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BACKGROUND OF THE INVENTION
The invention relates to a system for transmitting an n-level data signal
at a given symbol rate 1/T. This system including a data transmitter with
a data signal source, a transmission channel and a data receiver with an
equalizer of the decision feedback type, which equalizer comprises a
feedforward filter connected between the input of the data receiver and a
first input of a difference circuit, a symbol decision circuit connected
to the output of the difference circuit, and a feedback filter connected
between the output of the symbol decision circuit and a second input of
the difference circuit, in which the linear part of the transmission path
between the output of the data signal source and the first input of the
difference circuit can be described by a linear signal transformation .
Such a system is generally known and is described, for example, in the book
"Digital Communications" by J. G. Proakis, McGraw-Hill, 1983, Chapter 6,
Section 6.5, pp. 382-386. In such systems the feedforward filter belonging
to the equalizer provides for suppression of noise and cancellation of
pre-cursive intersymbol interference (ISI), whilst post-cursive
intersymbol interference (ISI) is cancelled with the aid of the feedback
filter synthesizing a replica of this interference on the basis of the
symbol decisions already formed, by which replica is subtracted from the
output signal of the feedforward filter. In the system known from the book
by Proakis the equalizer is arranged for forming at the input of the
symbol decision circuit an estimate of a data signal generated by the data
transmitter. Normally, this estimate relates to the original n-level data
signal, but in the case when the data transmitter includes a linear
encoder, it is likewise possible to have this estimate relate to the
output signal of the encoder and reconstruct in the data receiver the
original n-level data signal from the symbol decisions formed then. The
latter possibility occurs, for example, in ISDN transmission systems in
which pseudo-ternary transmission codes are used, compare the article "A
Baud-Rate Line-Interface for Two-Wire High-Speed Digital Subscriber Loops"
by C. A. Ehrenbard and M. F. Tompsett, Proc. GLOBECOM 1982, Miami, USA,
pp. D.8.4.1-D.8.4.5, in which the use of a bipolar transmission code is
described.
In strongly dispersive transmission channels the output signal of the
feedforward filter shows a strongly post-cursive intersymbol interference
(ISI). Since the feedback filter has to synthesize a replica of this
post-cursive ISI, erroneous symbol decisions applied to the feedback
filter will more seriously affect subsequent symbol decisions according as
the transmission channel is more dispersive. This undesired continuing
influence of erroneous symbol decisions is known as error propagation and
entails a degradation of the transmission quality, as appears, for
example, from FIG. 6.5.2 on page 386 of the above book by Proakis.
SUMMARY OF THE INVENTION
The invention has for its object to provide a novel concept of a system of
the type set forth in the preamble in which the said error propagation is
reduced considerably without appreciably adding to the
implementation-complexity of the system.
Thereto, a system according to the invention is characterized in that the
equalizer is arranged for forming at the input of the symbol decision
circuit an estimate of a virtual m-level data signal correlating with the
n-level data signal applied to the input of the linear part of the
transmission path according to a linear signal transformation L.sub.v
which substantially characterizes the linear signal transformation and
corresponds with a partial-response polynomial g.sub.v (D) with D being a
delay operator representing the symbol interval T.
For completeness it should be observed that the m-level data signal to be
estimated is virtual if and only if g.sub.v (D).noteq.1, and if also
g.sub.v (D).noteq.g.sub.t (D), where g.sub.t (D) is the partial-response
polynomial corresponding with a linear signal transformation L.sub.t
optionally performed in the data transmitter.
The post-cursive ISI in the output signal of the feedforward filter is
substantially described by the linear signal transformation L.sub.v.
According to the partial-response technique which is used in conformity
with the novel concept, the major part of this ISI may be considered to be
controlled desired ISI, so that only a small amount of undesired residual
ISI remains which has to be cancelled by the feedback filter. The achieved
reduction of the amplitude of the feedback filter output signal results in
the erroneous symbol decisions applied to the feedback filter having a
weaker influence on subsequent symbol decisions, thereby achieving the
intended reduction in error propagation.
An embodiment of the system according to the invention that is attractive
with respect to its implementation is characterized in that the data
transmitter comprises a precoder connected between the data signal source
and the input to the linear part of the transmission path for performing a
non-linear signal transformation NL.sub.v which is unambiguously
determined by the linear signal transformation L.sub.v, in conformity with
the partial-response technique, and in that the feedback filter in the
data receiver is connected to the output of the symbol decision circuit
through a decoder and a precoder which is identical with the precoder in
the data transmitter, said decoder performing a memoryless inverse signal
transformation L.sub.v.sup.-1 .cndot.NL.sub.v.sup.-1 which converts the
m-level symbol decisions into an n-level data signal corresponding with
the original n-level data signal. The precoder connected to the decoder
subsequently converts this n-level data signal into a replica of the
precoded n-level data signal generated in the data transmitter applied to
the input to the linear part of the transmission path. In this way the
condition generally to be imposed on decision feedback equalization that
the input signal of the feedback filter is linearly related to the output
signal of the feedforward filter is satisfied. Besides, an n-level data
signal is applied to the feedback filter, and because n is smaller than m,
a digital implementation of this filter is thus simpler than when the
formed m-level symbol decisions are applied directly.
A further advantage of this embodiment is the possibility of adaptively
adjusting the feedback filter and also the feedforward filter in the data
receiver of the system under control of an error signal which can be
simply obtained and is representative of the difference between the input
signal of the symbol decision circuit and a symbol that can be derived
from the input signal of the feedback filter by performing the linear
signal transformation L.sub.v.
This adaptive embodiment finally enables to further improve the already
achieved transmission quality by adding a relatively simple non-adaptive
post-detector to which the input signal of the symbol decision circuit is
applied.
BRIEF DESCRIPTION OF THE DRAWING
The invention will be further explained hereinbelow with reference to the
drawing, in which:
FIG. 1 shows a block diagram of a conceptual embodiment of a data
transmission system in which the invention can be used;
FIG. 2 shows a functional discrete-time model of the system of FIG. 1 when
conventional measures are employed;
FIG. 3 shows a functional discrete-time model of the system of FIG. 1 when
the measures according to the invention are employed;
FIG. 4 shows a functional discrete-time model of an attractive embodiment
of a system according to the invention; and
FIG. 5 shows a functional discrete-time model of an adaptive embodiment of
a receiver of a system according to the invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
In FIG. 1 a block diagram is shown of a system for data signal transmission
with a data transmitter 1, a transmission channel 2 and a data receiver 3.
The data transmitter 1 comprises a data signal source 10 for generating a
data signal. This data signal is converted by an encoder 11 into a data
signal which is transmitted through transmission channel 2 at a symbol
rate 1/T. The intersymbol interference (ISI) and noise developed during
this transmission are combated in the data receiver 3. Thereto, data
receiver 3 comprises an equalizer 30 of the decision feedback type which
includes a feedforward filter 31 which is dismensioned for suppressing in
the best way possible pre-cursive ISI and noise. On the basis of symbol
decisions which are formed in a symbol decision circuit 32 a feedback
filter 33 subsequently forms a cancelling signal for post-cursive ISI
which is subtracted from the output signal of feedforward filter 31 by
means of a difference circuit 34 for obtaining the input signal of symbol
decision circuit 32. Finally, from the formed symbol decisions a decoder
35 forms a replica of the original data signal which is applied to a data
signal sink 36.
To illustrate the problem for which the invention provides a solution, FIG.
2 shows a functional discrete-time model of the system of FIG. 1 when
employing conventional measures. In the FIGS. 1 and 2 corresponding
elements are denoted by the same reference symbols. The model of FIG. 2 is
given for the case in which data signal source 10 generates a binary data
signal and data transmitter 1 applies a ternary data signal to
transmission channel 2.
A binary data signal d.sub.k generated by data signal source 10 is
converted by a non-linear part 12 of the encoder 11 into a likewise binary
data signal a.sub.k which, subsequently, by the linear part 13 of the
encoder 11 is converted into a ternary data signal b.sub.k to be applied
to discrete-time transmission channel 2. To characterize the operation
performed in this linear part 13 a partial-response polynomial g.sub.t (D)
can be used, D being a delay operator representing the symbol interval T.
Further details about these partial-response polynomials are to be found,
for example, in the article "Partial-Response Signaling" by P. Kabal and
S. Pasupathy, IEEE trans. Commun., Vol. COM-23, No. 9, pp. 921-934,
September 1975. For explaining the following description it should be
observed that such polynomials generally have a relatively low order and
also, apart from an otherwise unimportant scale factor, only have
integral-valued coefficients. In the present case, for the purpose of
illustration, the bipolar response 1-D for the polynomial g.sub.t (D) is
chosen such that
b.sub.k =a.sub.k -a.sub.k-1. (1)
The ternary data signal b.sub.k is converted into an output signal r.sub.k
by the cascade arrangement of transmission channel 2 and feedforward
filter 31 in FIG. 1 according to
r.sub.k =(b*(f*w)).sub.k +(n*w).sub.k, (2)
where the symbol "*" denotes the linear convolution-operator, f.sub.k and
w.sub.k represent the discrete-time impulse responses of transmission
channel 2 and feedforward filter 31, respectively, and n.sub.k represents
an additive discrete-time noise signal which is added by means of a
summator 20.
With a proper dimensioning of the feedforward filter 31 of FIG. 1 it holds
that the signal r.sub.k contains virtually only post-cursive ISI. This
implies that (f*w).sub.k can significantly differ from zero only for
non-negative instants k. In the present system post-cursive ISI is
combated by making feedback filter 33 have a causal impulse response
p.sub.k for which holds
##EQU1##
and applying to this feedback filter 33 the symbol decisions b.sub.k which
are formed by decision circuit 32. As a result of the causal character of
feedback filter 33 its output signal is at any instant k only determined
by symbol decisions b.sub.k-i with i.gtoreq.1 that have already been
formed. Under normal operating conditions these symbol decisions are
correct, so that the output signal of the feedback filter 33 can be
described as
(b*p).sub.k =(b*p).sub.k. (4)
The output signal b.sub.k of difference circuit 34 can now be described as
b.sub.k =r.sub.k -(b*p).sub.k. (5)
In the case in which signal r.sub.k only contains post-cursive ISI, this
formula when utilizing formulas (2), (3) and (4) can be simplified to
b.sub.k =b.sub.k +(n*w).sub.k =b.sub.k +n.sub.k ', (6)
where n.sub.k ' represents the version of noise signal n.sub.k that is
attennuated in amplitued by feedforward filter 31. According to the latter
formula, in the absence of error propagation, at the input of symbol
decision circuit 32 an ISI-free estimate b.sub.k is formed of the data
signal b.sub.k at the output of data transmitter 1.
For strongly dispersive transmission channels 2 the output signal of
feedforward filter 31 usually shows a strongly postcursive ISI because the
impulse response (f*w).sub.k for k.gtoreq.1 significantly differs from
zero. Consequently, the impulse response p.sub.k of feedback filter 33
according to formula (3) will also assume values significantly differing
from zero for k.gtoreq.1. This will unavoidably cause a relatively large
effect of erroneous symbol decisions b.sub.k-1 with i.gtoreq.1 that have
already been formed on symbol decisions b.sub.k+i with i.gtoreq.0 that
still have to be formed.
In FIG. 2 the cascade arrangement of the linear part 13 of encoder 11 in
data transmitter 1, the transmission channel 2 and the feedforward filter
31 of equalizer 30 in data receiver 3 constitutes the linear part of the
transmission path between the output of data signal source 10 and the
first input of difference circuit 34. The operation of this cascade
arrangement (13,2,31) can be described by a linear signal transformation
, as is symbolically shown in FIG. 2. Instead of inserting summator 20 at
the input of feedforward filter 31 in this cascade arrangement (13,2,31)
it is equally possible to insert same at the output of this feedforward
filter 31 having impulse response w.sub.k. On the basis of the above
considerations it will be evident that in the latter case summator 20 has
to add to the output signal of this cascade arrangement (13,2,31) an
additive noise signal (n*w).sub.k in order to produce the same signal
r.sub.k at the first input of difference circuit 34 as in the case shown
in FIG. 2.
The latter option is used for elucidating the description of FIG. 3 showing
a functional discrete-time model of the system of FIG. 1 when utilizing the
measures according to the invention. In the FIGS. 1, 2 and 3 corresponding
elements are denoted by the same reference symbols.
The linear part 13 of encoder 11 in FIG. 3 again performs an operation
which is characterized by the partial-response polynomial g.sub.t (D)=1-D.
At the output of data transmitter 1 in FIG. 3 then again a ternary data
signal b.sub.k according to formula (1) will occur
b.sub.k =a.sub.k -a.sub.k-1 (7)
and at the first input of difference circuit 34 in data receiver 3 a signal
r.sub.k according to formula (2)
r.sub.k =(b*(f*w)).sub.k +(n*w).sub.k. (8)
In many cases it is possible to present a relatively simple
partial-response polynomial g.sub.c (D) such that the associated impulse
response g.sub.c,k --which is built up out of the respective coefficients
of the polynomial--forms a proper styling of the impulse response
(f*w).sub.k of the cascade arrangement of transmission channel 2 and
feedforward filter 31. This implies that the linear signal transformation
corresponding with the impulse response (f*w).sub.k representative of the
overall linear transmission distortion can be considered to be built up as
a sequence of partial-response transformation L.sub.c which corresponds
with g.sub.c (D), and a residual transformation L.sub.r which takes into
account the generally minor effect of the residual linear transmission
distortion. In the present example, the duobinary response 1+D is taken
for g.sub.c (D), which response is illustrative of many transmission
channels 2 having a low-pass character such as, for example, ISDN
connections in the local public telephone network. This conceptual
splitting-up is expressed in FIG. 3 by a partial-response circuit 21
corresponding with linear signal transformation L.sub.c and having an
impulse response g.sub.c,k, which circuit 21 is followed by a residual
circuit 22 corresponding with linear signal transformation L.sub.r and
having an impulse response h.sub.k. In partial-response circuit 21 ternary
data signal b.sub.k at the output of data transmitter 1 is converted into a
virtual m-level data signal c.sub.k (signal c.sub.k is a "virtual" signal
because it is not explicitly visible at any point between the in and
output of the physical transmission channel 2). Then, for this m-level
data signal c.sub.k it holds that
c.sub.k =(b*g.sub.c).sub.k, (9)
which expression for the assumed duobinary response g.sub.c (D)=1+D is
simplified to
c.sub.k =b.sub.k +b.sub.k-1. (10)
On the basis of formula (7) it then follows that c.sub.k is related to
binary data signal a.sub.k at the input of linear part 13 of encoder 11 in
data transmitter 1 according to
c.sub.k =a.sub.k -a.sub.k-2, (11)
so that c.sub.k in this case is a ternary data signal (thus m=3). This
relationship can be described by a linear signal transformation L.sub.v
which can be assumed to be built up as a sequence of partial-response
transformations L.sub.t and L.sub.c which correspond with the polynomials
g.sub.t (D) and g.sub.c (D), as represented in FIG. 3. The signal
transformation L.sub.v then corresponds with a partial-response polynomial
g.sub.v (D) for which holds
g.sub.v (D)=g.sub.t (D).g.sub.c (D). (12)
In the present example the bipolar response 1-D is chosen for g.sub.t (D)
and the duobinary response 1+D for g.sub.c (D), so that
g.sub.v (D)=(1-D)(1+D)=1-D.sup.2. (13)
In view of the generally relatively small residual transmission distortion
which is represented by the impulse response h.sub.k, the signal
transformation of the linear part (13,2,31) of the transmission path
between the output of signal source 10 and the first input of difference
circuit 34 is substantially characterized by the linear signal
transformation L.sub.v which is performed by the cascade arrangement of
linear part 13 of encoder 11 and partial-response circuit 21.
The described conceptual splitting-up becomes explicitly visible in data
receiver 3 of FIG. 3 because in accordance with the invention equalizer 30
is arranged for forming at the input of symbol decision circuit 32 an
estimate c.sub.k of the virtual data signal c.sub.k instead of an estimate
b.sub.k of the data signal b.sub.k at the output of data transmitter 1. The
task to be performed by the equalizer 30 is less exacting in the case of
FIG. 3 in view of the relatively small residual transmission distortion
which is represented by the impulse response h.sub.k. This can be shown by
a further analysis of the model of FIG. 3. As appears from the splitting-up
of FIG. 3 the signal r.sub.k at the first input of difference circuit 34
can be written as
r.sub.k =(c*h).sub.k +(n*w).sub.k. (14)
By analogy with the foregoing, under normal operational conditions the
already formed symbol decisions c.sub.k-i with i.gtoreq.1 may be assumed
to be correct. Applying these correct symbol decisions to feedback filter
33, now having an impulse response q.sub.k, then results in an output
signal
(c*q).sub.k =(c*q).sub.k. (15)
By utilizing formulas (14) and (15) it now appears that at the input of
symbol decision circuit 32 a signal c.sub.k develops having the form
c.sub.k =(c*h).sub.k -(c*q).sub.k +(n*w).sub.k. (16)
In order to let this signal c.sub.k be as good an approximation as possible
of the virtual data signal c.sub.k, it is necessary according to this
formula that the impulse response q.sub.k of feedback filter 33 be a
faithful copy of the casual part of the impulse response h.sub.k, that is
to say
##EQU2##
As appears from the foregoing, impulse response h.sub.k usually represents
only a small amount of linear transmission distortion, so that the impulse
response q.sub.k will take on relatively small values, and already formed
erroneous symbol decisions c.sub.k-i with i.gtoreq.1 only affect to a
limited extent the symbol decisions c.sub.k+i with i.gtoreq.0 still to be
formed.
The reduction of error propagation achieved thus can be aptly illustrated
with reference to the situation in which no residual linear transmission
distortion occurs, so that
h.sub.k =.delta..sub.k, (18)
where .delta..sub.k represents the Kronecker delta function. The linear
signal distortion introduced by the cascade arrangement of transmission
channel 2 and feedforward filter 31 can then be characterized exactly in
both FIG. 2 and FIG. 3 by the partial-response transformation L.sub.c, so
that
(f*w).sub.k =g.sub.c,k. (19)
According to the conventional approximation of FIG. 2 the impulse response
p.sub.k according to formula (3) is a replica of the part with k.gtoreq.1
of (f*w).sub.k, that is to say
##EQU3##
For the chosen duobinary response g.sub.c (D)=1+D it holds that g.sub.c,1
=1 and g.sub.c,k =0 for k.gtoreq.2, so that the first coefficient of the
feedback filter 33 has a large non-zero value which may lead to
significant error propagation. Conversely, the approximation according to
the invention results in a feedback filter 33 whose impulse response
q.sub.k is a replica of the part with k.gtoreq.1 of the impulse response
h.sub.k, which part according to formula (18) is equal to zero for all
k.gtoreq.1. Consequently, all coefficients of feedback filter 33 are also
equal to zero, so that eror propagation is eliminated completely. It will
be evident that this ideal situation, in which a feedback filter 33 is
actually redundant, will not occur in practice. However, in general it
will still hold that the first coefficients q.sub.k according to FIG. 3
then have a considerably smaller amplitude than the corresponding first
coefficients p.sub.k according to FIG. 2, so that error propagation is
accordingly smaller.
In the configuration as shown in FIG. 3 an m-level signal c.sub.k is
applied to feedback filter 33, where m=3 for the present example with
g.sub.v (D)=1-D.sup.2. By carrying out in encoder 11 of data transmitter 1
a suitable non-linear signal transformation NL.sub.v, it is possible to
reduce this number of m signal levels and thus simplify a digital
implementation of feedback filter 33.
This possibility is represented in FIG. 4 showing a functional
discrete-time model of a system according to the invention. In the FIGS. 3
and 4 corresponding elements are denoted by the same reference symbols.
In addition to the said non-linear signal transformation NL.sub.v other
non-linear signal processes too can generally take place in the non-linear
part 12 of encoder 11. To simplify the following description these other
non-linear signal processes are assumed to be incorporated in data signal
source 10.
As explained hereinbefore, the operation of equalizer 30 according to the
invention is aimed towards combatting the residual linear transmission
distortion which is represented by the impulse response h.sub.k.
Consequently, with a proper functioning of equalizer 30 the relation
between the data signal a.sub.k at the input of the linear part (13,21,22)
of the transmission path and the input signal c.sub.k of symbol decision
circuit 32 can also be characterized by the linear signal transformation
L.sub.v. Since this linear signal transformation L.sub.V in its turn is
characterized by a partial-response polynomial g.sub.v (D), according to
the said article by Kabal and Pasupathy there is a non-linear signal
transformation NL.sub.v denoted "precoding" and having the feature that
the sequence of the inverse operations L.sub.v.sup.-1 and NL.sub.v.sup.-1
of L.sub.v and NL.sub.v, respectively, is a simple memoryless inverse
signal mapping (MIM) which can be symbolically denoted L.sub.v.sup.-1
.cndot.NL.sub.v.sup.-1. By using this precoding NL.sub.v in the non-linear
part 12 of encoder 11 it is achieved that from the formed symbol decisions
c.sub.k a direct estimate d.sub.k of input signal d.sub.k of encoder 11
can be obtained by carrying out this memoryless inverse signal mapping MIM
in decoder 35. By applying the data signal d.sub.k obtained thus to a
precoder 37 which is identical with precoder 12 in data transmitter 1, an
estimate a.sub.k is obtained of data signal a.sub.k at the input of the
linear part (13,21,22) of the transmission path and this estimate a.sub.k
is applied to feedback filter 33. Thus, the condition generally to be
imposed on the decision feedback equalization that the input signal of
feedback filter 33 be linearly related to the signal at the first input of
difference circuit 34 is satified. Since the precoded data signal a.sub.k
has the same number of n amplitude levels as the original data signal
d.sub.k, a digital implementation of feedback filter 33 is simpler in FIG.
4 than in FIG. 3, in which a data signal with m>n amplitude levels is
applied to feedback filter 33. In the present example with g.sub.v
(D)=1-D.sup.2 not a ternary, but a binary data signal is applied to
feedback filter 33.
As appears from the foregoing, there is a relationship between the data
signals c.sub.k and a.sub.k that can be characterized by the linear signal
transformation L.sub.v. Therefore, in absence of erroneous symbol decisions
c.sub.k the same holds for the relationship between the data signals
c.sub.k and a.sub.k of FIG. 4. Expressed in a formula this means that
c.sub.k =(a*g.sub.v).sub.k. (21)
In order to realize the same output signal of the feedback filter 33 in the
configuration of FIG. 4 as in FIG. 3, feedback filter 33 in FIG. 4 has to
have an impulse response q.sub.k ', so that
(a*q').sub.k =(c*q).sub.k. (22)
On the basis of the relationship between the data signals c.sub.k and
a.sub.k according to formula (21), q.sub.k ' has to be related to q.sub.k
according to formula (22) as
q.sub.k '=(q*g.sub.v).sub.k. (23)
The convolution in formula (23) generally has a shortening effect on the
impulse response of feedback filter 33, as will now be explained.
In the absence of erroneous symbol decisions data signal c.sub.k at the
output of symbol decision circuit 32 has a controlled ISI structure which
is characterized by the linear signal transformation L.sub.v. For the
prevailing partial-response transformations L.sub.v this structure leads
to zeros in the amplitude spectrum of data signal c.sub.k, which zeros are
often situated at the frequency 0 and/or at the Nyquist frequency 1/(2T).
As the above has shown, feedback filter 33 should cancel a residual
transmission distortion which is represented by the impulse response
h.sub.k. The desired feedback filter output signal defined well in this
manner has to be generated in FIG. 3 by a convolution of data signal
c.sub.k at its input and its impulse response q.sub.k. As the amplitude
spectrum of this input signal c.sub.k has zeros at frequencies determined
by L.sub.v, the transfer function of feedback filter 33 around these
frequencies can be chosen freely without an appreciable effect on the
desired output signal. Especially with an adaptive adjustment of feedback
filter 33 as shown in FIG. 3 this freedom may inadvertently result in
feedback filter 33 having a large transfer at the said frequencies
determined by L.sub.v. Such a large transfer is attended with an impulse
response q.sub.k of feedback filter 33 extends over a large time span
and/or has large amplitude values, and thus may lead to serious error
propagation in both cases. According to formula (23) impulse response
q.sub.k ' of feedback filter 33 in FIG. 4 is determined by the convolution
of the impulse response g.sub.v,k' , which itself is determined by the
linear signal transformation L.sub.v, and the just described impulse
response q.sub.k of feedback filter 33 in FIG. 3. Thus, it is achieved
that a possible large transfer of feedback filter 33 in FIG. 3 at the said
frequencies determined by L.sub.v is cancelled completely or substantially
completely in FIG. 4 by the very small transfer at these same frequencies
of the impulse response g.sub.v,k likewise determined by L.sub.v.
Consequently, the impulse response q.sub.k ' of feedback filter 33 in FIG.
4 will extend over a considerably smaller time span and/or have
considerably smaller amplitude values than the impulse response q.sub.k of
feedback filter 33 in FIG. 3, thus considerably reducing the risk of error
propagation.
It will be evident that this advantage of reduced error propagation in data
receiver 3 as shown in FIG. 4 is maintained if instead of virtual data
signal c.sub.k the actually transmitted data signal b.sub.k is
reconstructed by symbol decision circuit 32. Even then the configuration
as shown in FIG. 3, in which symbol decisions b.sub.k with respect to
actually transmitted data signal b.sub.k are applied directly to feedback
filter 33, could, according to the just described mechanism, lead to an
impulse response q.sub.k of feedback filter 33 extending over a large time
span and/or having large amplitude values. Thus, serious error propagation
may occur. In the configuration as shown in FIG. 4 the corresponding
impulse response q.sub.k ' of feedback filter 33 leads, under the same
circumstances, to a considerably smaller error propagation owing to the
convolution of impulse response q.sub.k and the impulse response g.sub.t,k
corresponding with linear signal transformation L.sub.t which is performed
in linear part 13 of encoder 11 in data transmitter 1.
As explained hereinbefore, the advantages of a simplified implementation of
feedback filter 33 and reduced error propagation realized by means of the
configuration of FIG. 4 apply both in the case where at the input of
symbol decision circuit 32 an estimate c.sub.k of virtual data signal
c.sub.k is formed and in the case where an estimate b.sub.k of actually
transmitted data signal b.sub.k is formed. Since these data signals
c.sub.k and b.sub.k, respectively, are related to data signal a.sub.k at
the input of the linear part (13,21,22) of the transmission path via the
linear signal transformations L.sub.v =L.sub.t .cndot.L.sub.c and L.sub.t,
respectively, it is evident that said two advantages generally occur if at
the input of symbol decision circuit 32 an estimate is formed of an
m-level data signal that is related to n-level data signal a.sub.k
according to a linear signal transformation L with L=L.sub.v or L=L.sub.t,
which linear signal transformation L corresponds with a partial-response
polynomial g(D)=g.sub.v (D) and g(D)=g.sub.t (D), respectively.
An additional advantage of the configuration of data receiver 3 shown in
FIG. 4 relates to the option of adaptively implementing feedback filter 33
and possibly also feedforward filter 31. This option is illustrated in FIG.
In FIG. 5, both filters 31 and 33 now comprise an adaptation circuit 31(a)
and 33(a), respectively, arranged according to conventional techniques.
These adaptation circuits 31(a) and 33(a) are controlled by the same error
signal .epsilon..sub.k which is representative of the difference between
input signal c.sub.k of symbol decision circuit 32 and a data signal
c.sub.k '. This data signal c.sub.k ' is derived in a simple way from the
input signal a.sub.k of feedback filter 33 by means of a partial-response
circuit 38 in which the desired partial-response transformation L.sub.v is
effected. By means of a difference circuit 39 the difference .DELTA..sub.k
between the signals c.sub.k and c.sub.k ' is formed, and in FIG. 5 this
difference .DELTA..sub.k is used directly as error signal .epsilon..sub.k.
As is well known, in adaptive filters prescribed functions of
.DELTA..sub.k, such as, for example, strongly quantized versions of
.DELTA..sub.k, can be used as error signal .epsilon..sub.k in order to
simplify their digital implementation. When using the error signal
.epsilon..sub.k thus obtained it is achieved in a simple manner that,
after convergence of the adaptive filters 31 and 33, the data component
c.sub.k -(n*w).sub.k of the input signal c.sub.k of symbol decision
circuit 32 is related in the desired manner to the data signal a.sub.k at
the output of precoder 12 in data transmitter 1, that is to say, via the
desired linear signal transformation L.sub.v embedded in partial-response
circuit 38. The apparently more obvious implementation, in which the in
and output signals c.sub.k and c.sub.k of symbol decision circuit 32 are
used directly for forming the error signal .epsilon..sub.k, true enough,
also results in a linear relationhip between the data component c.sub.k
-(n*w).sub.k of c.sub.k and the data signal a.sub.k after adaptation of
filters 31 and 33, but inevitably leads to the problem that it cannot be
predicted a priori which linear relationship exactly will be established,
so that an undesired adjustment of equalizer 30 cannot be precluded in
advance.
It is evident that the latter advantage of a predictable convergence
behaviour is maintained if a desired linear signal transformation
L=L.sub.t instead of a desired linear signal transformation L=L.sub.v is
performed in partial-response circuit 38. As already explained
hereinbefore, this linear signal transformation L=L.sub.t leads to symbol
decisions b.sub.k of actually transmitted data signal b.sub.k, so that in
this case decoder 35 has to perform a memoryless inverse mapping L.sup.-1
.cndot.NL.sup.-1 =L.sub.t.sup.-1 .cndot.NL.sub.t.sup.-1, whilst precoder
37 has to carry out the associated non-linear signal transformation
NL=NL.sub.t.
The predictable convergence behaviour of feedforward filter 31 and feedback
filter 33 which is garanteed by partial-response circuit 38 in FIG. 5 leads
to an input signal c.sub.k of symbol decision circuit 32 with a correlation
structure substantially corresponding with the well-defined correlation
structure of output signal c.sub.k ' of partial-response circuit 38, which
correlation structure can be characterized by a partial-response polynomial
g.sub.v (D) or g.sub.t (D). This well-defined correlation structure of
input signal c.sub.k of symbol decision circuit 32 in FIG. 5 can now be
used for realizing a further improvement of transmission quality by adding
a non-adaptive post-detector 40 for forming final symbol decisions
d.sub.k-M which are applied to a data signal sink 36', as shown in FIG. 5
by way of a dashed line. Such a post-detector is known from an article
"Maximum-Likelihood Sequence Estimation of Digital Sequences in the
Presence of Intersymbol Interference" by G. D. Forney, Jr., published in
IEEE Trans. Inform. Theory, Vol. IT-18, No. 3, pp. 363-378, May 1972. In
this article a non-adaptive detector is described which is arranged for
estimating the maximum-likelihood sequence of transmitted data symbols
d.sub.k and thereto makes optimum use of the correlation structure its
input signal c.sub.k. This leads to a transmission quality which is better
than when making symbol-by-symbol decisions as performed in symbol decision
circuit 32. For correlation structures of the partial-response type
considered, according to the article by Forney improvements of
transmission quality corresponding with an improvement of 2-3 dB in the
signal-to-noise ratio are often obtainable in this manner. In addition,
the implementation of non-adaptive post-detector 40 can remain relatively
simple as a result of the low order and the resulting short memory span of
the partial-response polynomial (g.sub.v (D) or (g.sub.t (D)) which
determines the correlation structure of input signal | | |
