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Description  |
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FIELD OF THE INVENTION
The invention relates generally to spread spectrum communication systems
operating in the presence of multipaths and more particularly to estimates
of path gain in receivers of such communication systems.
BACKGROUND OF THE INVENTION
Communication systems designed to incorporate the characteristic of
communicating with many remote subscriber units for brief intervals on the
same communication channel are termed multiple access communication
systems. One type of communication system which can be a multiple access
system is a spread spectrum system. In a spread spectrum system, a
modulation technique is utilized in which a transmitted signal is spread
over a wide frequency band within the communication channel. The frequency
band is much wider than the minimum bandwidth required to transmit the
information being sent. A voice signal, for example, can be sent with
amplitude modulation (AM) in a bandwidth only twice that of the
information itself. Other forms of modulation, such as low deviation
frequency modulation (FM) or single sideband AM, also permit information
to be transmitted in a bandwidth comparable to the bandwidth of the
information itself. However, in a spread spectrum system, the modulation
of a signal to be transmitted often includes taking a baseband signal
(e.g., a voice channel) with a bandwidth of only a few kilohertz, and
distributing the signal to be transmitted over a frequency band that may
be many megahertz wide. This is accomplished by modulating the signal to
be transmitted with the information to be sent and with a wideband
encoding signal.
Generally, three types of spread spectrum communication techniques exist,
including:
Direct Sequence
The modulation of a carrier by a digital code sequence whose bit rate is
much higher than the information signal bandwidth. Such systems are
referred to as "direct sequence" modulated systems.
Hopping
Carrier frequency shifting in discrete increments in a pattern dictated by
a code sequence. These systems are called "frequency hoppers." The
transmitter jumps from frequency to frequency within some predetermined
set; the order of frequency usage is determined by a code sequence.
Similarly "time hopping" and "time-frequency hopping" have times of
transmission which are regulated by a code sequence.
Chirp
Pulse-FM or "chirp" modulation in which a carrier is swept over a wide band
during a given pulse interval.
Information (i.e. the message signal) can be embedded in the spread
spectrum signal by several methods. One method is to add the information
to the spreading code before it is used for spreading modulation. This
technique can be used in direct sequence and frequency hopping systems. It
will be noted that the information being sent must be in a digital form
prior to adding it to the spreading code, because the combination of the
spreading code and the information, typically a binary code, involves
module-2 addition. Alternatively, the information or message signal may be
used to modulate a carrier before spreading it.
Thus, a spread spectrum system must have two properties: (1) the
transmitted bandwidth should be much greater than the bandwidth or rate of
the information being sent and (2) some function other than the
information being sent is employed to determine the resulting modulated
channel bandwidth. Spread spectrum communication systems can be
implemented as multiple access systems in a number of different ways; one
type of multiple access spread spectrum system being a direct sequence
code division multiple access (DS-CDMA) system.
Multiple communication channels are allocated by assigning unique spreading
code to each (and every) user in a shared frequency band. As a result,
transmitted signals are in the same broad frequency band of the
communication channel, but within unique portions of the broad frequency
band assigned by the unique spreading codes. These unique spreading codes
preferably are orthogonal to one another such that the cross-correlation
between the spreading codes is approximately zero. Particular transmitted
signals can be retrieved from the communication channel by despreading a
signal representative of the sum of signals in the communication channel
with a spreading code related to the particular transmitted signal which
is to be retrieved from the communication channel. Further, when the
spreading codes are orthogonal to one another, the received signal can be
correlated with a particular spreading code such that only the desired
signal related to the particular spreading code is enhanced while the
other signals are not enhanced.
Spread spectrum, and other communication systems, are often subject to
multipath distortion, in which several copies of a transmitted signal are
received with different delays, gains and phases as a result of multiple
radio path reflections. A type of receiver particularly well suited for
reception of multipath spread spectrum signals is a RAKE receiver, which
is well known in the art. The RAKE receiver is comprised of "fingers"
which optimally combine the separate paths in the receiver. In general,
the RAKE receiver can be analogized to a matched filter, where the path
gains of each "finger," like the taps of a matched filter, need to be
estimated to construct the RAKE receiver to accurately receive a
transmitted signal. Since a transmitted signal is subject to many
corruptions on its way to a receiver (multipath effects, Rayleigh fading,
etc.), the receiver must estimate the path gains utilizing the corrupted
transmitted signal. Clearly, the eventual received signal will only be as
good as the path gain estimation per "finger" in the RAKE receiver.
Thus a need exists for a receiver, and particularly a RAKE receiver, that
provides an accurate path gain estimate for each "finger" of the RAKE
receiver without relying on the corrupt transmitted signal to make the
estimate.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 generally depicts a portion of a coherent RAKE receiver which
estimates path gain in accordance with the invention.
FIG. 2 depicts a hyperbolic tangent function tanh(x).
DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT
A "blind block" path gain estimation scheme, based on a maximum likelihood
criterion, is described in accordance with the invention. It is "blind" in
that preliminary hard decisions on coded bits (i.e., coded bits from the
corrupt transmitted signal) are not used. Instead, a form of soft
decisions are used. It is a "block" scheme in that the complex path gains
are estimated for an isolated block, for example a block of B correlator
outputs. In the preferred embodiment, the receiver which effectively
utilizes the "blind block" path gain estimation scheme is a coherent RAKE
receiver implemented in a code-division multiple access (CDMA)
communication system. In an illustrative embodiment, blocks of data
comprising B=36 coded bits lasting 1.25 ms are transmitted, separated from
other blocks by pseudo-random time intervals. The "blind block" path gain
estimation scheme overcomes the shortcomings of typical CDMA systems where
there may be no assurance of continuous transmission upon which to base a
FIR filter-type prediction scheme. One consequence of this, or any other
estimation scheme not relying on knowledge of transmitted data symbols, is
that there is phase ambiguity in the estimates. As a result, the data bits
must be differentially encoded, and errors will tend to occur in pairs.
A coherent RAKE receiver requires accurate estimates of channel multipath
components to do optimum combining in a coherent spread spectrum
communication system. It processes the complex-valued outputs of
correlators or matched filters
##EQU1##
from L different multipath components or diversity antennas. Typically, L
is 1 to 4. In equation (1), n is the time index, N is the number of CDMA
chips per coded bit, Tc is the chip interval, y(t) is the complex received
waveform containing the desired signal plus noise, s(t) is the CDMA
spreading code for the desired signal, t.sub.m is the time delay of the
mth path (assumed accurately estimated), and * means complex conjugate.
Each sample u.sub.m (n) is then of the form
u.sub.m (n)=c(n)f.sub.m (n)+v.sub.m (n) (2)
where c(n)=.+-.1 is an unknown binary coded bit and v.sub.m (n)is a complex
noise sample. The noise v.sub.m (n) actually includes interfering CDMA
signals, thermal noise, and other multipath components at different path
delays (the contribution of these other multipath components is expected
to be small if the spreading sequence has low autocorrelation sidelobes
and N is large).
The objective is to find an estimate {f.sub.m (n), m=1, 2 . . . L, n=1, 2,
. . . B} of the path gains, given a block of B successive correlator
outputs {u.sub.m (n), m=1,2 . . . L, n=1,2, . . . B} for a given path
delay. Once such an estimate is found, the RAKE receiver forms
##EQU2##
which is then passed to a decoder for processing.
The L complex path gains f.sub.m (n) can vary significantly with time, due
to Doppler effects. Furthermore, co-channel interference will give rise to
relatively high noise components in the {u.sub.m (n)}. The estimates
{f.sub.m (n)} must be obtained from a block of B successive samples
u.sub.m (n), where B is typically around 36, corresponding to a time
duration of 1.25 ms in a representative CDMA system with a 9.6 kb/s data
rate, and employing a rate 1/3 binary code. Moreover they are to be
obtained in the absence of knowledge or explicit estimates of the c(n)
(i.e., without use of the corrupt transmitted signal).
A "blind block" estimation scheme can be derived and evaluated based on a
maximum likelihood (ML) principle. FIG. 1 generally depicts a portion of a
coherent RAKE receiver which estimates path gain in accordance with the
invention. A block of B samples u.sub.m (n) is stored in a recirculating
delay line or other memory device. What follows is a description of an
iterative algorithm for processing this block to achieve the estimates
{f.sub.m (n) for m=1,2 . . . L and n=1,2 . . . B}.
(1) Start with parameters a.sub.m (i)=1, b.sub.m (i)=0, m=1 , . . . L, i=1.
(2) Start the ith iteration, as shown by point 1 in FIG. 1, by
approximating f.sub.m (n) by
f.sub.m (n,i)=a.sub.m (i)+b.sub.m (i)[n-(B+1)/2] (4)
a.sub.m (i) is the ith iteration estimate of the average value of f.sub.m
(n) in the block and b.sub.m (i) is the ith iteration estimate of its rate
of change (slope). The block duration is assumed short enough relative to
the path time variation that it varies approximately linearly with time.
(3) Form a "soft decision" c(n,i), as shown at point 2 of FIG. 1, as
follows:
##EQU3##
where tanh(), as depicted in FIG. 2, is the hyperbolic tangent function
that behaves like a saturating amplifier or soft limiter. The
.sigma..sub..upsilon..sup.2 /2 is the receiver's estimate of the variance
of the each of the real and imaginary parts of the complex noise samples.
(4) Multiply c(n,i) by (1/B)u.sub.m (n), as shown at point 3 of FIG. 1, and
accumulate to form
##EQU4##
(5) Multiply c(n,i) by (12/B(B.sup.2 -1))(n-(B+1)/2)u.sub.m (n), as shown
at point 4 of FIG. 1, and accumulate to form
##EQU5##
(6) Update a.sub.m (i) and b.sub.m (i) on the ith iteration, as shown at
point 5 and 6 of FIG. I respectively, using a stochastic approximation
algorithm:
a.sub.m (n,i+1)=a.sub.m (n,i)-k.sub.i (a.sub.m (n,i)-p.sub.m (a,b))(8a)
b.sub.m (n,i+1)=b.sub.m (n,i)-k.sub.i (b.sub.m (n,i)-q.sub.m (a,b))(8b)
where k.sub.i =i/(i+K), and K is a suitable constant, such as K=20.
(7) Increment i by 1 and go back to step (2), until i reaches a fixed
count, such as i=30.
When the iterations are completed the estimates {f.sub.m (n)} are given by
(4). Note that there will be a sign ambiguity (.+-.1) in this or any other
estimation algorithm not making use of the true bits {c(n)}. Therefore
differential encoding of the bits must be used. When the ith iteration has
been completed, the entire block of B matched filter outputs u.sub.m (n)
is processed, and corresponding soft decisions c(n,i) are formed, to
update a.sub.m (i) and b.sub.m (i).
Expressions for a.sub.m (i) and b.sub.m (i) are derived as follows. The
path gain estimator is to determine f, the vector representing the complex
tap gains, given u, the vector which represents a sequence of B matched
filter outputs. Thus, as stated above, maximum likelihood (ML) is chosen
as the optimization criterion; i.e.
f=arg max{p(u.vertline.f)}
where p(u.vertline.f) is the conditional probability density of u given f.
The set of B c(n)'s which are contained in u are denoted by the vector c.
The components of c are assumed to be +1 or -1 independently, and with
equal probability. Then
##EQU6##
The path gains f.sub.m (n) vary with time n due to doppler. For example, a
doppler frequency of 85 Hz corresponds to a vehicle speed of about 60 m/h
and a carrier frequency of about 900 Mhz. A block length B of 1.25 ms,
then corresponds to about 11% of one doppler cycle. During this short time
interval, it is reasonable to approximate the variation of f.sub.m (n) as
being linear in n; i.e.
##EQU7##
where a.sub.m and b.sub.m are fixed parameters to be estimated; a.sub.m is
the average path gain of the mth path in a block and b.sub.m is its rate
of change, or slope. The quantity (B+1)/2 appearing in equation (11) was
chosen so that the summation of the second term in (11) from 1 to B is
zero. Note that the estimation problem now is to maximize
p(u.vertline.a,b) with respect to the vectors a and b which represent the
{a.sub.m } and {b.sub.m }.
Carrying out the averaging in (9) with respect to the independent random
variables {c(n)=.+-.1} we get
##EQU8##
To maximize p(u.vertline.a,b) with respect to the a's and b's, we set the
derivatives of p(u.vertline.a,b) with respect to a.sub.m and b.sub.m equal
to zero, to get
##EQU9##
for m=1,2, . . . L, and
##EQU10##
for m=1,2, . . . L.
The argument of the tanh function in (13) and (14) is the output of the
RAKE path combiner for the path estimates given by (11). Note that for
high signal-to-noise ratio (i.e. .sigma..sub..upsilon..sup.2 approaching
zero) the tanh function in (13) and (14) approaches the signum function
.+-.1, and thus it would constitute a hard preliminary decision on c(n)
based on RAKE receiver outputs. Expressions (13) and (14) can be
interpreted as weighted averages of products of u.sub.m (n) and
##EQU11##
u.sub.m (n), respectively, with soft decisions (determined by the tanh
function) on c(n). Note also that there will be a .+-.1 ambiguity in the
estimates; thus as mentioned earlier, differential encoding of the data
bits will be necessary.
Equations (13) and (14) are nonlinear equations which must be solved for
a.sub.m and b.sub.m. They may be rewritten as
a-p(a,b)=0 (15)
b-q(a,b)=0 (16)
where p(a,b)and q(a,b) are L-dimensional vectors whose m.sup.th components
are the right hand sides of (13) and (14) respectively. These equations
can be solved iteratively using stochastic approximation; i.e. on the ith
iteration,
a(i)=(1-k.sub.i)a(i-1)+k.sub.i p(a(i-1),b(i-1)) (17)
b(i)=(1-k.sub.i)b(i-1)+k.sub.i q(a(i-1),b(i-1)) (18)
where k.sub.i are decreasing step sizes; e.g. k.sub.i =1/(i+1). Note that
one solution of these equations is a=b=0. However, analysis has revealed
that this solution corresponds to a minimum of the likelihood function,
and so there is no danger of a stochastic approximation algorithm, with a
non-zero initial condition, converging to this solution.
The "blind block" path gain estimation scheme makes possible coherent BPSK
coded modulation for a digital cellular CDMA communication system
operating in a rapidly-fading, interference-limited environment.
Simulations have shown roughly a 3 dB improvement over noncoherent
orthogonal schemes which are utilized for the reverse channel of typical
CDMA communication systems. Furthermore, the scheme does not rely on the
existence of preliminary data decisions and is based on block-by-block
transmission rather than continuous transmission. Also, the coherent mode
of operation made possible by this scheme can be implemented with a single
matched filter at the receiver matched to the appropriate spreading
sequence. This would simplify synchronization, and facilitate rapid
response to the sudden appearances and disappearances of multipath
components associated with vehicle movement in urban environments.
While the invention has been particularly shown and described with
reference to a particular embodiment, it will be understood by those
skilled in the art that various changes in form and details may be made
therein without departing from the spirit and scope of the invention. For
example, in alternate embodiments, the scheme could include a monitor for
the presence of weak paths, and when detected, they would be eliminated
from further consideration. This can be done since it has been found that
there is little value in including paths in equation (3) for which f.sub.m
(n) is relatively small. Furthermore, the hyperbolic tangent function
appearing in equation (5) and FIG. 2 could be approximated by a digital
look-up table, implemented in a read only memory (ROM), or by a soft
limiter device.
* * * * *
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