harmonic by which each of
.Iadd.said at least ones of .Iaddend.said products is multiplied is
of the form e.sup.j[2.pi.f.sbsp.c.sup.nT(x-y)+.PHI..sbsp.x,y.sup.],
where f.sub.c is said carrier frequency, n is the sample time
index, T is the sample interval, x is the number of decisions in
said each of said products, y is the number of complex conjugates
of decisions in said each of said products and .PHI..sub.x,y is a
predetermined phase angle.
8. An arrangement operative during each one of a plurality of
successive sampling periods for .[.equalizing.]. .Iadd.processing
.Iaddend.a respective one of a succession of .Iadd.linearly
equalized .Iaddend.samples of a received modulated data signal
having a predetermined carrier frequency, said arrangement
including feedback means (FIG. 1, 44; FIG. 2, 44') for generating
an individual feedback signal associated with said one sample, and
decision forming means (FIG. 1-12, 14, 17, 46; FIG. 2-12, 14, 17,
46') jointly responsive to said one sample and its associated
feedback signal for forming a decision as to the value of .[.the.].
.Iadd.a .Iaddend.data symbol represented by said one sample, said
one sample and said decision being represented by respective
complex numbers,
characterized in that said feedback signal includes a plurality of
signal products .[.each.]. .Iadd.at least ones of which are
.Iaddend.multiplied by an associated coefficient and by a
predetermined harmonic of said carrier frequency, each multiplicand
of each signal product being derived from a respective decision
formed by said decision forming means during a previous one of said
sampling periods, each said respective decision bearing a
predetermined temporal relationship to said one sample, at least
one multiplicand of individual ones of said signal products being
the complex conjugate of the decision from which said one
multiplicand is derived.
9. The invention of claim 8 wherein said modulated data signal is
of the type in which both the carrier phase and amplitude are
information-bearing.
10. The invention of claim 9 wherein said modulated data signal is
a quadrature amplitude modulated signal.
11. The invention of claims 9 or 10 wherein said decision forming
means includes means (14, 46) for combining said individual
feedback signal with a demodulated version of said one sample to
form a data recovery input signal, and means (17) responsive to
said data recovery input signal for forming said decision.
12. The invention of claim 11 wherein the harmonic by which each of
.Iadd.said at least ones of .Iaddend.said products is multiplied is
of the form
e.sup.j[2.pi.f.sbsp.c.sup.nT(x-y-1)+.PHI..sbsp.x,y.sup.], where
f.sub.c is said carrier frequency, n is the sample time index, T is
the sample interval, x is the number of decisions in said each of
said products, y is the number of complex conjugates of decisions
in said each of said products and .PHI..sub.x,y is a selected phase
angle.
13. The invention of claims 9 or 10 wherein said decision forming
means includes means (46') for combining said individual feedback
signal with said one sample to form a combined modulated signal,
means (12) for demodulating said combined modulated signal and
means (17) responsive to the demodulated combined signal for
forming said decision.
14. The invention of claim 13 wherein the harmonic by which each of
.Iadd.said at least ones of .Iaddend.said products is multiplied is
of the form e.sup.j[2.pi.f.sbsp.c.sup.nT(x-y)+.PHI..sbsp.x,y.sup.],
where f.sub.c is said carrier frequency, n is the sample time
index, T is the sample interval, x is the number of decisions in
said each of said products, y is the number of complex conjugates
of decisions in said each of said products and .PHI..sub.x,y is a
selected phase angle.
15. A method operative during each one of a plurality of successive
sampling periods for .[.equalizing.]. .Iadd.processing .Iaddend.a
respective one of a succession of complex samples of a received
modulated data signal having a predetermined carrier frequency,
said method including the steps of generating an individual
feedback signal associated with said one sample, and forming a
complex decision as to the value of the data symbol represented by
said one sample in response to said one sample and its associated
feedback signal,
characterized in that said feedback signal includes a plurality of
signal products .[.each.]. .Iadd.at least ones of which are
.Iaddend.multiplied by an associated coefficient and by a
predetermined harmonic of said carrier frequency, each multiplicand
of each signal product being derived from a respective decision
formed during a previous one of said sampling periods, each said
respective decision bearing a predetermined temporal relationship
to said one sample and at least one multiplicand of individual ones
of said signal products being the complex conjugate of the decision
from which said one multiplicand is derived.
16. The invention of claim 15 wherein said modulated data signal is
of the type in which both the carrier phase and amplitude are
information-bearing.
17. The invention of claim 16 wherein said modulated data signal is
a quadrature amplitude modulated signal.
18. The invention of claims 16 or 17 wherein said decision forming
step includes the steps of combining said individual feedback
signal with a demodulated version of said one sample to form a data
recovery input signal, and forming said decision in response to
said data recovery input signal.
19. The invention of claim 18 wherein the harmonic by which each of
.Iadd.said at least ones of .Iaddend.said products is multiplied is
of the form
e.sup.j[2.pi.f.sbsp.c.sup.nT(x-y-1)+.PHI..sbsp.x,y.sup.], where
f.sub.c is said carrier frequency, n is the sample time index, T is
the sample interval, x is the number of decisions in said each of
said products, y is the number of complex conjugates of decisions
in said each of said products and .PHI..sub.x,y is a selected phase
angle.
20. The invention of claims 16 or 17 wherein said decision forming
step includes the steps of combining said individual feedback
signal with said one sample to form a combined modulated signal,
demodulating said combined modulated signal and forming said
decision in response to the demodulated combined signal.
21. The invention of claim 20 wherein the harmonic by which each of
.Iadd.said at least ones of .Iaddend.said products is multiplied is
of the form e.sup.j[2.pi.f.sbsp.c.sup.nT(x-y)+.PHI..sbsp.x,y.sup.],
where f.sub.c is said carrier frequency, n is the sample time
index, T is the sample interval, x is the number of decisions in
said each of said products, y is the number of complex conjugates
of decisions in said each of said products and .PHI..sub.x,y is a
selected phase angle.
22. A method for use in a receiver of the type in which a decision
is formed during the n.sup.th one of a plurality of successive
periods of duration T, said decision being formed by quantizing a
respective demodulated sample of a received complex modulated data
signal having a carrier frequency f.sub.c, both the carrier
amplitude and phase of said signal being information bearing, said
decision being represented by a complex number A(n), said method
including the steps of
combining a feedback signal V(n) with said sample to form a signal
Y(n) and forming said decision in response to said signal Y(n),
said method characterized in that said signal V(n) includes the
terms ##EQU22## where * indicates complex conjugate and
.PHI..sub.2,0 and .PHI..sub.1,1 are selected phase angles, the
coefficients ##EQU23## having respective values associated with
said decision A(n), and the index pairs (j.sub.1,j.sub.2) and
(j.sub.3,j.sub.4) having respective sets of predetermined
values.
23. The invention of claim 22 comprising the further steps .Iadd.of
.Iaddend.
forming a signal E(n) in response to said signal Y(n) and said
decision A(n), and
updating the coefficients ##EQU24## in accordance with ##EQU25##
.gamma..sub. (n) and .gamma..sub.2 (n) being selected scaling
factors.
24. The invention of claim 23 wherein said signal V(n) further
includes the term ##EQU26## the coefficients ##EQU27## having
respective values associated with said decision A(n) and the index
i having a set of predetermined values, and wherein said method
includes the further steps of
updating said coefficients ##EQU28## in accordance with ##EQU29##
.gamma..sub. (n) being a selected scaling factor.
25. The invention of claim 22 further characterized in that said
signal V(n) further includes at least a selected one of the terms
##EQU30## where .PHI..sub.3,0, .PHI..sub.2,1 and .PHI..sub.1,2 are
selected phase angles, the coefficients ##EQU31## having respective
values associated with said decision A(n), and the index triples
(k.sub.1,k.sub.2,k.sub.3), (k.sub.4,k.sub.5,k.sub.6) and
(k.sub.7,k.sub.8,k.sub.9) having respective sets of predetermined
values.
26. The invention of claim 25 including the further steps of
forming a signal E(n) in response to said signal Y(n) and said
decision A(n), and
updating the coefficients ##EQU32## in accordance with ##EQU33##
.gamma..sub. (n), .gamma..sub.4 (n) and .gamma..sub.5 (n) being
selected scaling factors.
27. A method for use in a receiver of the type in which a decision
is formed during the n.sup.th one of a plurality of successive
periods of duration T, said decision being as to the value of a
respective demodulated complex sample of a received data signal
modulated at a carrier frequency f.sub.c, both the carrier
amplitude and phase of said signal being information bearing, said
decision being represented by a complex number A(n), said method
including the steps of
combining a feedback signal V(n) with said sample to form a signal
Y(n) and forming said decision in response to said signal Y(n),
said method characterized in that said signal V(n) includes the
terms ##EQU34## where * indicates complex conjugate and
.PHI..sub.2,0 and .PHI..sub.1,1 are selected phase angles, the
coefficients ##EQU35## having respective values associated with
said decision A(n), and the index pairs (j.sub.1,j.sub.2) and
(j.sub.3,j.sub.4) having respective sets of predetermined
values.
28. The invention of claim 27 comprising the further steps
forming a signal E(n) in response to said signal Y(n) and said
decision A(n), and
updating the coefficients ##EQU36## in accordance with ##EQU37##
.gamma..sub. (n) and .gamma..sub.2 (n) being selected scaling
factors.
29. The invention of claim 28 wherein said signal V(n) further
includes the term ##EQU38## the coefficients ##EQU39## having
respective values associated with said decision A(n) and the index
i having a set of predetermined .[.value.]. .Iadd.levels.Iaddend.,
and wherein said method includes the further steps of
updating said coefficients ##EQU40## in accordance with ##EQU41##
.gamma..sub. (n) being a selected scaling factor.
30. The invention of claim 27 further characterized in that said
signal V(n) further includes at least a selected one of the terms
##EQU42## where .PHI..sub.3,0, .PHI..sub.2,1 and .PHI..sub.1,2 are
selected phase angles, the coefficients ##EQU43## having respective
values associated with said decision A(n), and the index triples
(k.sub.1,k.sub.2,k.sub.3), (k.sub.4,k.sub.5,k.sub.6) and
(k.sub.7,k.sub.8,k.sub.9) having respective sets of predetermined
values.
31. The invention of claim 30 including the further steps of
forming a signal E(n) in response to said signal Y(n) and said
decision A(n), and
updating the coefficients ##EQU44## in accordance with ##EQU45##
.gamma..sub. (n), .gamma..sub.4 (n) and .gamma..sub.5 (n) being
selected scaling factors. .Iadd. 32. Apparatus for processing a
passband signal representing a succession of complex signal values,
said apparatus comprising
means for forming a succession of weighted sums of products,
individual multiplicands of at least ones of said products being
derived from individual decisions as to respective ones of said
signal values, at least ones of said individual multiplicands being
the complex conjugates of the decisions from which they were
derived and each of at least ones of said products being multiplied
by a respective harmonic of the carrier frequency of said passband
signal, and
means for forming at least ones of said decisions in response to
said passband signal and ones of said weighted sums.
.Iaddend..Iadd. 33. The invention of claim 32 wherein said decision
forming means comprises
means for generating a succession of complex linearly equalized
samples of said passband signal, and
means for forming each of said ones of said decisions in response
to at least a respective one of said equalized samples and at least
a respective one of said weighted sums. .Iaddend..Iadd. 34. The
invention of claim 33 wherein each of said individual decisions
bears a predetermined temporal relationship to said respective one
of said samples. .Iaddend..Iadd. 35. The invention of claims 32, 33
or 34 further comprising means for updating the coefficients used
to form said weighted sums in a decision-directed manner. .Iaddend.
.Iadd. 36. A method for processing a passband signal representing a
succession of complex signal values, said method comprising the
steps of
forming a succession of weighted sums of products, individual
multiplicands of at least ones of said products being derived from
individual decisions as to respective ones of said signal values,
at least ones of said individual multiplicands being the complex
conjugates of the decisions from which they were derived and each
of at least ones of said products being multiplied by a respective
harmonic of the carrier frequency of said passband signal, and
forming at least ones of said decisions in response to said
passband signal and ones of said weighted sums. .Iaddend..Iadd. 37.
The invention of claim 36 wherein said decision forming step
comprises the steps of
generating a succession of complex linearly equalized samples of
said passband signal, and
forming each of said ones of said decisions in response to at least
a respective one of said equalized samples and at least a
respective one of said weighted sums. .Iaddend..Iadd. 38. The
invention of claim 37 wherein each of said individual decisions
bears a predetermined temporal relationship to said respective one
of said samples. .Iaddend..Iadd. 39. The invention of claims 36, 37
or 38 comprising the further step of updating the coefficients used
to form said weighted sums in a decision-directed manner..Iaddend.
Description
CROSS-REFERENCE TO RELATED APPLICATION
My U.S. patent application entitled "Feedforward Nonlinear
Equalization of Modulated Data Signals", Ser. No. 931,026, was
filed in the U.S. Patent and Trademark Office concurrently
herewith.
BACKGROUND OF THE INVENTION
My invention relates to the correction of the distorting effects of
limited bandwidth transmission media on modulated data signals.
The principal impediment to accurate reception of high-speed data
signals transmitted over limited bandwidth, e.g., switched
voiceband telephone, transmission channels is that form of
distortion known as intersymbol interference. This phenomenon is a
manifestation of the fact that a pulse passing through a
band-limited channel expands in the time domain. As a result, each
sample of the received signal is not simply derived from a single
transmitted data symbol but, rather, some combination of symbols.
Other impairments include phase jitter and additive noise.
Linear intersymbol interference, in particular, is manifested in
that each sample of the received signal contains a linear
combination of a transmitted symbol--which the sample nominally
represents--with symbols which precede and succeed it in the data
stream. Among known techniques which compensate for the distorting
effects of linear intersymbol interference in both baseband and
passband, e.g., quadrature amplitude modulated (QAM), signals are
linear feedforward equalization and linear decision feedback
equalization. In accordance with the former technique, each sample
of the received signal is weighted with a linear sum of past and
future samples prior to a decision being made as to the value of
the transmitted symbol. In accordance with the latter technique, a
weighted linear sum of past decisions is combined with each sample,
again prior to a decision being made as to the value of the
transmitted symbol. See, for example, my U.S. Pat. No. 3,974,449
issued Aug. 10, 1976.
Nonlinear intersymbol interference is manifested in that each
sample of the received signal includes a linear combination of
products of the current, past and future modulated data symbols,
and/or (in the case of QAM, for example) the complex conjugates of
such data symbols. In transmission systems that employ linear
modulation, such as QAM, the effect is to reduce the margin against
noise. Indeed, for data rates above 4800 bps, nonlinear distortion
is the dominant impairment on many voiceband channels. At least one
arrangement is known which compensates for nonlinear intersymbol
interference in baseband data signals. See, e.g., U.S. Pat. No.
3,600,681 issued Aug. 17, 1971 to T. Arbuckle. However, the known
arrangements will not, in general, effectively compensate for
nonlinear intersymbol interference in modulated data signals.
SUMMARY OF THE INVENTION
An object of my invention is to provide a method and arrangement
which compensates for nonlinear intersymbol interference in
modulated data signals.
A more particular object of my invention is to provide a method and
arrangement which compensates for nonlinear intersymbol
interference in modulated data signals in which both the carrier
phase and amplitude are modulated, i.e., information-bearing.
A still more particular object of my invention is to provide a
method and arrangement which compensates for nonlinear intersymbol
interference in quadrature amplitude modulated data signals.
In accordance with the invention, the above and other objects are
achieved by combining with each sample of the received signal an
associated feedback nonlinear signal. The feedback nonlinear signal
includes a weighted sum of products of (a) data decisions made on
individual demodulated samples, and (b) complex conjugates of such
data decisions. Each data decision/complex conjugate product, in
turn, modulates a predetermined harmonic of the carrier
frequency.
Each data decision/complex conjugate product has a predetermined
number of multiplicands, i.e., data decisions and/or complex
conjugates, each of which bears a predetermined temporal
relationship to the associated sample. In general, inclusion in the
feedback nonlinear signal of products having a total of m data
decisions and complex conjugates provides compensation for m.sup.th
order intersymbol interference.
The coefficients used in weighting the various products are
illustratively updated in an adaptive, decision-directed
manner.
BRIEF DESCRIPTION OF THE DRAWING
In the drawing,
FIGS. 1 and 2 are block diagrams of first and second illustrative
embodiments, respectively, of receivers for modulated data signals
including equalization circuitry which combines with each sample a
nonlinear feedback signal in accordance with the invention;
FIG. 3 is a block diagram of an illustrative feedback nonlinear
signal processor for use in the receivers of FIGS. 1 and 2;
FIG. 4 is an illustrative coefficient store and multiplier unit for
use in the processor of FIG. 3.
DETAILED DESCRIPTION
The receiver of FIG. 1 is illustratively employed in a high-speed
telephone-voiceband data transmission system using quadrature
amplitude modulation (QAM). The sampling interval is T seconds, the
signaling rate being 1/T symbols per second. QAM entails both phase
and amplitude modulation of a carrier, i.e., both the carrier phase
and amplitude are information-bearing. As a result, QAM signals are
referred to as "complex" signals and can be represented for
notational convenience as complex numbers. This notational
convention is followed herein so that all of the signal reference
letters used in the following description should be understood to
represent complex signals.
The receiver FIG. 1 is of the same general type as that disclosed
in my U.S. Pat. No. 3,974,449 issued Aug. 10, 1976, which is hereby
incorporated by reference. Thus, as in my earlier patent, a sample
R(n) of a received QAM data signal is provided on input lead 10,
the index n indicating that R(n) is the sample of the QAM signal at
time nT. Sample R(n) is applied to a feedforward processor 11.
After some delay, the latter generates an equalized version of
sample R(n), feedforward signal G(n), on lead 35, thereby providing
at least some compensation for intersymbol interference in sample
R(n) as well as for some of the additive noise present therein.
Feedforward processor 11 may include a feedforward linear processor
of conventional design for generating as part of signal G(n) a
linear combination of past, present and future received samples,
providing compensation for linear intersymbol interference. If
desired, feedforward processor 11 may also include a feedforward
nonlinear processor of the type disclosed in my above-referenced
copending U.S. patent application. Such a feedforward nonlinear
processor generates as part of signal G(n) a linear combination of
products of samples on lead 10 and their complex conjugates,
thereby providing at least some compensation for nonlinear
intersymbol interference.
Signal G(n) is extended to a demodulator 12 over lead 35.
Demodulator 12 produces a demodulated baseband data signal Z(n)
which is applied to one input of a subtractor 14.
The receiver of FIG. 1 further includes data recovery circuit, or
quantizer, 17. This unit quantizes the output signal of subtractor
14--data recovery input signal Y(n)--to form a decision A(n) as to
the value of the original modulating data symbol represented by,
and to be recovered from, sample R(n). (Quantization of complex
signals amounts to partitioning the complex plane into decision
regions surrounding the ideal received points.) Decision A(n)
passes on to data sink 25. Decision A(n) is also applied to
feedback linear processor 15 over lead 31.
Feedback linear processor 15 operates in conventional fashion to
generate a feedback linear signal C(n) on lead 16. Signal C(n) is
comprised of a linear combination of decisions made by data
recovery circuit 17 prior to decision A(n). Processor 15 includes a
delay line 15a to facilitate the formation of signal C(n). Signal
C(n) is combined with--illustratively subtracted from--signal Z(n)
in a manner described below to form the abovementioned signal Y(n),
thereby removing at least a portion of the linear intersymbol
interference and additive noise not compensated for upstream in
feedforward processor 11.
In accordance with the present invention, a feedback nonlinear
signal D(n) is provided on lead 45 by a feedback nonlinear
processor 44. Signal D(n) is also subtracted from signal Z(n),
thereby removing at least a portion of the nonlinear intersymbol
interference and additive noise not compensated for upstream in
processor 11. As described in detail below, signal D(n) is
comprised of a weighted sum of products of decisions made by data
recovery circuit 17 and the complex conjugates of such data
decisions, each product, in turn, modulating a predetermined
harmonic of the carrier frequency. Signals C(n) and D(n) are
illustratively subtracted from signal Z(n) by first adding them
together in an adder 46 generate a composite feedback signal V(n).
The latter is then subtracted from a signal Z(n) in subtractor 14
to generate signal Y(n).
So-called weighting, or tap, coefficients for forming the
aforementioned combinations of (a) received signal samples and
products of signal samples and complex conjugates thereof in
feedforward processor 11, (b) data decisions in feedback linear
processor 15, and (c) products of data decisions and complex
conjugates thereof in feedback nonlinear processor 44, are
automatically adjusted in an adaptive, decision-directed manner.
This automatic adjustment of tap coefficients is implemented by
circuitry including error computer 20. This unit provides on lead
22 the complex conjugate, E(n), of an estimated error signal E(n),
the latter representing the difference between signal Y(n) and
decision A(n). The tap coefficients used in processors 15 and 44
are adjusted in response to signal E(n) in such a way as to
minimize the average squared magnitude of that signal. The tap
coefficients used in processor 11 are adjusted in response to the
complex conjugate of a modulated version of the estimated error
signal--signal J(n)--again in such a way as to minimize the average
squared magnitude of that signal. Signal J(n) is provided to
processor 11 by remodulator 28 on lead 27.
Phase jitter and frequency offset in modulated data sample R(n) can
hinder accurate data recovery. In order to compensate for these
impairments, demodulator 12 and remodulator 28 perform their
functions using complex exponential signals of the form
e.sup.-j[2.pi.f.sbsp.c.sup.nT+.theta.(n)], which are generated by
carrier recovery circuit 24. The phase angle .theta.(n) is an
estimate of the carrier phase .theta.(n) of sample R(n). The
estimated phase .theta.(n+1) during the (n+1).sup.st sampling
period is updated in accordance with
Carrier recovery circuit 24 receives signals J(n) and G(n) for
purposes of computing .theta.(n+1) in accordance with Eq. (1).
The factor .alpha.(n) in Eq. (1) may simply be a constant stored
within the carrier recovery circuit 24. Alternatively, factor
.alpha.(n) may be a function of current signal values so that
updating of .theta.(n) is carried out in response only to the phase
angle error [.theta.(n)-.theta.(n)] and not in response to errors
due to imperfect equalization and random amplitude modulation by
data symbols in processors 11, 15 and 44. In deriving an expression
for such an .alpha.(n), perfect equalization is postulated by
assuming that the only discrepancy between Y(n) and A(n) is in the
phase error, [.theta.(n)-.theta.(n)]. Therefore,
Moreover, E(n)=Z(n)-V(n)-A(n) and it can be shown that J*(n)G(n) is
mathematically equivalent to E*(n)Z(n). Therefore, Eq. (2) can be
substituted into Eq. (1) to yield
Therefore, a suitable choice for .alpha.(n) is seen to be
where .alpha. is a small constant, because then
Thus, as desired, the updating of .theta.(n) is based only on the
phase error, providing a smoother, more direct acquisition of
carrier phase. Carrier recovery circuit 24 illustratively receives
decision A(n) and signal V(n) for purposes of generating .alpha.(n)
in accordance with Eq. (3).
FIG. 2 illustrates an alternate embodiment of a receiver which
includes a feedback nonlinear processor in accordance with the
invention. Here, the output of the feedback nonlinear processor
44'--feedback nonlinear signal D'(n)--is subtracted from signal
G(n) in a subtractor 46' to form a combined modulated signal F(n)
rather than being subtracted from signal Z(n) via adder 46 as in
FIG. 1. Signal D'(n) differs from signal D(n) in that different
harmonics multiply each data decision/complex conjugate product, as
described below. In addition, signal V(n) is generated for purposes
of carrier recovery, as previously described, by passing signal
D'(n) through a demodulator 12' and adding the output thereof to
signal C(n) in an adder 13. The embodiments of FIGS. 1 and 2 are
otherwise similar, however, with corresponding elements having the
same reference numeral in each FIG. Thus the preceding discussion
relating to the structure and operation of the receiver of FIG. 1
is generally applicable to the receiver of FIG. 2.
With the exception of processor 44 (FIG. 1), processor 44' (FIG.
2), and the feedforward nonlinear circuitry in processor 11, if
any, the specific circuitry comprising the various components of
the receivers of FIGS. 1 and 2, as well as their functional and
timing interrelationships, are all well known in the art and need
not be discussed in further detail. See, for example, my
above-cited U.S. Patent for a description of the receiver generally
and my above-cited copending U.S. Patent application for a
description of the feedforward nonlinear circuitry. The remainder
of this detailed description, then, is principally directed to (a)
characterization of feedback nonlinear signals D(n) and D'(n) and
(b) description of illustrative circuitry, shown in FIGS. 3 and 4,
for generating them.
In accordance with the present invention, the feedback nonlinear
signal associated and combined with each sample of the received
signal includes a weighted sum of products of individual ones of
the data decisions made by data recovery circuit 17 and complex
conjugates of such data decisions. Each data decision/complex
conjugate product--hereinafter referred to for generality as
"decision/conjugate product" even though a particular product may
not have any complex conjugates--in turn, modulates a predetermined
harmonic of the carrier frequency, thereby providing a plurality of
modulated weighted products. Each decision/conjugate product has a
predetermined number of multiplicands, each of which bears a
predetermined temporal relationship to the associated sample. In
general, inclusion in the feedback nonlinear signal of products
having a total of m data decisions and complex conjugates provides
compensation for m.sup.th order intersymbol interference.
In the case where the feedback nonlinear signal is added to the
associated sample after demodulation, as in FIG. 1, the
above-mentioned harmonic is of the general form
where
f.sub.c =carrier frequency
n=sample time index
x=number of data decisions in the decision/conjugate product which
the harmonic multiplies
y=number of complex conjugates in the decision/conjugate product
which the harmonic multiplies
.PHI..sub.x,y =a selected phase angle (discussed below).
In the case where the feedback nonlinear signal is added to the
associated sample prior to demodulation, as in FIG. 2, the harmonic
is of the general form
The phase angle .PHI..sub.x,y in Eqs. 4(a) and 4(b) may be, for
example, a term which corrects for distortion due to phase jitter
and/or frequency offset in the nonlinear terms of each received
sample, i.e., the products of modulated data symbols which
constitute the nonlinear intersymbol interference to be removed
from the sample. If at least some of this distortion was introduced
in the transmission system prior to the nonlinearity which caused
the nonlinear intersymbol interference, different values of
.PHI..sub.x,y may have to be selected for each combination of
values of the parameters x and y.
In the embodiments disclosed herein, however, it is presumed that
any phase jitter or frequency offset was introduced after the
nonlinearity. As a result, all the .PHI..sub.x,y 's may have the
same value. In particular, any phase jitter and/or frequency offset
in the nonlinear terms is compensated for in the embodiment of FIG.
1 by virtue of the fact that those terms are removed from each
sample after a demodulation which multiplies the sample by
e.sup.-j[2.pi.f.sbsp.c.sup.nT+.theta.(n)]. Thus each .PHI..sub.x,y
can be set to an arbitrary constant, illustratively zero. In the
embodiment of FIG. 2, on the other hand, the nonlinear terms are
removed from the sample being processed prior to demodulation. In
order to compensate in this embodiment for phase jitter and/or
frequency offset in the nonlinear terms, each .PHI..sub.x,y is
illustratively set to .theta.(n).
Attention is now particularly directed to the embodiment of FIG. 1.
Processor 44 thereof illustratively provides compensation for
second- and third-order nonlinear intersymbol interference. Thus,
composite feedback signal V(n) can be expressed as follows:
where ##EQU1## C(n), the prior art feedback linear signal, is
comprised of a linear combination of data decisions A(n-i), each
sample being weighted by the complex conjugate of complex
weighting, or tap, coefficient ##EQU2## The index i typically spans
a range of positive values .gtoreq.1 so that C(n) includes a
sufficient number of data decisions made in data recovery circuit
17 prior to decision A(n) to yield effective equalization. As is
conventional, the values of coefficients ##EQU3## are adjusted
adaptively in a decision-directed manner in processor 15
illustratively using a gradient adaptation algorithm, yielding the
updating relationship ##EQU4## with .gamma..sub.0 (n) being a
selected factor which may be updated each sampling period or which
may more simply be a constant.
The first two terms of feedback nonlinear signal D(n), defined for
convenience as D.sub.1 (n) and D.sub.2 (n), provide compensation
for second-order intersymbol interference. (In a given application,
it may be desired to include only one of these terms in signal
D(n).) Each of the terms D.sub.1 (n) and D.sub.2 (n) is comprised
of a weighted sum of two-multiplicand products which are modulated,
in turn, by a harmonic of the carrier frequency defined by Eq. 4a.
Each multiplicand of each product is derived from a selected data
decision. That is, each multiplicand is either a data decision or
the complex conjugate of a data decision.
In particular, the two multiplicands of each decision/conjugate
product of term D.sub.1 (n) are a selected two data decisions
A(n-j.sub.1) and A(n-j.sub.2) weighted by the complex conjugate of
an associated weighting coefficient. ##EQU5## and modulated by
e.sup.j2.pi.f.sbsp.c.sup.nT (all the .PHI..sub.x,y 's being zero in
this embodiment, as discussed above). Index pairs (j.sub.1,j.sub.2)
are predetermined and are selected keeping in mind that the
nonlinear (and, indeed, linear) intersymbol interference in a data
decision can usually be most effectively dealt with by generating
the feedback signal in response to data decisions which are
relatively close in the output data decision stream to the data
decision currently being made. Moreover, increasing the number of
index pairs to encompass data decisions which are more remote in
time will have increasingly less effect in removing intersymbol
interference, on the one hand, while possibly requiring increased
hardware costs and/or processing time on the other hand. In the
present embodiment, the following (j.sub.1,j.sub.2) index pairs are
illustratively used: (1,1)(1,2)(1,3)(2,2)(2,3)(3,3). The modulated
weighted products of term D.sub.1 (n) are thus given by ##EQU6##
This term, then, encompasses a modulated weighted sum of all
possible two-multiplicand products in which each multiplicand is
one of the three previous data decisions.
The second term of signal D(n), D.sub.2 (n), is similar to D.sub.1
(n) except that the second multiplicand of each product is a
complex conjugate and except that, per Eq. 4(a), the modulated
harmonic is different. An illustrative set of index pairs
(j.sub.3,j.sub.4) for this second term is
(1,1)(1,2)(1,3)(2,1)(2,2)(2,3)(3,1)(3,2)(3,3). Note that reversing
the order of the (j.sub.3,j.sub.4)index pairs, e.g., (1,2) and
(2,1), provides different products in term D.sub.2 (n), although
not in term D.sub.1 (n). Thus, even though all of the indices
j.sub.3 and j.sub.4 are each either 1, 2 or 3, just as in the case
of indices j.sub.1 and j.sub.2, here there are nine possible
different decision/conjugate products, rather than six as in the
case of term D.sub.1 (n).
The final three terms of signal D(n), D.sub.3 (n), D.sub.4 (n) and
D.sub.5 (n), provide compensation for third-order intersymbol
interference. (Again, in a given application, it may be desired to
use less than all of these terms.) In particular, term D.sub.3 (n)
is comprised of a weighted sum of three-multiplicand products each
having an associated weighting coefficient and each modulating the
appropriate harmonic from Eq. 4(a). Terms D.sub.4 (n) and D.sub.5
(n) are similar to term D.sub.3 (n) but include one and two complex
conjugates of data decisions, respectively. Index triples
(k.sub.1,k.sub.2,k.sub.3) for term D.sub.3 (n) illustratively take
on the values
(1,1,1)(1,1,2)(1,2,2)(1,2,3)(2,2,2,)(2,2,3)(3,2,3)(3,3,3). Index
triples for terms D.sub.4 (n) and D.sub.5 (n) illustratively take
on the values
(1,1,1)(1,1,2)(1,2,1)(1,2,3)(1,3,2)(2,1,2)(2,2,1)(2,2,2)(2,2,3)(2,3,1)(2,3
,2)(3,2,3)(3,3,2)(3,3,3) in each case. Note that for index triples
(k.sub.1,k.sub.2,k.sub.3), (k.sub.4,k.sub.5,k.sub.6) and
(k.sub.7,k.sub.8,k.sub.9) less than all possible combinations
yielding unique three-multiplicand decision/conjugate products are
used. This is done simply to minimize the amount of signal
processing needed to generate signal D(n). In general, using all
possible combinations yielding unique three-multiplicand
decision/conjugate products in generating terms D.sub.3 (n),
D.sub.4 (n) and D.sub.5 (n) will provide additional reduction of
third-order intersymbol interference.
Compensation for fourth- or higher-order intersymbol interference
may be provided in accordance with the invention by obvious
extension of the second- and third-order cases.
As previously indicated, the values of the weighting coefficients
used in feedback nonlinear processor 44, like those used in
feedback linear processor 15, are adjusted adaptively in a
decision-directed manner. As in the case of processor 15, a
gradient adaptation criterion is illustratively used. By way of
example, this criterion is expressed for the coefficients
##EQU7##
The other four sets of weighting coefficients used in generating
term D(n) are generated similarly to coefficients ##EQU8## That is,
##EQU9## Although, in general, multiplicative scaling factors
.gamma..sub.1 (n)-.gamma..sub.5 (n) can be updated at each sampling
time, they, like .gamma..sub.0 (n), can more simply be fractional
constants, the values of which are determined empirically. As seen
in FIG. 1, feedback nonlinear processor 44, like feedback linear
processor 15, receives signal E(n) for purposes of coefficient
updating.
Feedback nonlinear signal D'(n) of FIG. 2 is similar to signal D(n)
except that the multiplicative harmonics are given by Eq. 4(b).
(The same index pairs and triples can be used, however.) Thus,
D'(n)= ##EQU10##
In addition, the coefficient updating relations for the FIG. 2
embodiment are given by ##EQU11##
As previously discussed, all the .PHI..sub.x,y 's illustratively
have the value .theta.(n) in this embodiment which parameter could
be provided, for example, from carrier recovery circuit 24.
Attention is now directed to FIG. 3, which shows an illustrative
embodiment of feedback nonlinear processor 44. Feedback nonlinear
processor 44' of FIG. 2 may be substantially the same except that,
again, the harmonics which the decision/conjugate products modulate
(in CSM units 71-75) are given by Eq. 4(b) rather than Eq.
4(a).
Processor 44 includes multiplexers 51-55, complex multipliers
61-65, coefficient store and multiplier (CSM) units 71-75 and
accumulators 81-85. During each sampling period, the serially
connected chain of multiplexer 51, multiplier 61 and CSM unit 71
generates and stores the six modulated weighted products of term
D.sub.1 (n) of signal D(n) in accumulator 81. The modulated
weighted products of terms D.sub.2 (n)-D.sub.5 (n) are generated
and stored similarly, each by its own multiplexer-multiplier-CSM
unit-accumulator chain. Since the chains which begin with
multiplexers 51 and 52 generate terms of signal D(n) which have
two-multiplicand decision/conjugate products, i.e., terms D.sub.1
(n) and D.sub.2 (n), those multiplexers each extend two output
leads to two-input complex multipliers 61 and 62, respectively.
Multiplexers 53-55 each extend three output leads to multipliers
63-65, respectively, in order to generate the three-multiplicand
decision/conjugate products which make up terms D.sub.3 (n)-D.sub.5
(n).
After terms D.sub.1 (n)-D.sub.5 (n) have all been stored in their
respective accumulators, they are added together in adder 86 to
generate feedback nonlinear signal D(n) on lead 45.
Processor 44 operates under the control of a clock 91. The latter,
in turn, operates at a frequency sufficient to ensure that the
generation of signal D(n) is completed during a single sampling
interval, T. As described in further detail below, the clock pulses
on output lead 91a of clock 91 control the shifting through
processor 44 of serial bit streams representing data decisions,
complex conjugates of data decisions and intermediate products of
these with each other and harmonics of the carrier frequency. The
clock pulses on lead 91a are, in addition, received by a
divide-by-twelve counter 93. The output pulses from counter 93 on
lead 93a initiate multiplication operations in multipliers 61-65
and CSM units 71-75.
Counter 93 also drives selection register 92--illustratively a
divide-by-seventeen counter. Register 92 increments the five-bit
number represented by the signals on its five output leads 92a by
one count in response to each pulse from counter 93 on lead 93a.
During each sampling period, three previous data decisions--A(n-1),
A(n-2) and A(n-3)--are received by multiplexers 51-55 from delay
line 15a of feedback linear processor 15, the two feedback
processors advantageously sharing this delay line between them.
Each of the three decisions is illustratively represented by twelve
serial bits which are stored internally by each multiplexer in
response to the first twelve clock pulses on lead 91a. The count on
leads 92a at any given time indicates to each of the multiplexers
which of the three decisions is to be provided on each of the
multiplexer output leads in response to each group of twelve clock
pulses.
By way of illustration, operation of the chain which begins with
multiplexer 51 in generating term D.sub.1 (n) will now be
described, the operation of the other chains being similar. For
purposes of explanation, it is assumed that the first sixty clock
pulses within the n.sup.th sampling period have elapsed. Thus, at
this point, the first three modulated weighted products of term
D.sub.1 (n) have been summed and stored in accumulator 81. The
fourth modulated weighted product, ##EQU12## has just been
generated in CSM unit 71, while the fifth, unweighted modulated
product, A(n-2)A(n-3)e.sup.j2.pi.f.sbsp.c.sup.nT has just been
generated in multiplier 61.
A number of operations occur concurrently in response to the next
twelve clock pulses. The twelve bits representing ##EQU13## are
shifted via lead 71a from CSM unit 71 into accumulator 81, where it
is added to the current contents of the accumulator. In addition,
the unweighted, fifth product
A(n-2)A(n-3)e.sup.j2.pi.f.sbsp.c.sup.nT is shifted via lead 61a
from multiplier 61 into CSM unit 71. The binary count on leads 92a
is now 00101. In response to that count and to the twelve clock
pulses currently being generated, multiplexer 51 provides the
decision A(n-3) on both of its output leads 51a and 51b since the
sixth (and last) value of index pair (j.sub.1,j.sub.2) is (3,3).
The subsequent pulse on lead 93a initiates the accumulation
operation in accumulator 81. It also initiates the multiplication
in CSM unit 71 of A(n-2)A(n-3) with the complex conjugate of the
current value of its associated weighting coefficient, ##EQU14##
stored in the CSM unit. The pulse on lead 93a also initiates the
multiplication in multiplier 61 of decision A(n-3) by itself and by
the harmonic e.sup.j2.pi.f.sbsp.c.sup.nT. The latter may be
provided in any of several ways, such as from the oscillator
section of carrier recovery circuit 24. (For drawing clarity, a
specific lead connection from the latter is not shown in the
drawing.)
The count on leads 92a, in addition to the function described
above, is also used to indicate to the various components of
feedback nonlinear processor 44 when and when not to respond to the
clock pulses on lead 91a. For example, the fact that the last,
i.e., sixth, two-multiplicand decision/conjugate product in term
D.sub.1 (n) has now been generated is manifested by the fact that
the count on leads 92a is 00101. Simple logic circuitry within
multiplexer 51 and multiplier 61 precludes them from responding to
further clock pulses. CSM unit 71 begins and ceases operation
twelve clock pulses after multiplexer 51 and multiplier 61 begin
and cease their operation; for accumulator 81 the number is
twenty-four clock pulses. Thus, similar logic circuitry in CSM
units 71 and accumulator 81 allows them to respond to clock pulses
only when the count on leads 92a is at or between 00001 and 00110,
for the former, and 00010 and 00111 for the latter. The other
components within each chain of processor 44 similarly have logic
circuits for controlling which clock pulses they will respond to,
depending on (a) how many products are to be computed in that chain
and (b) the position of the particular component within its chain.
A typical such logic circit is shown in the illustrative embodiment
of CSM unit 71 in FIG. 4, as described below.
When the count on leads 92a has reached 01111, terms D.sub.1
(n)-D.sub.5 (n) have all been generated and stored in accumulators
81-85, respectively. AND gate 94 now generates a pulse on lead 94a
which causes the contents of accumulators 81-85 to be added
together in adder 86, the resultant signal on lead 45 being
feedback nonlinear signal D(n). When the count on leads 92a reaches
its last value, 10000, the output of NOT gate 95 on lead 95a goes
low, clearing multiplexers 51-55, multipliers 61-65, CSM units
71-75, and accumulators 81-85 in preparation for generating
feedback nonlinear signal D(n+1) during the next, (n+1).sup.st,
sampling period.
It will be appreciated that FIG. 3 represents but one of numerous
possible approaches for realizing feedback nonlinear processor 44
(or, as previously indicated, processor 44'). Thus, for example,
the terms D.sub.1 (n)-D.sub.5 (n) could be generated serially, one
after the other, rather than in parallel. Such an approach would
require less arithmetic hardware. However, the circuitry needed to
manipulate the decisions and complex conjugate and their products
would be more complicated. In addition, all of the arithmetic
operations which have to be performed in generating signal D(n)
would still have to be completed during a single sampling period,
imposing more stringent requirements on the speed with which the
various arithmetic operations would have to be performed. These
requirements might be advantageously satisfied by generating signal
D(n) using a microprocessor. In any event, it will be appreciated
that the needs of the particular application will govern the
structure of processor 44.
Each of the functional blocks depicted in FIG. 3 may be of
conventional design and need not be described in further detail
herein. However, a particularly advantageous realization for CSM
unit 71 (CSM units 72-75 being similar) is shown in FIG. 4.
Each component of CSM unit 71 received clock pulses via lead 113a.
As previously indicated, CSM unit 71 is to operate only when the
count on leads 92a is at or between 0001 and 0110. This mode of
operation is achieved by logic circuit 113 which controls the flow
of clock pulses onto lead 113a from lead 91a in response to the
count on leads 92a.
It will be remembered from Eq. (6) that the updated value of each
coefficient is given by its previous value plus a term which
includes signal E(n). The latter, however, is not known until
signal D(n) has been generated. Thus, as shown in FIG. 4, the
modulated products
A(n-j.sub.1)A(n-j.sub.2)e.sup.j2.pi.f.sbsp.c.sup.nT received by CSM
unit 71 are delayed in a serial in/serial out shift register 101
such that as the first modulated product of term D.sub.1 (n),
A(n-1).sup.2 e.sup.j2.pi.f.sbsp.c.sup.nT, emerges from shift
register 101 at the beginning of the next, (n+1).sup.st, sampling
period, signal E(n) is first becoming available on lead 22.
A(n-1).sup.2 e.sup.j2.pi.f.sbsp.c.sup.nT is multiplied in
multiplier 103 by signal E(n) and by .gamma..sub.1
(n)--illustratively a constant, .gamma..sub.1 --to generate the
correction term .gamma..sub.1 A(n-1).sup.2
E(n)e.sup.j2.pi.f.sbsp.c.sup.nT.
At this time, coefficient ##EQU15## is just beginning to appear at
the output of coefficient store 108, illustratively another serial
in/serial out shift register. The correction term at the output of
multiplier 103 is added to ##EQU16## in adder 106 to generate
##EQU17## Since at this time the first decision/conjugate product
of term D.sub.1 (n+1)--A((n+1)-1).sup.2 --is being introduced on
lead 61a, coefficient ##EQU18## is passed directly to multiplier
110, so that the latter is able to form on lead 71a the product
##EQU19## i.e., the first weighted modulated product of term
D.sub.1 (n+1). In addition, coefficient ##EQU20## is entered into
coefficient store 108 from which it will emerge for updating at the
beginning of the (n+2).sup.nd sampling period to generate
##EQU21##
Similarly, as each subsequent decision/conjugate product making up
term D.sub.1 (n+1) is introduced on lead 61a, the corresponding
coefficient emerges from coefficient store 108, is updated, and is
multiplied by that product and the harmonic
e.sup.j2.pi.f.sbsp.c.sup.nT in multiplier 110. At the end of the
(n+1).sup.st sampling period, the pulse on lead 95a clears signal
E(n) stored in multiplier 103 in preparation for storage therein of
signal E(n+1).
Althouh specific embodiments of my invention have been shown and
described, such merely illustrate the principles of my invention.
For example, although the invention has been illustrated in
conjunction with a QAM system, it is equally applicable to any
modulated system in which both the carrier phase and amplitude are
modulated, i.e., information-bearing.
Thus, it will be appreciated that numerous arrangements embodying
the principles of the invention may be devised by those skilled in
the art without departing from their spirit and scope.
* * * * *