FR2705499A1 - Adaptive signal processing system - Google Patents

Abstract

This system, including first signal processing means (2) receiving input signals and delivering processed output signals, and the processing parameters of which are established by adaptation means (3) with a feedback loop using a least-squares method, these means receiving delayed input signals on one input and a correction signal on another input derived on the basis of a reference signal delivered by a reference signal generator (4) from processed output signals, and processed and delayed output signals, the delayed input and output signals being shifted by a duration corresponding to the delay inherent in the reference signal generator, is characterised in that the processed and delayed output signals are delivered by second signal processing means (7) equivalent to the first ones (2), the processing parameters of which are also established by the adaptation means (3) and receiving the delayed input signals on one input.

Description

 The present invention relates to an adaptive signal processing system.

 This system can for example be used to process the output signals of an antenna with an adaptive network.

 Antennas of this type generally comprise an array of antenna elements, a beam forming array which will also be called BFN (for BeamForming Network) thereafter and an adaptation processor which controls the weights of the variables or processing parameters, in the BFN network.

 The weight values determine the radiation pattern of the antenna under the control of the matching processor.

 The main objective of these adaptive array antennas is to improve the reception of certain desired signals in the presence of unwanted spurious signals.

 For this purpose, the radiation configuration is established in such a way that the main lobe is pointed towards the desired signal, while the zeros are directed in the direction of the parasites.

 To achieve this adaptive beam formation, different means must be used to allow a distinction between the desired signals and the spurious signals.

 In time reference based beamforming systems, this distinction is made by means of a time reference signal which is correlated with the desired signals and not correlated with the spurious signals.

 This reference signal is generated from the output of the BFN network on the basis of any prior knowledge of the waveform of the desired signal.

 Such a time-based training technique well known in the state of the art is based on the use of an adaptive algorithm implementing a method of least squares means which will also be called hereinafter LMS algorithm (for Least Mean Square). This algorithm is suitable for reducing the mean square error between the reference signal and the actual network output.

Additional information concerning this algorithm can be found in the document "ADAPTIVE ANTENNA SYSTEMS" B. WIDROW et al.,
Proc. IEEE, volume 55, December 1967.

 In many practical applications, the generation of a reference signal from the output of the BFN network results in the appearance of an inherent delay which requires modification of the LMS algorithm.

 Thus, for example, this problem becomes clear when we study the application of adaptive beamforming to a distribution code multiple distribution and scattered spectrum telecommunications system.

We will refer in particular to the document
ADAPTIVE BEAMFORMING in A CDMA MOBILE
SATELLITE COMMUNICATIONS SYSTEM "DSP - The Enabling
Technology for Communications, S. MUNOZ-GARCIA
Amsterdam, March 9-10, 1993.

To solve the delay problems mentioned above, we then developed in the state of the art, an algorithm called LMS delayed and which is in fact a variant of the LMS algorithm and which results in a delay in the adaptation of coefficients (see the document "THE LMS ALGORITHM WITH
DELAYED COEFFICIENT ADAPTATION ", G. Long et al, IEEE trans. On Acoustics, Speech and Signal Processing, volume 37, nX 9, September 1989.

 However, this delayed LMS algorithm has a reduced convergence speed and degraded performance in steady state.

 The object of the invention is therefore to solve these problems associated with the delay linked to the generation of the reference signal in the context of the use of a so-called LMS algorithm in an adaptive signal processing system.

 To this end, the subject of the invention is an adaptive signal processing system, of the type comprising first signal processing means receiving input signals and delivering processed output signals and whose processing parameters are established by reaction loop adaptation means using a least squares method receiving delayed input signals on one input and on another input a correction signal established from a reference signal delivered by a signal generator from the processed output signals, and from processed and delayed output signals, the delayed input and output signals being shifted by a duration corresponding to the delay inherent in the reference signal generator, characterized in that the processed and delayed output signals are delivered by second signal processing means equivalent to the first and whose para processing meters are also established by the adaptation means and receiving delayed input signals on an input.

The invention will be better understood with the aid of the description which follows, given solely by way of
example and made with reference to the accompanying drawings, in which
- Fig.l, 2 and 3 show block diagrams illustrating structures of adaptive systems of the prior art; and
- Fig.4 shows a block diagram illustrating the structure of an adaptive system according to the invention.

 A description will then be given of the invention in the context of adaptive beamforming, but it goes without saying of course that this invention is not limited to this application and can also be used in other fields of adaptive signal processing in which the presence of a delay is an inherent problem, such as decision-oriented adaptive correction, adaptive reference echo cancellation or the implementation of adaptive algorithms using parallel architectures such as structures pipeline type or systolic networks.

 For reasons of clarity, equivalent elements of the systems represented in these FIGS. 1 to 4 are designated by the same reference numbers and the description of the adaptive signal processing system according to the invention will be given in the context of signal processing. used in adaptive beamforming for array antennas.

 We recognize in Figure 1, an adaptive system for processing the output signals of a network antenna.

 This system in fact comprises an array of antenna elements, generally designated by the reference 1, the output of which delivers signals to the input of a beam forming network designated by the general reference 2 and which will be also called the BFN network.

 This system also includes an adaptive or adaptation processor designated by the general reference 3.

This adaptive processor 3 is suitable for controlling the weights of the variables and therefore of the signal processing parameters in the network.
BFN.

 As mentioned above, these weight values determine the radiation pattern of the antenna.

 This adaptive processor 3 receives as input on the one hand the input signals from the BFN network and on the other hand, the output signals from the latter in order to develop the weights mentioned previously, in a conventional manner.

 In Fig.2, an adaptive system is illustrated comprising an algorithm implementing a method of least squares means called LMS algorithm which is the most frequently used time-based adaptation method.

 This algorithm is a gradient-based algorithm which reduces the mean square value of an error signal e (t), this error signal being the difference between a reference signal r (t) generated locally and the output of the BFN network, y (t).

The synoptic diagram represented on this figure 2 can be translated by the following equations
W (n + l) = W (n) + ge (n) .X * (n); (1)
e (n) = r (n) - XT (n) .W (n); (2)
in which the complex vectors W (n) and X (n) are the samples at time n of the antenna weights and the signals in the antenna elements respectively, e (n) is the corresponding sample of the instantaneous error, g is the step of progression in the algorithm and W (n + l) is the update of the weight vector.

The convergence speed of the LMS algorithm is proportional to the progression step g. However, for this algorithm to be stable, this progression step must be between the limits set by the following stability condition
O <g <1 / Pt (3)
where Pt is the total power received by the network. (see the document "ADAPTIVE
ANTENNAS. CONCEPT AND PERFORMANCE "RT Compton
Englewood Cliffs, NJ: Prectice-Hall, 1988).

 The so-called LMS algorithm assumes that a reference signal r (t) is generated and can be correlated with the desired signals and not correlated with the spurious signals.

 However, in many practical applications, the generation of the reference signal induces a delay which destroys the correlation with the desired signals.

 For example, a dispersed spectrum division code multiple access telecommunications system allows a reference signal to be easily generated due to knowledge of the desired user pseudo-noise signature sequence.

For further information concerning this point, reference may be made to the document by S. MUNOZ-GARCIA mentioned above and to the documents "AN ADAPTIVE ARRAY IN A SPREAD SPECTRUM
COMMUNICATION SYSTEM "RT Compton, Proc. IEEE, volume 66, n" 3, March 1978 and
"COMBINATION OF AN ADAPTIVE ANTENNA AND A
CANCELLER OF INTERFERENCE FOR DIRECT-SEQUENCE SPREAD
SPECTRUM MULTIPLE ACCESS SYSTEMS ", R.Kohno et al, IEEE
J-SAC, volume 8, n "4, May 1990.

 The desired user signal is then concentrated and demodulated using a conventional correlation receiver and the received data is then dispersed again using the same pseudo-noise sequence.

 This method induces a delay which is much longer than the correlation time of the received signal and this, by a factor which is of the order of the dispersion factor.

 The delay applied during the generation of the reference signal then requires a modification of the basic LMS algorithm.

The synoptic diagram represented on the
Fig.3 illustrates the implementation of a delayed LMS algorithm in an adaptive array antenna.

 Thereafter, it will be assumed that the generation of the reference signal introduces a delay equivalent to a duration of D samples. The input signals applied to the input of the adaptation means must therefore be shifted by a corresponding duration, as well as the output signals from the BFN network which are compared to the reference signal.

The output of the BFN network and the signals in the elements of the antenna element network are then stored for a period corresponding to D samples to obtain the correct delayed error signal. These signals are applied to the delayed LMS algorithm which is represented by the following equations
W (n + 1) = W (n) + ge (nD) .X * (nD) (4)
m
e (nD) = r (nD) -XTn-D) .W (nD) (5)
It results from this delay in the reaction loop of the LMS algorithm, that the step of progression
g should be limited to a much narrower range than previously.

Indeed, the stability condition for this delayed LMS algorithm is roughly given by the relation
O <g <l / D.Pt (6)
It can therefore be seen that the progression step in the delayed LaS algorithm is significantly reduced.

This has two consequences. On the one hand, the convergence of the algorithm is slower and on the other hand r the delayed LMS algorithm presents a mean squared error in steady state increased compared to that of a classic LMS algorithm
In this FIG. 3, the reference signal generator has been designated by the general reference 4, while the means for delaying the input signals of the adaptation means and the output signals of the BFN network 2, are designated by the references 5 and 6 respectively.

 In Fig.4, there is shown a block diagram of an adaptive system according to the invention which makes it possible to solve the problems inherent in the delay during the generation of the reference signal.

It can be seen in the light of this FIG. 4 that in this system, second means of signal processing equivalent to the first are used and in the example illustrated, a second network
BFN designated by the reference 7 equivalent to the first designated by the reference 2, whose processing parameters are also established by the adaptation means 3, the second BFN network 7 receiving on an input the delayed input signals delivered by the means late 5.

 The output signals of this second network BFN 7, then take the form of processed and delayed output signals which are compared with the reference signal delivered by the reference signal generator 4, to determine the correction signal applied to the processor. adaptation 3.

The new algorithm of this configuration can then be described by the following equations
w (n + 1) = w (n) + ge '(nD) .X' * (nD) (7)
e '(nD) = r' (nD) -y '(nD) (8)
m
y '(nD) = X' (nD) .W (n) (9)
We can then imagine that the second network
BFN designated by the reference 7 in this figure 4, receives a delayed version of the signals of the antenna elements X '(nD). The reference signal is generated from the output of the first BFN network 2 and it is compared with the output of the second BFN network 7, output y ′ (nD) which is correlated with the reference signal without applying additional delay.

 We can see that in this way the LaS feedback loop is implemented through the second BFN network 7.

 Since the loop does not include any delay, the stability condition is that of a classic LMS algorithm, which is given by equation (3) mentioned above.

 The weight vector calculated by the LMS algorithm can be directly applied to the first BFN 2 network with the sole condition that the configuration of signals seen by the antenna, ie the directions of arrival, the powers of the signals, etc ... does not change significantly during a time interval corresponding to a duration of D samples. This condition is encountered in the majority of practical cases.

It can therefore be seen that the proposed structure implements a conventional LMS algorithm driven by a signal X '(nD) instead of X' (n). This can be represented by replacing in the previous equations
X (n) = X '(nD) (10) r (n) = r' (nD) (11) e (n) = e '(nD) (12)
and comparing them to equations (1) and (2) mentioned above.

 The convergence speed of the algorithm is then accelerated and the steady-state performance is that of a conventional LMS algorithm.

 A practical embodiment of this system may consist in using the same physical device to realize the two BFN networks, by operating this device at a higher frequency and by using an appropriate multiplexing of the input signals.

 Furthermore, it will also be noted that the memory capacities of this system are less important than that required in a delayed LMS configuration since the storage of the network output signals is not necessary.

Claims (2)

 1. Adaptive signal processing system, of the type comprising first signal processing means (2) receiving input signals and delivering processed output signals and whose processing parameters are established by adaptation means ( 3) with feedback loop using a mean least squares method receiving on one input delayed input signals and on another input a correction signal established from a reference signal delivered by a reference signal generator ( 4) from the processed output signals, and from the processed and delayed output signals, the delayed input and output signals being shifted by a duration corresponding to the delay inherent in the reference signal generator, characterized in that the processed and delayed output signals are delivered by second signal processing means (7) equivalent to the first (2), whose processing parameters t are also established by the adaptation means (3) and receiving on an input the delayed input signals.  2. System according to claim 1, characterized in that the signal processing means comprise adaptive beam forming means receiving at the input signals delivered by an array of antenna elements (1).