Apparatus and method for utilizing a blind equalizer based on a Bayesian symbol sequence estimator for use in digital communication

A Bayesian blind equalizer which approximates the optimum symbol-by-symbol detector for an unknown intersymbol interference pattern in a communication channel is provided in a plurality of parallel processors. Each processor operates in parallel from a common data bus with each of the other processors. Each of the processors in turn generates an estimated signal and updated metric for the communication channel for a corresponding one of each of the possible data subsequences which could cause intersymbol interference. The estimated signals or innovations are then combined with the updated metrics in a supervisory processor to generate unconditional channel coefficients for the next received data sample. Using the estimated channel coefficients and received data samples, the transmitted data sample is reliably decoded notwithstanding intersymbol interference without the use of data preambles or training data and notwithstanding that the channel coefficients may be rapidly varying.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The invention relates to the field of digital communication and in 
particular to circuits and methods for correcting for multipath 
interference or intersymbol interference in digital communication 
channels. 
2. Description of the Prior Art 
In any type of communication channel, whether it be by wire or radio 
transmission, the digital information waveform becomes smeared or spread 
in time so that the bits or data become at least partially superimposed on 
each other in the received signal. In the case of cellular telephones, 
this may occur as a result of the transmitted signal reaching the 
receiving station by a multiple number of paths, each having substantially 
different path lengths. In other types of communication channels, data 
smearing can occur due to bandwidth limitations. To add to the complexity, 
the physical causes of data smearing in communication channels is time 
dependent. 
Therefore, the prior art has developed equalizers for sorting out the true 
signal from the data smeared signal. These circuits must be able to 
perform their iterative functions to converge quickly to a unique solution 
and to do so in a manner which will rapidly track the time variations of 
the channel communication characteristics. 
The prior art has used recursive least squares methodologies employed in 
adaptive equalizers for this purpose. See, M. S. Mueller, "Least-Squares 
Algorithms for Adaptive Equalizers"; Bell Systems Technical Journal, Vol. 
60, (October, 1991). However, recursive least-squares methods require some 
type of training using a known data sequence or a data preamble in 
combination with a decision directed adaptation. In systems in which there 
is a time-division multiple access (TDMA) systems such as that proposed 
for cellular telephones, the channel estimation or equalization problem is 
particularly difficult, since only a very short preamble is available for 
equalizer training and the channel characteristics vary greatly from one 
communication time slot to the next. 
The use of Bayesian blind equalizers which approximate the optimum 
symbol-by-symbol detector for unknown intersymbol interference (ISI) 
channels is known. For a discussion of the class of algorithms of this 
type, see for example, R. A. Iltis el.al., "Recursive Bayesian Algorithms 
for Blind Equalization", Proceedings of the Asilomar Conference on 
Signals, Systems and Computers, Pacific Grove, Calif., pp. 710-15 
(November, 1991); and K. Giridhar et.al., "Bayesian/Decision-Feedback 
Algorithm for Blind Adaptive Equalization"; Optical Engineering, Vol. 31, 
pp 1211-23 (1992), both incorporated herein by reference. These 
methodologies employ parallel structures well suited to very large scale 
integration. Furthermore, the Bayesian equalizers implement the 
methodology extremely rapidly, e.g. within as few as 20 data symbols when 
Kalman filter channel estimators are employed, and can track rapid 
variations (large Doppler spread) in the effective channel coefficients. 
In contrast, known blind equalization methodologies, i.e. those that do not 
require preambles or training, such as constant modulus methodologies as 
described by J. R. Treichler et.al., "A New Approach to Multipath 
Correction of Constant Modulus Signals"; IEEE Transactions on Acoust. 
Speech and Sig. Proc., Vol. ASSP-31, pp. 459-72 (1983) and the Bussgang 
type techniques typically require thousands of data symbols in order to 
converge to a unique solution. Furthermore, constant modulus methodologies 
and the Bussgang methodologies only partially open the eye of the 
intersymbol interference channel and once the open eye condition is met, 
the blind equalizer of the prior art must be switched off and a 
conventional decision feedback equalizer turned on to obtain adequate bit 
error rate performance. Furthermore conventional decision feedback 
equalizers are prone to catastrophic error propagation particularly when 
the channel characteristics are rapidly changing. Still further, 
conventional decision feedback equalizers are incapable of blind start up 
and require transmission of the training sequence if a separate blind 
equalization methodology is not available. 
What is needed is a Bayesian blind equalizer which can assume dynamic 
channel control and provide a performance approaching that of an optimum 
symbol-by-symbol detector. What is further needed is a Bayesian equalizer 
that can operate continuously providing both blind start up and tracking 
of time varying channels. 
Therefore, what is needed is some type of blind equalization that can be 
performed without the use of a preamble or training, which can be 
effectively implemented even when the communication channel 
characteristics vary rapidly, and which converges rapidly to a unique 
decision and solution without a large number of data symbols being 
required. 
BRIEF SUMMARY OF THE INVENTION 
A Bayesian blind equalizer which approximates the optimum symbol-by-symbol 
detector for an unknown intersymbol interference pattern in a 
communication channel is provided in a plurality of parallel processors. 
Each processor operates in parallel from a common data bus shared by the 
other processors. Each of the processors in turn generates an estimated 
signal and updated probability metric for the communication channel for a 
corresponding one of each of the possible data subsequences which could 
cause intersymbol interference. The estimated signals or innovations are 
then combined with the updated metrics in a supervisory processor to 
generate unconditional channel coefficients for the next received data 
sample. Using the estimated channel coefficients and received data 
samples, the transmitted data sample is reliably decoded notwithstanding 
intersymbol interference, without the use of data preambles or training 
data, and notwithstanding that the channel coefficients may be rapidly 
varying. 
More specifically the invention is an apparatus for performing blind 
equalization of digital waveforms received over a communication channel 
comprising a memory for storing every possible data subsequence in which 
intersymbol interference could occur and for storing updated channel 
coefficients. A first data bus is coupled to the memory for communicating 
received data signals, stored data subsequences and stored communication 
channel coefficients. A plurality of signal processors are each coupled in 
parallel to the first data bus. Each processor generates estimated 
received data signals and updated estimated communication channel 
coefficients. Each processor generates the estimated received data signals 
and estimated communication channel coefficients for one of the stored 
possible data subsequences. A second data bus is coupled in parallel to 
the plurality of signal processors for communicating the estimated data 
signals and updated communication channel coefficients. A central 
processing circuit is coupled to the first and second data buses for 
controlling operation of the first and second data buses and the plurality 
of signal processors, for estimating unconditional channel coefficients, 
for storing the estimated unconditional channel coefficients in the 
memory, and for decoding the received data according to a Bayesian 
estimation scheme based on the estimated signals and updated communication 
channel coefficients for each of the stored possible subsequences. As a 
result, the received data which is subject to data smearing is reliably 
decoded notwithstanding intersymbol interference and without the use of 
training data or signaling preambles. 
In one embodiment the central processing circuit comprises a supervisory 
processor and an address bus coupled to the supervisory processor and 
memory for communication therebetween. 
The memory is comprised of a read only memory for storing the plurality of 
sets of data subsequences and a random access memory for temporarily 
storing the unconditional channel coefficient estimates. 
Each of the signal processors comprises a circuit for computing an 
estimated received value (innovation) for each one of the predetermined 
number of possible data subsequences. 
Each of the signal processors further comprises a corresponding channel 
estimator for computing a normalized least squares update of the channel 
coefficient estimates read from the first data bus. 
The apparatus is used in combination with a transmitter and each of the 
signal processors further comprises a read only memory (g-ROM) for storing 
a corresponding pulse function, g(t), corresponding to the transmitter. 
The predetermined number is four and wherein four of the signal processors 
comprise the plurality of parallel signal processors. 
The invention is also characterized as a method for communicating digital 
information in a communication channel subject to intersymbol interference 
by using blind equalization comprising the steps of receiving a sample 
r(k) and determining the likelihood of having received the sample given a 
possible data sample sequence and given a sequence of prior received 
samples. The likelihood is p(r(k).vertline.d.sub.i.sup.k,L, r.sup.k-1) for 
each possible data subsequence. d.sub.i.sup.k,L. The probability that the 
sequence of data signals possibly received given the received samples 
including the presently received sample is updated. The updated metric is 
P(d.sub.i.sup.k,L .vertline.r.sup.k). The updated channel coefficient 
corresponding to the communication channel is conditionally estimated for 
each possible data subsequence of possible intersymbol interfering 
samples. The channel coefficients for the communication channel for each 
next possible subsequence, d.sub.i.sup.k+1,L, are unconditionally 
estimated for every possible intersymbol interfering received sample for 
the next received data sample. The next data sample, r(k+1), is then 
received and the process is repeated. As a result, data may be decoded 
notwithstanding intersymbol interference without the use of data preambles 
or training data. 
The method further comprises the step of decoding the transmitted data 
sequence from the received data sequence by selecting the oldest received 
data symbol from the most probable data subsequence when the oldest 
received data symbol can no longer be involved in intersymbol 
interference. 
The steps of updating the probability that the sequence of data signals 
possibly received given the received samples including the presently 
received sample, and the step of conditionally estimating the updated 
channel coefficient corresponding to the communication channel for each 
possible data subsequence of possibly intersymbol interfering samples are 
simultaneously performed for each possible data subsequence, 
d.sub.i.sup.k,L. 
The invention can be better visualized by now turning to the following 
drawings wherein like elements are referenced by like numerals.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
In the illustrated embodiment, what is described is a Bayesian blind 
equalizer circuit and methodology which has application in all types of 
communication channels and is particularly adapted for use in 
time-division multiple access mobile digital radio. The illustrated bit 
rate is 16 kilobits per second although it is anticipated that much higher 
bit rates can be accommodated. The Bayesian equalizer of the invention 
uses up to four parallel adaptive channel estimators each of which have an 
operation based on a normalized least-squares method of operation. The 
bank of channel estimators is implemented in a high speed integrated 
circuit. A programmable digital signal processing device is employed as a 
supervisory circuit and is used to generate metric updates for final 
symbol decisions. It is also entirely within the scope of the invention 
that the programmable digital single processor will be replaced by a 
custom logic integrated circuit processor for implementing in hardware the 
signal processing described below. 
Consider first a simplified illustration of the problem. A driver driving 
down the freeway uses a cellular, low power phone to contact a cellular 
base station a few miles away. The communication channel is generally line 
of sight, but the base station also receives a number of reflected signals 
from the car phone. The car phone does not have a directional antenna for 
the least reason of which the user has no idea where the base station is. 
The car phone transmits its signal therefore in every direction. 
Additional paths or signal traces of the transmitted message may, for 
example, bounce off a passing overpass, a nearby high rise building, an 
oncoming eighteen wheeler, a passing cloud etc.. All these signals of the 
original transmission arrive at slightly different times at the base 
station. The resulting degradation in an analog voice signal may be a 
slight echo, noise, and loss of sound quality. Recipients of current 
cellular car phone calls are familiar with the poor quality sometimes 
encountered in such calls. The poor quality is acceptable, because the 
human brain is still one of the world's best computers for picking out 
data patterns or meaningful information, i.e. the caller's voice, from 
noisy signals. The problem becomes exacerbated however when you attempt to 
transmit digital data to a nonintelligent computer. If it looks like a 1 
or 0, the ordinary computer has no way of picking out the meaningful 1's 
and 0's from those which shouldn't be there. Everything the computer 
receives is equally meaningful, therefore in a bad channel, nothing 
becomes meaningful. The message will be hopelessly garbled. If the 
receiving computer had some way of picking out the meaning or true signal, 
then we could carry on conversations on cellular car phones with near 
perfect digital quality sound, in stereo if desired. 
In very simplified terms the invention solves this problem without having 
any information whatsoever about how bad or what the communication channel 
is doing to corrupt the signal, but makes its best guess for each possible 
logical signal which could have been transmitted. The invention guesses 
what the communication is doing to corrupt the signal. At first the guess 
is a wild one, but the invention quickly corrects it to make better and 
better guesses. Guessing how the data is being corrupted, the invention 
deduces what it would expect to receive for every possible logical signal 
which could have been sent and possibly subject to corruption. This 
estimated received signal is compared in parallel processors against what 
was actually received for each possible transmitted sequence of data. The 
errors revealed by the comparison are then used to make an improved guess 
as to what the communication channel is doing to the data. This is termed 
an updating of the effective channel coefficients. Based on the new guess 
for the data corruption a new expected received signal is estimated for 
the next data symbol received, again for every possible logical sequence 
of data which could have been sent and subject to corruption. 
The process continues with each new data symbol and the guesses are 
improved each time. Even more desirable, the guesses very quickly and 
naturally track the changes in the communication channel's behavior. When 
the car zooms by the base station and the Doppler effect corrupts the 
received data, the invention sees it and automatically accounts for it. 
Eventually enough time passes since the data was transmitted that no 
better information can be obtained with respect to what the communication 
channel was doing to it when it was sent. At that point the invention has 
attached a probability to each possible logical sequence of data that 
could have been sent based on its degree of match to the actually received 
signal. The oldest data symbol in the most probable data sequence is then 
chosen as the most likely data symbol that was sent at that time. Thus, 
symbol by symbol the true or very likely the true data transmission is 
divined from the received signal notwithstanding how bad the data channel 
is, how it changes, or whether the receiving station has any knowledge of 
the quality of the data channel or nature of the data being sent to it. If 
in fact the receiving channel makes a bad guess as to the data, the error 
is restricted to the one bad data symbol and is not propagated because the 
estimated data is constantly being revised based on a constantly revised 
estimate of how bad the channel is for every possible data sequence that 
ever could have been sent and been corrupted. 
Before considering the circuitry of the invention, first consider the 
methodology which is implemented in it in the general communication 
scenario of the illustrated embodiment. FIG. 1 is a highly idealized block 
diagram of the communication scenario. A data sequence, d(n), is generated 
in a transmitter 10. In the illustrated embodiment, the transmitter 
waveform in general is comprised of a sequence of quadrature amplitude 
modulated pulses corresponding to the data sequence d(n). Any data format 
now known or later devised may be used. These pulses are transmitted by 
wire or wireless though a channel 12. Channel 12 can be modelled as 
essentially a tapped-delay line or in discrete time, a finite impulse 
response filter. The receiver 14 can generally be thought of as a Nyquist 
sampler with an anti-aliasing filter (not shown) in combination with a 
Bayesian blind equalizer 16. The Bayesian equalizer 16 is described in 
greater detail below in connection with FIG. 2. Again the exact nature of 
the transmitter, channel or receiver is not critical to an understanding 
of the invention or to its operability. 
The transmitted waveform in the model of FIG. 1 is modelled by Equation 1 
where d(n) is a complex-valued data sequence for quadrature amplitude 
modulated pulses and g(t) is a bandwidth efficient pulse, such as a raised 
cosine pulse. 
##EQU1## 
where t is time and T the period of a single data symbol. If d(n) is 
transmitted as binary phase shifted keyed pulses, it takes on the values + 
or -1. If quadrature phase shift keyed pulses instead are used, then d(n) 
is a series of complex numbers taking on the four possible values + or -1, 
and + or -j. 
In FIG. 1, transmitter 10 multiplies the pulse generator input, g(t), by 
the current data symbol, d(n), and then upconverts the baseband signal of 
Equation 1 into a transmission frequency for communication over channel 
12. 
Channel 12 may, for example, be a subscriber-loop telephone line with voice 
band modems, or a radio frequency channel in a mobile, time division 
multiple access (TDMA) system. In many applications, channel 12 can be 
modeled as a time varying digital filter with an impulse response, h(k, 
n), given by Equation 2 below, where .delta.(k) is a unit impulse, f.sub.1 
(k) the channel coefficients describing the behavior of channel 12, and 
N.sub.f represents the number of data symbols or data periods in which 
intersymbol interference can practically be expected. 
##EQU2## 
In general, only N.sub.f -1 past data symbols of the data sequence d{n}, 
would interfere with or be spread over the detection of the currently 
transmitted symbol, d(n). N.sub.f is determined by the characteristics of 
channel 12. In many practical embodiments such as normal TDMA, N.sub.f can 
be practically and safely treated as equal to 4, in other words, typically 
no more than three prior digital pulses will spread to interfere with 
current pulse being transmitted. 
The Nyquist sample is received by digital receiver 14 after down-conversion 
to baseband and is modelled by the sequence r(k) described as a complex 
valued series in Equation 3 below, where f.sub.1 (k) are the time varying 
channel coefficients in Equation 2, .tau.(k) is the symbol timing jitter, 
and the additive sequence, n(k), represents a combination of receiver 
internal amplifier and channel noise which is typically modeled as white 
Gaussian noise. 
##EQU3## 
It will be helpful in understanding the methodology to be able to refer to 
and bear in mind that certain data subsequences and cumulative data 
sequences are received or transmitted as defined below in Equation 4. 
##EQU4## 
The cumulative sequence, r.sup.k, represents all Nyquist samples actually 
received from a start time, k=0, to the present time, k. The cumulative 
sequence, d.sub.i.sup.k, represents the ith sequence of all logically 
possible data sequences beginning from the start time to the present. For 
example, in the case of a binary signal across two time periods, k=0 to 1, 
there are four possible sequences, d.sub.i.sup.1, namely {0, 0}, {1, 0}, 
{0, 1} and {1, 1}. In general in binary signaling, there will be 2.sup.k 
logically possible cumulative sequences for d.sub.ik. The subsequence 
d.sub.i.sup.k,L represents the data symbols directly contributing to 
intersymbol interference. Typically, L is equal to N.sub.f+1 since there 
is an uncertainty in timing which adds an additional symbol duration to 
possible intersymbol interference. As discussed above, where N.sub.f is 
practically treated as equal to 4, in the practical sequences 
contemplated, L=5. For binary signaling for example, in general there 
would be 2.sup.L such subsequences of data bits which would be bit 
sequences which logically could have been present and contributed to the 
intersymbol interference. 
The output of Bayesian equalizer 16 in FIG. 1 is a set of maximum a 
posteriori metrics or probabilities for each of the possible subsequences, 
d.sub.i.sup.k,L, representing sequences which could have been transmitted 
and possibly corrupted. The probability set forth in Equation 5 below is 
the metric update or conditional probability which is optimum when the 
transmission characteristics of channel 12 is known a priori. 
##EQU5## 
where c is a normalization constant. Equation 5 is equivalent to the 
methodologies discussed by Abend and Fritchman to describe a maximum a 
posteriori symbol-by-symbol detector. See R. A. Iltis, "Recursive Bayesian 
Algorithms for Blind Equalization", supra previously incorporated by 
reference. Equation 5 is the equation for the probability that a 
particular sequence of data, d.sub.i.sup.k,L, was transmitted given that 
the currently received sequence of data is given by the set r.sup.k. The 
summation is taken over all subsequences such that the first L-1 symbols 
in the subsequence, d.sub.i.sup.k-1,L, are the same as the last L-1 
symbols in the subsequence d.sub.i.sup.k,L. In other words, the summation 
is taken over all the logical possible data subsequences just prior to the 
currently transmitted data interval which match the possible subsequence 
of data currently transmitted. 
FIG. 3b is a diagrammatic drawing of a method and means for generating an 
updated metric according to equation (5) above. 
When the characteristics of channel 12 are unknown, the update Equation 5 
is approximated with the likelihood or gaussian distribution density, 
p(r(k).vertline.d.sub.i.sup.k,L, r.sup.k-l) given in terms of a set of 
common or least mean square fit filter innovations as described more 
particularly in R. A. Iltis, "Recursive Bayesian Algorithms for Blind 
Equalization", supra. The likelihood or gaussian distribution density, 
p(r(k).vertline.d.sub.i.sup.k,L, r.sup.k-1), is readily determined from 
its mean given in Equation 7 below and its variance which can be 
determined from the data received through conventional means, namely 
statistical computation. 
FIG. 3a is a diagrammatic drawing of a method and means for generating both 
an estimated signal according to equation (7) below and an updated 
likelihood of a data symbol given a prior sequence and received signal as 
discussed above. 
Eventually a decision must be made as to what the true data was. The 
decision is made when the last time interval is past during which the data 
symbol could have contributed to the intersymbol interference. At time k 
this is the data symbol d(k-L+1). The decision on the data symbol, 
d(k-L+1), is found by computing the marginal probability, which requires a 
summation over the probabilities or metrics in Equation 5. In practice, 
the maximum subsequence metric in Equation 5 is selected and the 
corresponding data symbol, d(k-L+1), is used as the decision. 
For each subsequence, d.sub.i.sup.k,L, a separate channel or symbol timing 
estimator is used. A normalized least mean square (LMS) algorithm works 
well and requires only vector and scalar arithmetic operations. The least 
mean square update for both timing, .tau..sub.i (k.vertline.k), and 
channel coefficients, f.sub.i (k.vertline.k), is given by Equation 6 below 
where K(k) is a conventional Kalman gain matrix and where the estimated 
signal, r.sub.i (k.vertline.k-1), is given by Equation 7 below. 
##EQU6## 
In Equation 6 above, .tau..sub.i (k.vertline.k) and f.sub.i (k.vertline.k) 
represent the timing and symbol coefficient estimates respectively 
corresponding to the data subsequence, d.sub.i.sup.k,L. The estimates are 
then combined in a Bayesian formula to yield .tau..sub.i (k+1.vertline.k) 
and f.sub.i (k+1.vertline.k) for the next iteration. 
FIG. 3c is a diagrammatic drawing of a method and means for generating 
conditional timing and channel coefficients according to equation (6) 
above. 
The methodology modeled by Equation 6 is virtually identical to the least 
mean square adaptation algorithm used in decision-feedback equalizers in 
existing high speed modems. However, a conventional decision feedback 
equalizer only generates a single update of the form shown in Equation 6, 
namely that corresponding to the most likely subsequence, d.sub.i.sup.k,L. 
In contrast, the Bayesian equalizer of the invention considers all 
possible updates corresponding to the subsequences, d.sub.i.sup.k,L. In 
the case of binary data, this amounts to 2.sup.L subsequences. 
Although the methodology of the invention is therefore potentially much 
more complex than that encountered in a conventional decision feedback 
equalizer, the updates modeled by the Equation 6 are generated according 
to the invention in parallel for each subsequence and therefore are 
implemented simply and at high speed in an integrated circuit chip. 
The actual methodology implemented in circuitry includes several 
refinements to speed up overall operation. At each iteration only the N 
largest metrics, p(d.sub.i.sup.k,L .vertline.r.sup.k) are considered. 
Thus, only N channel measurement updates steps modeled from Equation 6 
need be performed for each input sample. For a time division multiple 
access applications, four such channel estimators are believed to be 
sufficient. 
Turn now to FIG. 2 wherein a block diagram of the circuit architecture of 
the invention is depicted. An integrated circuit is fabricated with N 
parallel channel/symbol timing estimators 18 included in N corresponding 
parallel signal processors 28. A digital supervisory processor 20 is also 
included and is coupled to data buses 22 and 34, and an address bus 24. In 
the embodiment of FIG. 2, processor 20 is used to update and sort the 
metrics in a methodology which is modeled by Equation 5 above as well as 
to provide overall system timing and control. It is specifically 
contemplated that the invention also includes an embodiment where 
programmable processor 20 is replaced by custom logic which fast sorts the 
metrics in order to select the N largest and to rapidly generate the 
likelihoods needed for the methodology modeled in Equation 5 above. 
The data subsequence table for all possible data subsequences 
d.sub.i.sup.k,L, is stored in read only memory (ROM) 32. RAM 30 and ROM 32 
are each coupled to data bus 34 to which is also coupled the received data 
sequences, r(k). Data bus 34 in turn is coupled to each of the parallel 
processors 28. Each processor 28 generates in parallel the estimated 
signals or r(k.vertline.k-1) and updated channel and timing estimates, 
f.sub.i (k.vertline.k) and .tau..sub.i (k.vertline.k), for the N data 
signals which contribute to intersymbol interference. These generated 
output values are then output to main data bus 22. 
The proper channel coefficient estimates, f.sub.i (k.vertline.k-1) and 
t.sub.i (k.vertline.k-1), and data subsequences corresponding to the N 
largest metrics are written to each of the parallel signal processors 28 
under the control of supervisory processor 20. 
Processors 28 in FIG. 2 generate by a custom logic circuit 29 the estimated 
innovations, r(k)-r.sub.i (k.vertline.k-1), which form the last factor in 
the right side of Equation 6 above for all possible subsequences of data, 
d.sub.i.sup.k,L. In the example where quadrature phase shifted keying 
modulation is used, there are 4.sup.N subsequences in each iteration. In 
each signal processor 28 a read only memory (ROM) 26 is provided in each 
estimator to store a look-up table in order to generate the pulse 
function, g(t), corresponding to the known performance of transmitter or 
pulse generator 10 in FIG. 1. This is labeled in FIG. 2 as the g-ROM 26. 
The integrations or estimated signals are then used to generate the 
updated metrics or probabilities according to the methodology modeled by 
Equations 6 and 7 above. 
These updated estimates are then read by supervisory processor 20 which 
generates one step predictions of these parameters for the next iteration 
according to the methodology modeled by Equation 8 below. 
##EQU7## 
where F is a conventional matrix describing the bandwidth channel 
coefficient process, which can be set to an estimated value since Equation 
8 is not sensitive to its true value. These one step predictions are then 
stored by supervisory processor 20 in channel coefficient random access 
memory 30. 
FIG. 3d is a diagrammatic drawing of a method and means for generating 
unconditional channel coefficients according to equation (8) above. 
Supervisory processor 20 then generates the decoded symbols d(n) consistent 
with the predictions made according to Equation 5. In other words at time 
k, the last data symbol, d(k-L+1), of the most probable one of the 
sequences, d.sub.i.sup.k-L+1,L, is chosen as the true data symbol which 
was transmitted. This symbol is then output as the decoded received data. 
Parallel processors 28 implement the methodology and modeled by Equations 6 
and 7 to generate the predicted estimated signal r.sub.i (k.vertline.k-1), 
the estimated channel coefficients f.sub.i (k.vertline.k-1), and the 
estimated timing coefficient t.sub.i (k.vertline.k-1). The computations 
within parallel processors 28 are intensive, requiring many complex number 
multiplications and additions. Therefore, at least processors 28 are 
implemented in high speed integrated circuits in order to perform the 
updated estimates during a single time cycle of the supervisory processor 
20. In addition the clock frequency of parallel processors 28 is much high 
than the clock frequency of supervisory processor 20. 
Many alterations and modifications may be made by those having ordinary 
skill in the art without departing from the spirit and scope of the 
invention. Therefore, it must be understood that the illustrated 
embodiment has been set forth only for the purposes of example and that it 
should not be taken as limiting the invention as defined by the following 
claims. The following claims are, therefore, to be read to include not 
only the combination of elements which are literally set forth, but all 
equivalent elements for performing substantially the same function in 
substantially the same way to obtain substantially the same result. The 
claims are thus to be understood to include what is specifically 
illustrated and described above, what is conceptionally equivalent, and 
also what essentially incorporates the germ of the invention.