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Description  |
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BACKGROUND
To get high quality reception, communication systems, which include radio
and television, require a strong signal that is not corrupted by noise or
interference. One form of interference that can severely degrade reception
is multipath. Multipath occurs when the transmitted signal arrives at the
receiver simultaneously from more than one direction. The multiple paths
are generally due to reflections of the transmitted signal from hills,
buildings, etc.; they can also be the result of atmospheric phenomena. The
indirect paths are longer than the direct path, and consequently, the
indirect path signals arrive at the receiver later in time than the
corresponding direct path signal. This makes them arrive at the receiver
with a different phase than the direct path signal, and, consequently,
causes distortion in both the phase and the amplitude of the received
signal. This can result in deep signal strength fades, overlapping data,
clicking, etc. Examples of multipath distortion are ghosts on TV, degraded
fidelity in commercial FM stereo, and loss of data in communication links.
Designing the antenna pattern gain characteristics to reject the indirect
paths by placing a null in their direction of arrival is one of the better
approaches to reducing multipath distortion. This eliminates the indirect
paths altogether. It is easy to accomplish when conditions are known and
do not change. But in most communication situations, conditions do change.
The adaptive array has been used to automatically change the antenna
pattern as the conditions change.
In applying an adaptive array to the general communications problem where
the direction of arrival (DOA) and the time of arrival (TOA) of the signal
of interest are unknown, the least means squared error algorithm (LMS) is
well suited. For optimal results, the LMS adaptive array requires a
reference signal which is a replica of the signal of interest.
Generation of the reference signal can pose a problem. In practice, a
replica of the transmitted signal is not available at the receiver. The
reference signal must be derived from the adaptive array output signal.
Robert Riegler and Ralph Compton (Proceedings of the IEEE, Vol. 61, No. 6,
June 1973, p. 748) have discussed the application of the adaptive array to
amplitude modulated communications signals, where the adaptive array
output signal is processed to generate a representation of the carrier of
the transmitted signal for use as the reference signal. But this approach
addresses interference signals, not the multipath problem.
R. T. Compton and D. M. DiCarlo (IEEE Transactions on Aerospace and
Electronic Systems, VOL. AES-14, NO. 4, July 1978, p. 599) and Y. Bar-Ness
(IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-18, No.
1, January 1982, p. 115) analyze another adaptive array which uses the
array output to generate the reference signal. But their system was
designed to address a signal environment in which the signal of interest
is received along with a wideband interference signal. They do not address
the multipath problem.
Ralph Compton (Proceedings of the IEEE, Vol. 66, No. 3, March 1978, p. 289)
discusses an adaptive array for communication signals using a spread
spectrum technique. The adaptive array uses knowledge of the spreading
code to generate a reference signal. August McGuffin (U.S. Pat. No.
4,217,586) has extended this approach by utilizing the multipath in the
reference signal generation. The pseudo random (PN) code based reference
signal generator can keep lock even in severe multipath fading. But both
these approaches require a known PN code be present in the transmitted
signal to generate a reference signal.
G. H. Persinger (1977 International Conference on Communications, IEEE, Pt.
III, Chicago, Ill., 12-15 June, 1977, Pp. 259-262) has used a low level PN
code placed in quadrature (90 degrees out of phase) with a transmitted AM
signal. It is used to generate the reference signal at the receiver. The
reference generation is dependent on the injection of this special signal
with a known code.
Peder Hansen (IEEE Transactions on Antennas and Propagation, Vol. AP-29,
No. 6 November 1981, p. 836) has placed a special modulated pilot signal
in the transmitted signal to be used to generate the reference signal.
This technique was used specifically to discriminate against multipath.
But it does not work without the special pilot signal.
Gayle Martin (U.S. Pat. No. 4,255,791) uses noise decorrelation to generate
a reference signal for an adaptive array. This method addresses an
environment where there is a large interfering signal, not the multipath
environment.
Kenneth F. Rilling in U.S. patent application Ser. No. 819,416, filed on
Jan. 16, 1986, entitled Anti-multipath Signal Processor, has amplitude
limited the adaptive array output signal to generate the reference signal.
This system rejects unwanted multipath and low level noise. But this work
is limited to a reference signal implementation.
In a related technology, transversal filters (single input adaptive
filters) which reduce TV ghosts by signal processing (not by using the
antenna pattern) use the known portions of the transmitted TV signal
structure to generate the reference signal (Shri Goyal, others, IEEE
Transactions on Consumer Electronics, Vol. CE-26, February 1980).
Transversal filters remove the ghosts after the received signal has been
demodulated. But, they require a large number of loops, and they are
generally microprocessor or computer based. Consequently, they are quite
complicated and expensive.
An alternative to deriving the reference signal, is the elimination of the
reference signal altogether by changing the feedback equations. Work along
this line has been performed by John Treichler in a related technology
with a single input adaptive filter for constant modulus (amplitude)
signals (John R. Treichler and Brian G. Agee, IEEE Transactions on
Acoustics, Speech, and Signal Processing, Vol. ASSP-31, No. 2, 1983, P.
459; M. G. Larimore and J. R. Treichler, International Conference of
Acoustics, Speech, and Signal Processing 1983, Boston, P. 13). The
Constant Modulus Algorithm (CMA) can be used to remove unwanted multipath
for constant amplitude signals because it exploits the amplitude
fluctuations induced by multipath. The CMA approach has limitations: (1)
It only applies to wideband signals; it can not handle narrowband signals
or an unmodulated carrier. (2) It requires a relatively large number of
adaptive loops.
To summarize, with the exception of the patent application by Kenneth
Rilling, the prior art is limited. It either does not address the
multipath problem, it applies to a very limited range of signal
classifications, its approach to the problem is complex, or it requires
special tones or codes in the transmitted signal. And consequently, with
the exception of the work by Rilling, there is no effective and
inexpensive method of removing multipath interference at the
communications receiver.
SUMMARY OF INVENTION
The object of this invention is to reduce distortions such as fading, data
overlap, multiple images, and clicking caused by multipath in
communication receivers. An adaptive array is used to reject unwanted
signals with spatial filtering by placing an antenna pattern null in the
direction of arrival of the unwanted signals. A second object of this
invention is to reduce the negative effects of other types of noise and
interference signals with amplitudes less than the amplitude of the
desired signal by rejecting them also. The invention does this for a
signal environment in which the TOA and the DOA of the desired signal and
indirect path/interference signals are unknown and for which the
transmitted desired signal contains no known codes, pilot signals, or
signal waveform structures. This is accomplished by changing the feedback
equation for the LMS adaptive array so that a reference signal is no
longer required.
In addition, feedback equation approximations lead to new feedback
equations, resulting in new CMA filter implementations.
DESCRIPTION OF FIGURES
FIG. 1 is a block diagram of a two element array for the suppression of
multipath and interference: prior art.
FIG. 2 is a block diagram of a two element adaptive array using an LMS
analog implementation: prior art.
FIG. 3 is a block diagram of an N element CMA adaptive array with tapped
delay lines having M output signals respectively.
FIG. 4 is a block diagram of the feedback function implemented by Rilling
in the reference signal model: prior art.
FIG. 5 is a block diagram of a first implementation of the feedback
function for p=1 and q=2.
FIG. 6 is a block diagram of a second implementation of the feedback
function for p=1 and q=2.
FIG. 7 is a block diagram of a first implementation of the feedback
function for p=2 and q=2.
FIG. 8 is a block diagram of a second implementation of the feedback
function for p=2 and q=2.
FIG. 9 is a block diagram of a first implementation of the approximate
feedback function for p=1 and q=2.
FIG. 10 is a block diagram of a second implementation of the approximate
feedback function implementation for p=1 and q=2.
FIG. 11 is a block diagram of a computer implementation of the invention.
FIG. 12 is the flowchart of a software CMA adaptive array and filter
implementation of the invention.
FIG. 13 is a flow chart of the approximate feedback function for a software
implementation for p=1 and q=2.
FIG. 14 is a flow chart of the feedback function for the software
implementation for p=1 and q=2.
FIG. 15 is a block diagram of a phase shifter added to the N element CMA
adaptive array and CMA filter in FIG. 3.
FIG. 16 is a block diagram of the implementation of the feedback function
for p=3 and q=1 when the range of .delta. is restricted.
FIG. 17 is a block diagram of the implementation of the feedback function
for p=1 and q=1 when the range of .delta. is restricted.
FIG. 18 is a block diagram of the implementation of the feedback function
for p=2 and q=1 when the range of .delta. is restricted.
FIG. 19 is a block diagram of the implementation of the logarithmic
feedback function.
DETAILED DESCRIPTION
Before describing the preferred embodiment of the invention in detail, a
discussion of multipath theory, adaptive arrays, and the new feedback
equation theory of the class of adaptive arrays and filters used in this
invention to solve the multipath problem will be presented to facilitate
understanding.
NATURE OF MULTIPATH
In a multipath environment the transmitted signal arrives at the receiver
from several directions simultaneously where there is a direct path and
one or more indirect paths. The indirect paths are longer than the direct
path, so the signals traveling these paths arrive at the receiver at a
later time than the direct path signal. It is this difference in the time
of arrival that causes distortion in both the amplitude and the phase of
the received signal. For example, consider angle modulation (FM, PM,
etc.); the direct path signal, in real notation, is
X.sub.1 (t)=B.sub.1 sin [w(t-R.sub.1 /c)+.alpha.f(t-R.sub.1 /c)]+n.sub.1
(t) (1)
where w is the angular frequency, t is the time, f(t) is the modulation,
B.sub.1 is a constant amplitude, R.sub.1 is the path length, c is the
speed of light, .alpha. is the phase deviation, and n.sub.1 (t) is a
random noise term. The indirect path signal has the form
X.sub.i (t)=B.sub.i sin [w(t-R.sub.i /c)+.alpha.f(t-R.sub.i /c)]+n.sub.i
(t) (2)
where the x.sub.i (t) indicates the "i"th path signal, B.sub.i is a
constant signal amplitude for the "i"th path, R.sub.i is the distance
traveled by the "i"th path signal, and n.sub.i (t) is a random noise term.
The n.sub.i (t) and n.sub.1 (t) are all independent. The X.sub.i (t)'s are
all delayed versions of the direct path signal. The total signal present
at a given point in space is the sum of the direct and indirect path
signals. Using equations (1) and (2), the total received signal can be
written as
##EQU1##
In equation (3), for mathematical convenience, the term X.sub.1 (t) has
subscript one and refers to the direct path signal, the X.sub.i (t) in the
summation, where i=2 to i=N, refers to the indirect paths signals (or the
interference signals). Summing over sinusoids, and for convenience
assuming that the noise terms are small and can be neglected, equation (3)
can be written as
E(t)=A(t) sin [wt+a(t)] (4)
where
##EQU2##
and
P.sub.i =-(wR.sub.i /c)+.alpha.f(t-R.sub.i /c).
It should be noted that if equation (4) represents the net signal present
at an antenna array phase center, it can be immediately seen that the net
signal received at each antenna element is different because the distance
traveled, R.sub.i, for the received signals is different for each antenna
element.
ADAPTIVE ARRAY
Interference signals and multipath create different signal environments for
a communications receiver. Multipath occurs when the transmitted signal of
interest arrives at the receiver simultaneously from more than one
direction. An interference source is a signal source unrelated to the
communications system, such as the signal from another transmitter, that
may or may not have the same frequency as the signal of interest.
Historically, adaptive arrays were developed to reject external
interference signals. More recently, adaptive arrays have been shown
capable of rejecting multipath.
An adaptive array is an antenna array that has adjustable weights in each
of the antenna elements which automatically adjusts the weights so that
the multipath or interference signals are rejected. The weights can be
amplitude scale factors multiplying the antenna element signals or
implementations that are equivalent to this.
To demonstrate the way in which an array with adjustable weights can reject
an indirect multipath signal or an interference signal, consider the two
element array in FIG. 1. Let antenna elements 10 be omni-directional and
let the spacing between them be a half-wave length of the desired signal.
The desired signal, P(t), arrives from the normal direction, 0 degrees, and
the multipath or interference signal I(t) arrives from 30 degrees
displaced from the desired signal. To simplify the calculation, let both
P(t) and I(t) have zero phase at the array phase center, PC, which is
located midway between the antenna elements. The output signal of each
antenna element 10 goes to a variable complex weight 26", where W.sub.1
+jW.sub.2 and W.sub.3 +jW.sub.4 correspond to elements E1 and E2
respectively. The complex weights output signals are summed in adder 30,
the output of which is the array output signal.
The signal of interest, in complex notation, is
P(t)=P.sub.o exp (jwt), (5)
where P.sub.o is the signal amplitude, t is time, and w is the signal
angular frequency. The array output signal due to the signal of interest
is
SI(t)=P.sub.o {(W.sub.1 +W.sub.3)+j(W.sub.2 +W.sub.4)} exp (jwt). (6)
The desired array output signal is an unaltered copy of the signal of
interest. By equating equations (5) and (6), and collecting the real and
imaginary terms, the required weight relationships to get the desired
output signal are
W.sub.1 +W.sub.3 =1 (7)
and
W.sub.2 +W.sub.4 =0. (8)
The unwanted indirect path signal is
I(t)=I.sub.o exp (jwt) (9)
where I.sub.o is the signal amplitude. The distance traveled by the
received signal is different for each antenna element. I(t), which is
incidenting the antenna array from an angle of 30 degrees, will arrive at
antenna element E2 with a phase lead relative to the antenna array phase
center of
.sigma.=2(1/4) sin (30)=.pi./4 (10)
radians and, similarly, it will arrive at antenna element E1 with a phase
lag of .sigma.=-.pi./4 radians. Therefore, the array output signal due to
I(t) is
SM(t)=I.sub.o {[W.sub.1 +jW.sub.2 ] exp [j(wt-.pi./4)]+[W.sub.3 +jW.sub.4 ]
exp [j(wt+.pi./4)]}. (11)
Since it is desired to reject the unwanted multipath signal, equation (11)
must equal zero. By using the relationships
exp (-j.pi./4)=(1/.sqroot.2)(1-j) (12)
and
exp (j.pi./4)=(1/.sqroot.2)(1+j) (13)
and collecting the real and imaginary terms, equation (11) gives
W.sub.1 +W.sub.2 +W.sub.3 -W.sub.4 =0 (14)
and
-W.sub.1 +W.sub.2 +W.sub.3 +W.sub.4 =0. (15)
The weights must satisfy equations (14) and (15) to reject the multipath
signal.
Equations (9), (10), (14), and (15) give 4 equations and 4 unknowns.
Solving for the weights gives
W.sub.1 =0.5, W.sub.2 =-0.5, W.sub.3 =0.5, W.sub.4 =0.5. (16)
With these weight values the antenna array will accept the signal of
interest, P(t), and reject the unwanted multipath signal, I(t). The array
is functioning as a spatial filter.
In an adaptive array the weights are changed automatically to the correct
values that reject the unwanted multipath/interference signals and accept
the signal of interest. As the signal environment changes, the weights
adapt to continue rejecting the multipath/interference. To be an adaptive
array, the simple array in FIG. 1 requires a means for automatically
changing the weights.
There are a number of approaches for changing the array weights
automatically. Many examples of adaptive arrays can be found in: Robert A.
Monzingo and Thomas W. Miller, Introduction to Adaptive Arrays, John Wiley
& Sons, New York, 1980; Bernard Widrow and Samuel D. Stearns, Adaptive
Signal Processing, Prentice-Hall, 1985; and C. F. N. Cowan and P. M. Grant
Eds., Adaptive Filters, Prentice-Hall, Inc., 1985.
The Least Means Square (LMS) adaptive array, which requires a reference
signal, is the best known and the best understood approach to
automatically adjust the weights. It is also the simplest to implement.
In the LMS adaptive array the difference between the array output signal
and the reference signal is called the error signal, .epsilon., and is
used as a measure of merit in a least means squares sense to adapt the
weights by minimizing .epsilon..sup.2. The basic theory and technology for
the LMS adaptive array has been presented by Bernard Widrow, Proceedings
of the IEEE, Vol. 55, No. 12, December 1967, p. 2143 and by Ralph Compton,
Proceedings of the IEEE, Vol. 61, No. 1, June 1973, P. 748. The books
cited in the previous paragraph also present much theory about LMS
adaptive array.
FIG. 2 shows a two element adaptive array using an LMS implementation.
After the received signals, which include the signal of interest and
multipath/interference, enter the antenna elements 10, each element splits
the signal into two components; one component is phase shifted 90 degrees
by 20', and the other component's phase is unshifted. Each signal then
goes to its respective amplitude weight 26, which are W.sub.1, W.sub.2,
W.sub.3, and W.sub.4 respectively. Because the signals going to each of
the respective antenna element weight pairs are 90 degrees out of phase,
they adjust the signal in the element in both amplitude and phase. For
element E1, the amplitude weighting is
##EQU3##
and the phase shift weighting is
.phi..sub.w =-tan.sup.-1 (W.sub.1 /W.sub.2). (17b)
Element E2 has a similar result for weights W.sub.3 and W.sub.4. The
weighted signals from weights W.sub.1, W.sub.2, W.sub.3, and W.sub.4 go to
adder 30 where they are summed. The output signal of the adder 30 is the
adaptive array output signal and it goes to subtractor 34. The second
input signal to subtractor 34 is the reference signal, which, ideally, is
a replica of the desired signal. The array output signal is subtracted
from the reference signal by subtractor 34. It is this resulting
difference .epsilon. between the array output signal and the reference
signal that is used in the LMS adaptive arrays to automatically adjust the
weights.
It can be shown that
dW.sub.i /dt=-k.gradient.Wi(<.epsilon..sup.2 >) i=1, . . . ,N (18a)
where W.sub.i is the "i"th weight, k is a constant, .gradient.Wi
(<.epsilon..sup.2 >) is the component of the gradient of <.epsilon..sup.2
> with respect to W.sub.i and <> denotes the time average of the function
contained therein. This gives for the value of the "i"th weight
W.sub.i =W0.sub.i -2k.intg.<.epsilon.X.sub.i >dt i=1, . . . , N (18b)
where W0.sub.i is the value of the "i"th weight at time zero, and X.sub.i
is the input signal to the "i"th weight. Equations (18b) are the feedback
equations for the weights in the analog implementation. The error signal
.epsilon. from subtractor 34 and the weight input signals X.sub.1,
X.sub.2, X.sub.3, X.sub.4 are multiplied by multipliers 22 respectively.
The output signals from multipliers 22 go to integrators 24 respectively.
The output signals of each of the integrators 24 is applied to its
associated weight circuit 26, where that signal is weighted. The output
signal from each weight circuit is then applied to adder 30 where they are
summed. Each set of multiplier, integrator, weight circuit and input
signal together with the error signal, subtractor, and adder constitute an
adaptive loop.
The equivalent feedback equation for a discrete/digital implementation of
the LMS adaptive array is
W.sub.i (j+1)=W.sub.i (j)-2k .gradient.Wi(<.epsilon.(j).sup.2 >) i=1, . . .
N (19a)
and
W.sub.i (j+1)=W.sub.i (j)-2k.epsilon.(j)X.sub.i (j) i=1, . . . , N (19b)
where the antenna element input signals are discrete time samples with
X.sub.i (j) being the "i"th antenna element input signal at the "j"th time
sample, .epsilon.(j) is the error signal at the "j"th time sample, W.sub.i
(j) is the amplitude weight for the "i"th antenna element input signal at
the "j"th sample, and W.sub.i (j+1) is the weight value update at the
"j+1" time sample for the "i"th antenna element input signal.
The adaptive array is not restricted to two antenna elements and a 90
degree phase delay. It can have many antenna elements. And it can have
many time (phase) delays in each antenna element.
CMA ADAPTIVE ARRAYS
The LMS adaptive array minimizes the mean square error between the array
output signal and a reference signal. The CMA filter developed by
Treichler minimizes a positive definite measure of the signal modulus
variation given by
J.sub.pq (t)=<.vertline..vertline.Y(t).vertline..sup.p -.delta..sup.p
.vertline..sup.q > (20 )
where "p" and "q" are constants, .delta. is a positive constant, and Y(t)
is the adaptive filter output signal at time t. The feedback equation for
the "i"th weight is
W.sub.i (t)=WO.sub.i -2k.intg..gradient..sub.Wi {J.sub.pq (t)}dt (21)
where k and WO.sub.i are constants and .gradient..sub.Wi {J.sub.pq (t)} is
the component of the gradient of J.sub.pq (t) with respect to W.sub.i. It
can be shown that
.gradient..sub.Wi J.sub.pq =<qpX.sub.i
(t)Y(t).vertline.Y(t).vertline..sup.p-2 (.vertline.Y(t).vertline..sup.p
-.delta..sup.p).sup.q-1 [sgn(.vertline.Y(t).vertline..sup.p
-.delta..sup.p)].sup.q > (22)
where X.sub.i (t) is the input signal to the "i"th weight and
##EQU4##
The feedback equations can be rewritten in the form
W.sub.i (t)=W0.sub.i -2k.intg.<.epsilon.X.sub.i (t)>dt (23)
where .epsilon. is determined from equations (21) and (22). Table I shows
.epsilon. for different values of p and q.
TABLE I
______________________________________
p,q Eq #
______________________________________
1,1 {Y(t)/.vertline.Y(t).vertline.}sgn[.vertline.Y(t).vertline. -
.delta.] (24)
1,2 2{Y(t)/.vertline.Y(t).vertline.}[.vertline.Y(t).vertline. - .delta.]
(25)
2,1 2Y(t)sgn{.vertline.Y(t).vertline..sup.2 - .delta..sup.2 }
(26)
2,2 4Y(t){.vertline.Y(t).vertline..sup.2 - .delta..sup.2 }
(27)
1,3 3{Y(t)/.vertline.Y(t).vertline.}{.vertline.Y(t).vertline. - .delta.}.
sup.2 sgn[.vertline.Y(t).vertline. - .delta.]
(28)
1,4 4{Y(t)/.vertline.Y(t).vertline.}{.vertline.Y(t).vertline. - .delta.}.
sup.3 (29)
3,1 3Y(t).vertline.Y(t).vertline.sgn{.vertline.Y(t).vertline..sup.3 -
.delta..sup.3 } (30)
3,2 6Y(t).vertline.Y(t).vertline.{.vertline.Y(t).vertline..sup.3 -
.delta..sup.3 } (31)
______________________________________
Equations of .epsilon. for values of "p" and "q" other than those shown in
Table I have similar but more complicated form.
Feedback equation (25) is mathematically the same, within a sign and scale
factor, as the equation obtained for the error signal in an LMS adaptive
array that generates its reference signal by amplitude limiting the
adaptive array output signal (Kenneth Rilling, U.S. patent application
Ser. No. 819,416).
The adaptive array implementation of equation (25) results in a means for
removing multipath that is very different from the CMA filter
implementation:
(1) The CMA filter exploits the fact that for a constant modulus signal,
multipath causes the amplitude to fluctuate significantly when the signal
has a wide bandwidth. The LMS adaptive array is a spatial filter that also
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