Receiving method and receiver for discrete signals

The invention relates to an adaptive receiving method and a receiver comprising an adaptive equalizing device for processing a received signal. The receiver further comprises an adaptive detector utilizing the self-organizing map principle and operationally connected after the adaptive equalizer. The adaptive equalizer is controlled on the basis of an error between a processed signal and a detected signal.

FIELD OF THE INVENTION 
The invention relates to a method of receiving discrete signals, in which a 
received discrete signal is processed prior to detection to compensate for 
distortion caused by the transmission channel. 
BACKGROUND OF THE INVENTION 
A common problem with the reception of digital signals is that in addition 
to noise the transmission channel also causes linear and non-linear 
distortions in the signal. Prior art methods for eliminating the effects 
of linear distortions from the received signal include linear and 
non-linear transversal equalizers, which may be adaptive so that they 
adapt to possible changes in the transmission channel during the signal 
transmission. 
To compensate for non-linear distortions, International Application 
PCT/FI89/00037 discloses an adaptive detection method for quantized 
signals, which utilizes the self-organizing map principle during detection 
to automatically take into account the effects of changes taking place in 
the channel properties on a signal constellation used in the detection. 
The same method is described in Kohonen, Raivio, Simula, Venta, 
Henriksson: An Adaptive Discrete-Signal Detector Based on Self-Organizing 
Maps. International Joint Conference on Neural Networks IJCNN-90-WASH DC, 
Jan. 15-19, 1990, Washington D.C., Vol. II, P. II-249-52. 
The above-described solutions are not, however, able to operate in an 
optimal way in surroundings where both distortion types occur 
simultaneously. A linear or non-liner transversal equalizer is not able to 
compensate for non-linear distortions (or is able only limitedly), and the 
map method compensating for non-linear distortions is disturbed by the 
linear distortions. 
SUMMARY OF THE INVENTION 
The object of the present invention is to provide a receiving method and a 
receiver which are able to efficiently compensate for non-linear and 
linear distortions simultaneously. 
This is achieved by means of a method according to the invention, wherein 
the processed discrete signal is detected by an adaptive detection method 
based on a self-organizing map and the distortion compensation to be 
performed prior to detection is controlled on the basis of an error 
between an instantaneous signal sample of the processed signal and a 
signal constellation formed by the self-organizing map. 
The invention eliminates or alleviates the drawbacks of the prior methods 
by introducing a combined method in which the signal is first equalized 
linearly by a desired adaptive method, e.g., by using a linear transversal 
equalizer or decision-feedback equalizer and the equalized signal is 
detected by a detection method based on the self-organizing map. 
Thereafter the error of an instantaneous signal sample of the equalized 
signal is calculated with respect to a signal constellation formed by the 
self-organizing map. The error term so obtained is used to control the 
linear equalizer, e.g., the determination of the tap coefficients of the 
equalizer. In one embodiment of the invention, the equalization is made 
even more efficient by using and controlling simultaneously both a 
conventional linear equalizer and a decision-feedback equalizer. 
As compared with a conventional transversal equalizer, the most significant 
difference is that the error term controlling the linear equalizer is 
calculated in this method with respect to an adaptive signal 
constellation. In traditional methods, the signal constellations and 
decision limits used in the detection are fixed so that they do not take 
into account changes possibly taking place in the transmission channel due 
to the aging of the apparatus or for some other reasons. 
In the preferred embodiment of the invention, the signal constellation 
formed by the self-organizing map, and to be used in the detection, is 
corrected on the basis of the signal the linear distortion of which has 
been equalized. In an alternative embodiment of the invention, the 
correction of the signal constellation is accomplished by the received 
signal as such, which method in most cases has a lower performance than 
the preferred method; but it may provide advantages in cases where 
non-linear distortion is so extensive that the linear equalizer is not 
able to converge in the initial situation. In a further embodiment of the 
invention, it is possible to select adaptively between the two 
above-mentioned alternatives.

DETAILED DESCRIPTION OF THE INVENTION 
The primary purpose of a typical communication system is to transmit data 
or messages from one point to another. To achieve this, the messages must 
be coded and modulated in an optimal way to make them as suitable for 
transmission as possible. Especially long-distance communication usually 
requires a high-frequency carrier, which is modulated by the coded 
messages. In the well-known amplitude modulation (AM), for instance, the 
carrier is simply multiplied by the message signal. Phase and frequency 
modulations are also used generally. 
The transmission channel bridges the two ends of the system. The carrier 
and the message are usually affected by signal attenuation, noise, 
interference, distortion, etc. A standard method to suppress noise and 
interference is to use proper filtering. For linear distortions, various 
so-called equalizing techniques have been developed. However, many 
distortions have non-linear characteristics, which make them difficult to 
compensate. In digital communication, modulating signals assume only 
discrete values at sampled time positions. The problem at the receiver is 
thus to identify the discrete values, e.g. .+-.A.sub.c, .+-.3A.sub.c, . . 
. One of the most efficient modulation techniques is the 
Quadrature-Amplitude Modulation (QAM). It is based on having two identical 
carriers simultaneously in the same channel with a 90 degrees phase shift. 
Both carrier components can be modulated independently, whereby the signal 
x(t) is obtained from the equation 
EQU x(t)=x.sub.i (t)A.sub.c cos (.omega..sub.c t+.theta.)-x.sub.q (t)A.sub.c 
sin (.omega..sub.c t+.theta.) (1) 
The coefficient x.sub.i (t)A.sub.c is called the "inphase" i component and 
the coefficient x.sub.q (t)A.sub.c the "quadrature" q component. In the 
coordinate system shown in FIG. 1A, the horizontal axis represents the 
phase of the i component and the vertical axis represents the phase of the 
q component so that the phase of the signal x(t) is the sum of the two 
component phases. In a digital QAM signal, the i and q components can take 
only discrete values. Thus, in the above-mentioned coordinate system, each 
possible (i,q) pair occupies a discrete grid point so that a so-called 
signal constellation is formed. Demodulation is an inverse operation to 
modulation, i.e. it attempts to recover the discrete x.sub.i and x.sub.q 
codes from the transmitted waveform. More precisely, the problem is to 
detect discrete signal values .+-.A.sub.c, .+-.3A.sub.c, etc. when the 
signal levels are affected by the noise, interference, distortions, etc. 
FIG. 1A also shows the point density function (pdf) of the received 
signals in ideal circumstances, whereby the function contains peaks at the 
possible grid points. In FIG. 1B, the peaks of the pdf have become widened 
due to noise and, moreover, the peaks themselves have been shifted due to 
distortion. Distortion is usually caused by slowly changing phenomena, 
such as a change in temperature in the circuitry or transmission medium so 
that in the short term, let alone noise, the discrete signal levels of two 
successive received signals are not too far apart. Linear distortion can 
easily be compensated for by various equalization techniques but 
non-linear distortion is more difficult to cope with. 
Simultaneous equalization of linear and non-linear distortion is 
accomplished efficiently according to the basic principles of the 
invention by equalizing the linear distortion of the received signal and 
by detecting the equalized signal by an adaptive detection method based on 
a self-organizing map. In the detection method, the used signal 
constellation adaptively adapts to the signal states of the received 
signal distorted by the transmission channel. The distortion may take 
place, e.g., from the ideal signal constellation of FIG. 1A to the 
non-linearly distorted signal constellation of FIG. 1B. In the invention, 
the linear equalizer is further controlled on the basis of an error 
between an instantaneous signal sample of a processed signal y(n) and the 
signal constellation formed by the self-organizing map. 
FIG. 3 is a block diagram of a preferred embodiment of a receiver for 
discrete signals according to the invention for realizing the method. A 
discrete signal x(n) received from the transmission channel is fed to the 
input of a linear equalizer 1 to reduce or eliminate the linear distortion 
caused by the channel. An output signal y(n) from the equalizer 1, i.e. 
the processed received signal is fed to a control input in a 
self-organizing map 2 and to an input in a detector 3. Adaptive values are 
developed in the cells of the self-organizing map 2, which values follow 
up changes taking place in time in the discrete signal states of the 
signal y(n) and form an adaptive signal constellation mi(n) which is fed 
to the detector 3, in which the m.sub.i values are used as decision levels 
so that the detector interprets the nearest signal point in the signal 
constellation m.sub.i (n) as the value of the instantaneous signal sample 
of the signal y(n) and gives this value to the detected signal y'(n). The 
detection error is e(n)=y'(n)-y(n) and it is used for controlling the 
equalizer 1 according to the invention. In the preferred embodiment of the 
invention the processed signal y(n) and the detected signal y'(n) are fed 
to a subtraction circuit 4 which forms the difference signal e(n) of these 
two signals. The difference signal is fed back to the linear equalizer 1 
to adaptively alter the coefficients of the linear equalizer in a suitable 
manner by using, e.g., the gradient method (MMSE criterion) or the zero 
compression method. The formation of the error term e(n) is illustrated in 
FIG. 6, which shows one quadrant in the signal constellation m.sub.i (n) 
formed by the self-organizing map 2 in the case of a 16QAM signal. On 
account of the linear distortion occurring in the channel, a point m.sub.3 
in the signal constellation has shifted from its ideal place. The error 
term e(n) to be used for controlling the linear equalizer is calculated by 
the instantaneous signal sample y(n) obtained from the output of the 
linear equalizer 1 and the signal point m.sub.3 used in the detection. 
FIG. 4 shows another receiver realizing the method of the invention. The 
received signal x(n) is fed to the inputs of the self-organizing map 2 and 
the linear equalizer 1. The output signal y(n) of the equalizer 1 is 
detected by the detector 3, at which the self-organizing map 2 forms the 
adaptive signal constellation m.sub.i (n) used in the detection. A 
difference signal e(n) is formed from the signals y(n) and y'(n) by the 
subtraction circuit 4, which difference signal controls the linear 
equalizer 1 according to the invention. In this embodiment, the 
self-organizing map forms the signal constellation m.sub.i (n) to be used 
in the detection directly on the basis of the received signal x(n), which 
may be of advantage when the signal x(n) is so severely distorted that the 
equalizer 1 is not able to converge in the initial situation. 
FIG. 5 shows a third receiver realizing the method of the invention. This 
receiver is formed by adding a decision-feedback equalizer (DFE) to the 
receiver of FIG. 3. Accordingly, the blocks indicated with the same 
reference numerals in FIGS. 3 and 4 represent the same functions or 
circuits. In FIG. 5, the decision-feedback equalizer comprises a unit 14 
accomplished e.g. by a transversal filter. The detected signal y'(n) is 
applied to the input of the unit 14, and it is processed by the unit, 
whereafter the output signal of the unit 14 is subtracted from the output 
signal of the linear equalizer 1 in a subtraction circuit 15 and the 
obtained difference signal is fed to the detector 3. The error signal e(n) 
is also fed to the unit 14, and it controls the formation of the 
coefficients of the unit 14 similarly as in the case of the equalizer 1. 
This combination makes the equalization of the distortion even more 
efficient. 
The decision-feedback equalizer can also be similarly positioned in the 
receiver of FIG. 4. It is also possible to realize the receiver of the 
invention merely by the decision-feedback equalizer without the equalizer 
1. 
In the following the operation of the different blocks of FIGS. 3, 4 and 5 
will be described in greater detail. The equalizer 1 may be any adaptive 
linear or non-linear equalizer known in the art, which is used to 
compensate for channel distortions and intersymbol interference. The most 
common equalizer structure is an adaptive transversal filter, the output 
signal of which is obtained from the equation 
##EQU1## 
where the tap coefficients c(n) represent the impulse response of the 
filter and y(n) is an estimate for the nth input sample. Various suitable 
equalizer structures are described e.g. in Proakis: Advances in 
Equalization for Intersmol Interference, Advances in Communication Systems 
Theory and Applications, Vol. 4, Academic Press, 1975. 
The adaptive detection based on the self-organizing map, which is performed 
by the blocks 2 and 3, is described in International Patent Application 
PCT/FI89/00037 and the following articles: Kohonen, Raivio, Simula, Venta, 
Henriksson: An Adaptive Discrete-Signal Detector Based on Self-Organizing 
Maps. International Joint Conference on Neural Networks IJCNN-90-WASH DC, 
Jan. 15-19, 1990, Washington D.C., Vol. II, P. II-249-52; T. Kohonen, 
Clustering, Taxonomy, and Topological Maps of Patterns, Sixth 
International Conference on Pattern Recognition, Munich, Germany, Oct. 
19-22, 1982, p. 114-128; T. Kohonen, Self-Organization and Associative 
Memory, Springer-Verlag, Series in Information Sciences, Vol. 8, 
Berlin-Heidelberg-New York-Tokyo, 1984, 2nd ed. 1988. 
These publications are incorporated in the description by reference. The 
structure and operation of the blocks 2 and 3 will, however, be described 
in short below. A typical self-organizing map is a linear array of 
learning cells, each cell containing an adaptive parameter or signal point 
m.sub.i. The map may be one-dimensional (FIG. 2A) or two-dimensional (FIG. 
2B). When the ideal and distorted signal values are one-dimensional, the 
m.sub.i values are also scalars. In the beginning of the communication, 
the m.sub.i values are initialized to the ideal values or according to the 
signal levels received in the beginning of the transmission, or they may 
be random values because the m.sub.i values will effectively converge to 
possible asymptotic values of the received quantized values in the course 
of the self-organizing learning process. The adaptive and time-varying 
signal identification performed by the blocks 2 and 3 proceeds according 
to the following rules that are based on the original self-organizing 
algorithm. 
(i) At each discrete time instant t, the cell c with the best matching 
parameter m.sub.i (t) for the detection result of the current received 
signal sample x(t) is determined. In the preferred embodiment of the 
invention, the parameter m.sub.i to which the Euclidean distance of the 
signal sample is the smallest is chosen, i.e. 
EQU .parallel.x(t)-m.sub.c (t).parallel.=min.sub.i {.parallel.x(t)-m.sub.1 
(t).parallel.} (4) 
(ii) Adapt the parameters m.sub.i in the neighborhood N.sub.c of the chosen 
cell c 
##EQU2## 
The topological neighborhood N.sub.c consists of the selected cell itself 
and its direct neighbors up to depth 1, 2, . . . (see FIG. 2B). 
The neighborhood learning is always applied symmetrically in each direction 
in the array of adaptive cells. Because cells near the edges of the array 
may not have neighbors in both directions, the learning causes some bias 
in the m.sub.i values of these cells towards the parameter in the center 
of the group. In one embodiment of the invention, this is compensated by 
modifying the input signal x(t) to the form b.sub.i +d.sub.i x(t), in 
which b.sub.i and d.sub.i are node-specific parameters, i.e. the space of 
the input signal x(t) is effectively enlarged. 
The ability of the method to preserve a signal space topology becomes even 
more evident when the quantization of the signal space is two- or 
multi-dimensional, i.e. the ideal signal values occupy the coordinate 
values of the grid points of a rectangular area and the m.sub.i values are 
two-dimensional vectors. Otherwise, the above adaptation equations are 
directly applicable to the two-dimensional case, too. Two-dimensional 
signal quantization is utilized in the so-called QAM coding. Therefore it 
is advantageous to use a respective rectangular array of learning cells 
familiar from the multitude of demonstrations given of the self-organizing 
maps. 
As a result of such adaptation based on self-organizing, the algorithm is 
able to follow up distortions in the signal constellation if the 
distortions in the receiver are such that the local order of the peaks of 
the point density function is preserved. The grid points in a 
two-dimensional space may be shifted, zoomed, rotated, etc., in various 
ways but still the order of the signal levels tends to be preserved, i.e., 
the rectangular grid-like structure is preserved. 
FIGS. 7 and 8 show two receivers in which the received signal s(t) may be 
e.g. an N-phase modulated signal or a MQAM signal, such as a 16QAM signal. 
In FIG. 7, the received signal s(t) is detected to the base frequency by 
means of mixers 5 and 8 by using a local oscillator 14 and a phase shifter 
14 to produce local carriers having a phase shift of 90.degree.. The 
output signals of the mixers 5 and 8 are lowpass-filtered in a usual way 
in filters 6 and 9, respectively. The lowpass-filtered signals are 
sampled, one sample for each transmitted symbol, by switches 10 and 11 
which may be e.g. sampling and holding circuits. After sampling, signal 
samples x.sub.I (n) and x.sub.Q (n) occurring at symbol time slots T are 
obtained, which are the quadrature-phase signal components of the QAM 
signal. 
The signal samples x.sub.I (n) and x.sub.Q (n) are applied to the linear 
equalizer 1, in which the sample is subjected to an equalization depending 
on the linear equalizer used in each particular case. For example, a 
transversal equalizer comprises signal samples in the memory from the time 
period of several symbols and by suitably emphasizing these signal samples 
in a manner depending on the tap coefficients and the impulse response of 
the equalizer, a corrected signal pair y.sub.I (n) and y.sub.Q (n) is made 
to correspond to each sampled time position. The samples y.sub.I (n) and 
y.sub.Q (n) are digital words of e.g. 8 bits. 
Thereafter the signal samples y.sub.I (n) and y.sub.Q (n) are applied both 
to a decision circuit 7 and the self-organizing network 2, which together 
form an adaptive detector. The self-organizing map 2 calculates an optimal 
signal constellation m.sub.i for a two-dimensional signal by a method 
based on self-organizing maps. The most probable values are thereby 
calculated by means of the detected signal samples y.sub.I (n) and y.sub.Q 
(n) for the signal points m.sub.i, taking into account the noise, 
interference and distortions contained in the signal. The decision circuit 
7 utilizes these signal points m.sub.i as reference points when it decides 
to which transmitted symbol the received signal sample pair y.sub.I (n) 
and y.sub.Q (n) corresponds. In the preferred embodiment of the invention, 
the criterion for deciding is that the received signal sample pair 
corresponds to the reference point m.sub.i to which the Euclidean distance 
.parallel.y-m.sub.i .parallel. is the smallest. The decision circuit 7 
also calculates an error term e the components of which are 
EQU e.sub.I =y.sub.I -y'.sub.I 
EQU e.sub.Q =y.sub.Q -y'.sub.Q 
where y'.sub.I and y.sub.Q are the quadrature-phase output signals of the 
decision circuit 7. The error term e is used as described above for 
calculating and updating the tap coefficients of the linear equalizer. 
The receiver of FIG. 8 is otherwise similar to that of FIG. 7 except that 
the linear equalizer is now an analog equalizer which is positioned to 
directly equalize a received signal s(t) before the signal is mixed with 
the base frequency. The signals are not converted into digital form until 
by analog-to-digital converters 12 and which are positioned after the 
sampling switches 10 and 11. 
Many of the operational blocks shown in FIGS. 3, 4, 5, 7 and 8 can also be 
realized programmatically by means of a microprocessor or the like, 
whereby the self-organizing map 2, the detector 3 and the decision circuit 
7 shown as separate in the figures may, in fact, be different parts of the 
programme of one and the same processor. 
It is further possible to combine the operations of FIGS. 3 and 4 in the 
receiver in such a way that the received signal x(n) directly or the 
signal y(n) processed by the equalizer 1 can be connected adaptively 
according to a given decision making criterion as the control signal of 
the self-organizing map 2. In the beginning of the transmission, for 
instance, the control of the map 2 may be connected directly to the signal 
to be received to facilitate the converging of the linear equalizer 1 and 
then to the processed signal for the rest of the transmission time.