Channel estimation device

A channel estimation device receives at one end of the channel a training sequence corresponding to a learning sequence produced at the other end of the channel. The estimation device generates a replica of the learning sequence and establishes the correlation of the learning and training sequences in order to produce a set of correlation coefficients. The estimation device includes a corrector device for eliminating the coefficients having the lowest moduli. The criteria used for eliminating the lowest moduli coefficients is that the sum of the squares of the moduli of the eliminated coefficients is less than a fraction of the sum of the squares of the moduli of all the correlation coefficients.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention concerns a channel estimation device. 
2. Description of the Prior Art 
In a transmission system such as a radio transmission system a transmitter 
sends a sequence of symbols to a receiver on a transmission channel. The 
sequence is subject to deterioration in the transmission channel with the 
result that the sequence of symbols received by the receiver is no longer 
identical to the sequence transmitted. The main deterioration is 
intersymbol interference caused by the fact that a symbol can take more 
than one path in the transmission channel. If at least two paths have a 
time difference exceeding the distance between two symbols transmitted in 
succession a symbol on one of these paths will interfere with a following 
symbol on another, shorter path. 
An equalizer is used to correct intersymbol interference in the receiver. 
To operate correctly it must know the impulse response of the transmission 
channel. To this end special symbols are transmitted in a learning 
sequence. These are known symbols, unlike the data symbols transmitted 
which can be assumed to be unknown to the receiver. It is therefore 
standard practise for a packet of symbols sent to a specific receiver to 
comprise data symbols, a learning sequence and further data symbols, i.e. 
the learning sequence in the middle of the packet. 
The learning sequence is chosen to suit the characteristics of the 
transmission channel and in particular its length. 
Given that the symbols are transmitted regularly at a period called the 
symbol duration the length of the channel is defined as the number of 
symbol durations which is equal to the difference between the longest and 
shortest paths. 
A channel estimator is used in the receiver to establish the impulse 
response of the transmission channel. It generates a replica of the 
learning sequence and correlates it with the received sequence of symbols. 
The result of this correlation is a set of coefficients h.sub.i with i 
varying from 0 through L where L is the length of the channel. This set of 
coefficients is supplied to the equalizer. The most direct path in the 
channel is represented by h.sub.0 and the other coefficients represent 
longer paths which cause interference with the first. 
In the most usual case the coefficients are complex because the received 
symbols comprise "in-phase" and "quadrature" components which are 
orthogonal. Hereinafter the set of coefficients is called the impulse 
response. 
To allow for the most diverse transmission conditions the length L of the 
channel would theoretically be infinite but in practise it is a constant 
chosen to suit the transmission system and supplied to the channel 
estimator. If this length is assigned a low value the longest paths of the 
channel are deliberately eliminated and the performance of the equalizer 
is degraded if these paths are actually used because the equalizer does 
not have all of the data representing the transmission channel. It would 
therefore seem desirable to use a high value for the channel length. 
However, this considerably increases the complexity of the equalizer, 
whether operating on the principle of symbol by symbol detection (for 
example the "Decision Feedback Equalizer" or DFE) or on the principle of 
maximum likelihood, by estimating a sequence of symbols (for example the 
"Viterbi" equalizer). The complexity of the equalizer, equivalent in the 
present context to the number of operations to be effected, is directly 
related to the number of correlation coefficients. 
The patent application WO 92/11 708 proposes to eliminate all the 
coefficients whose modulus is less than a given fraction of the largest 
modulus of these coefficients. 
This solution is directed to the specific instance of a channel having a 
profile in which the only meaningful paths correspond to coefficients 
which have substantially the same modulus, all the other coefficients 
representing paths which do not contribute any additional information. 
This solution is not generally applicable. 
An object of the present invention is therefore a channel estimation device 
which, using a large channel length, enables the equalizer that it feeds 
to be simplified, regardless of the channel profile. 
SUMMARY OF THE INVENTION 
The present invention consists in a channel estimation device receiving at 
one end of said channel a training sequence corresponding to a learning 
sequence produced at the other end of said channel, generating a replica 
of said learning sequence and establishing the correlation of said 
learning and training sequences in order to produce a set of correlation 
coefficients. It comprises corrector means for eliminating coefficients 
having the lowest moduli so that the sum of the squares of the moduli of 
the coefficients is less than a fraction of the sum of the squares of the 
moduli of all the correlation coefficients. 
In one embodiment of the channel estimation device corrector means are 
adapted to cancel a particular number of correlation coefficients in order 
of increasing modulus. 
The invention will emerge more clearly from the following description of 
embodiments of the invention given by way of example with reference to the 
accompanying drawing which shows the estimator applied to a transmission 
channel.

DETAILED DESCRIPTION OF THE INVENTION 
The invention applies to most transmission systems provided that they 
satisfy certain constraints explained hereinafter. 
Referring to the figure, the transmission channel 1 which has an impulse 
response H receives the transmitted symbols s.sub.i forming a learning 
sequence and delivers the received symbols r.sub.i forming a training 
sequence. 
The transmission channel estimator 2 also receives the learning sequence 
s.sub.i generated locally and the training sequence r.sub.i to produce an 
estimate of the impulse response H of the transmission channel 1. If L 
denotes the length of the channel and P the length of the learning 
sequence the estimator 2 must produce an estimate H of the impulse 
response represented by the coefficients h.sub.i with i varying from 0 
through L from the h transmitted symbols s.sub.i with i varying from 1 
through P and the received symbols r.sub.i with i varying from L+1 through 
P using the least squares criterion. The object is thus to minimize the 
root mean square error J: 
##EQU1## 
Adopting the following notation: 
##EQU2## 
and given that the hermitian transposition operator is represented by 
..sup.H and that the conjugation operator is represented by ..sup.* : 
Introducing the transmission matrix A and its hermitian transposition 
A.sup.H : 
##EQU3## 
We may write: 
EQU E=R-A.sup.H 
EQU J=E.sup.H E 
The solution is given by the set of coefficients h.sub.i which cancels the 
drift in the root mean square error J relative to the estimated impulse 
response H: 
##EQU4## 
It can be seen that for the coefficients h.sub.i to be accessible it must 
be possible to invert the matrix A.sup.H A. In this case these 
coefficients are obtained from the following equation: 
EQU H=(A.sup.H A) .sup.-1 A.sup.H R 
The condition whereby it must be possible to invert the matrix A.sup.H A 
for the invention to be implemented is satisfied if the learning sequence 
is a Constant Amplitude Zero Amslitude Correlation (CAZAC) sequence. 
Sequences of this type are described in the article by A. MILEWSKI: 
"Periodic sequences with optimal properties for channel estimation and 
fast start-up equalization", IBM Journal of Research and Development, vol. 
27, n.degree. 5, Sept. 83, pages 426-431. 
This condition is also satisfied if the learning sequence is a pseudo-CAZAC 
sequence in the sense that it behaves like a CAZAC sequence near the 
correlation peak. The pseudo-CAZAC sequences include the sequences used in 
the European GSM digital cellular mobile radio system. 
When the coefficients h.sub.i have been calculated the invention consists 
in providing corrector means 3 for cancelling the lowest of them, i.e. 
those with the smallest contribution to the impulse response of the 
transmission channel. One possible basis for comparison for this 
contribution is the sum of the squares of the moduli of all the 
coefficients h.sub.i for example. 
In one embodiment of the invention the squares of the moduli of the 
coefficients h.sub.i are listed in increasing order. The sum T of the 
squares of the moduli of all the coefficients h.sub.i is also calculated. 
A threshold S is defined by means of a specific coefficient C such that 
S=CT. The first p items from the list such that their sum is less than. S 
and the sum of these p items and the (p+1)th item of the list is greater 
than S are then determined. Once the number p has been determined, the p 
coefficients h.sub.i corresponding to the first p items of the list are 
forced to zero, i.e. eliminated. 
The list of the squares of the moduli need not be complete, it being 
sufficient that it comprises p items. A procedure is therefore feasible in 
which this list is established progressively, item by item, while 
determining the number p and is interrupted as soon as the number p has 
been found. 
The threshold S or the coefficient C is determined empirically, for example 
by simulation using a model of the transmission channel. The man skilled 
in the art will readily understand that it is a matter of achieving a 
compromise, i.e. that the threshold must be neither too high nor too low 
but adjusted to optimise the operation of the equalizer. 
The performance of the estimator of the invention is inversely proportional 
to the signal to noise ratio at the receiver. To give a numerical example, 
the value of C may be 0.05 for a signal to noise ratio of up to 20 dB 
while a value of 0.02 may be required for a signal to noise ratio 
exceeding 20 dB. 
The criterion adopted for eliminating some of the coefficients h.sub.i is 
entirely satisfactory. Other criteria are feasible within the scope of the 
invention, however, for example: 
eliminating all the coefficients h.sub.i for which the square of the 
modulus is less than a particular fraction of the sum T of the squares of 
the moduli of all the coefficients, or 
eliminating unconditionally a particular number of coefficients h.sub.i 
having the lowest moduli, this number possibly being 1.