The theoretical properties of a novel self adaptive source separation algorithm are studied. It is a normalized version of a modified relative gradient. It is shown that its stability domain in terms of the normalized kurtosises of sources is complementary of the unmodified gradient algorithm. So it can separate a source with a very high kurtosis from other sources having positive kurtosis. The algorithm is then used to analyze EEG signals because they often have positive kurtosises especially for patients suffering from epilepsy. The good behavior of this novel algorithm is illustrated via simulated data and then demonstrated with real signals in an EEG analysis to separate an epileptic source from other brain signals.

This paper presents a novel unsupervised (blind) adaptive decision feedback equalizer (DFE). It can be thought of as the cascade of four devices, whose main components are a purely recursive filter (/spl Rscr/) and a transversal filter (/spl Tscr/). Its major feature is the ability to deal with severe quickly time-varying channels, unlike the conventional adaptive DFE. This result is obtained by allowing the new equalizer to modify, in a reversible way, both its structure and its adaptation according to some measure of performance such as the mean-square error (MSE). In the starting mode, /spl Rscr/ comes first and whitens its own output by means of a prediction principle, while /spl Tscr/ removes the remaining intersymbol interference (ISI) thanks to the Godard (1980) (or Shalvi-Weinstein (1990)) algorithm. In the tracking mode the equalizer becomes the classical DFE controlled by the decision-directed (DD) least-mean-square (LMS) algorithm. With the same computational complexity, the new unsupervised equalizer exhibits the same convergence speed, steady-state MSE, and bit-error rate (BER) as the trained conventional DFE, but it requires no training. It has been implemented on a digital signal processor (DSP) and tested on underwater communications signals-its performances are really convincing.

Extracting one specific component of a linear mixture is to isolate it due to the observation of several mixtures of all the components. This is done in an unsupervised way, based on the sole knowledge that the components are independent. The classical solution is independent component analysis which extracts the components all at the same time. In this paper, given at least as many sensors as components, we propose a simpler approach which independently extracts each component with one neuron. The weights of the neuron are optimized by minimizing an even polynomial of its output. The corresponding adaptive algorithm is an extended anti-Hebbian rule with very low complexity. It can extract any specific negative kurtosis component. Global stability of the algorithm is investigated as well as steady-state fluctuations. The influence of additive noise is also considered. These theoretical results are thoroughly confirmed by computer simulations.

We propose a new adaptive algorithm to separate a linear mixture of sources using an extended anti-Hebbian rule. This solution can be viewed as a stochastic gradient way to minimize certain output high order statistics. The system is modular: it is decomposed into parallel and independent subsystems. Each one is capable of extracting one source with negative kurtosis out of the mixture, provided the number of observations is greater or equal to the number of sources and provided it is appropriately initialized.

In order to perform separation of a mixture of sources, an interesting approach is to maximise a contrast function: e.g. the contrast of Comon. This paper brings two novel contributions (i) a novel algorithm as proposed in order to adaptively maximise Comon's contrast. However it requires a preprocessing whitening operation which is awkward when the mixture is ill-conditioned. (ii) A new criterion is defined that is free of the prewhitening step. In the case of two sources it can be proved that this criterion is a contrast. This contrast can also be adaptively maximized and has the additional advantage not to require identical signs for the fourth-order cumulants of the sources. Achievement of these two adaptive algorithms is demonstrated using a new performance index.>

Most self-adaptive equalizers are FIR filters controlled by a nonlinear function of the output. But they can present local minima which do not equalize the channel. For a QAM system, this paper brings two novel ideas which jointly suppress this drawback (i) the complex equalizer is the cascade of a backward innovator, a forward innovator and a complex gain realizing both the power control and the carrier phase tracking; (ii) a novel minimization criterion combines the two criteria of prediction and equalization. This criterion is unimodal and is minimized by the optimum equalizer. It can be minimized adaptively at the same low computational cost as any other Bussgang technique. By implementing the forward innovator second, the latter can be made recursive and if output decisions are fed back in its loop, the structure resumes to a classical feedback equalizer. This method is successful with very severe channels, such as that of Porat and Friedlander (see IEEE Trans. on Signal Processing, vol.39, p.522-526, 1991), where other methods fail.>

In order to avoid the coding noise accumulation in successive transcoders, a new fully digital structure is used where all the filters have quantized inputs. Whereas the coding noise spectrum is flat with the CCITT algorithm, with this new structure it presents a spectral shaping which can be further improved in high-frequency region, by filtering the quantizing noise.>

The behavior of autoregressive moving average (ARMA) predictors is analyzed for neglected dynamic cases with nonstationary signals. For this analysis, nonstationarity types must be considered (abrupt or smooth changes in the mean and variance). Some procedures can be used to improve the algorithm performances and limit the self-stabilization oscillations. The resulting algorithm is not much more complex than the NLMS algorithm and can be used for applications like ADPCM or data compression with highly nonstationary signals.>

The robustness of adaptive differential pulse code modulation (ADPCM) systems versus transmission errors is addressed. To secure the stability of the decoder, it is necessary to modify the form of the LMS (least-mean-square) algorithm used to adapt the predictor. Solutions introducing soft constraints are investigated. The leakage algorithm is proved to be not fully satisfactory, and a new stabilizing algorithm is presented that makes it possible to achieve good performances. Compared to existing methods, the main advantage of this algorithm is its low computational complexity. Form a theoretical point of view, the effect of transmission errors is described by a set of nonlinear recurrent equations. An analysis is carries out in the deterministic second-order case.>

The stability of the classical differential pulse code modulation (DPCM) transmission systems is considered in the sense of having a bounded prediction error e=s-s for a bounded input s. The difficulty stems from the nonlinear and recursive nature of the predictor, due to the inclusion of quantization in the filtering loop that achieves prediction. The classical stability constraints of linear filters are currently imposed on the loop filter. It is shown that these constraints are unnecessarily restrictive. For instance, when the loop filter is a one-order cell, its unique coefficient can overcross the value 1. In the second-order case, the coefficients a/sub 1/, a/sub 2/ may lie outside the stability triangle. This is a consequence of the amplitude limitation at the quantizer output.>

The unfavorable effects of narrowband inputs on the decoder adjustment when the LMS algorithm is used are analyzed. An explanation is given for the behavior of the CCITT algorithm. Suboptimality of prediction is granted to achieve adjustment, resulting in a satisfactory tradeoff between reduction rate and adjustment. The link between adjustment and uniform stability is enhanced.>

Consideration is given to the influence of the noise and data sequences present in the received data signal on a nondecision-aided timing recovery scheme in digital modem receivers, It is known that white noise is not particularly disturbing for timing recovery, whereas data signals such as local echo (or residual echo) introduce a bias, called jitter, into the sampling recovered phase. It is shown that when the disturbing data signal has power P less than the power S of the useful signal (whose timing must be recovered), the jitter is sinusoidal with amplitude proportional to the ratio P/S. In the opposite situation, the bias increases indefinitely with time.>

The authors study the capabilities of the exponentially weighted recursive-least-squares (RLS) and least-mean-squares (LMS) algorithms, when configured as adaptive predictors, to track a chirped sinusoid in white background noise. The lag and fluctuation behaviors of each of the algorithms are calculated, and their influence on the misadjustment error is determined. The optimum tracking parameters for each algorithm are evaluated. The misadjustment errors for these optimum values are compared as a function of the chirp rate psi , the SNR rho , and the number of filter taps M. It is shown that for sufficiently small psi , small rho , and M such that rho M>>1, the LMS algorithm is superior to RLS because it has a smaller lag.>

The authors consider adaptive prediction with an IIR (infinite impulse response) moving average (MA) part, controlled either by the recursive least-mean squares (LMS) algorithm or by an extended least squares (ELS) algorithm based on a posteriori errors. The predictor input is either the sum of bandpass components or a nonstationary speech sentence. The bounded input/bounded output (BIBO) stability is a major issue. Although both algorithms enjoy the self-stabilization property when the input is stationary, it is shown that with a nonstationary input the LMS algorithm can be unstable due to power jumps in the speech. The ELS algorithm always ensures BIBO stability.>

An analysis is presented of the causes of the accumulation of quantizing noise found in the transient state for successive CCITT adaptive differential pulse-code-modulation (ADPCM) transcoders connected synchronously. By decoupling the predictor and quantizer effect it is proved that, owing to a self-stabilization phenomenon, narrowband inputs cause local instabilities in the predictor of the jointly adaptive autoregressive moving-average-prediction/quantization used in the ADPCM 32-kb/s algorithm. Despite the assured global stability, these local instabilities are not synchronized at the encoder and its preceding decoder, and a mistracking occurs which creates quantizing noise accumulation. The tracking is then shown to be very sensitive to predictor/quantizer interaction. The discontinuities introduced in the standardized adaptive quantizer extend the mistracking problem to wideband inputs. A smoothed quantizer with reduced inauspicious interaction is proposed to remedy the problem.>

It is shown that an adaptive echo canceller with asynchronous inputs affected by sampling time jitter can be modeled as the identification of a time-varying channel by an adaptive filter, both the channel and the adaptive filter being fed with synchronous data. This allows application of theoretical results of the identification problem which are already known. It is proved that the problem is similar when the transmitter itself is slaved on an external jittered clock and the echo canceller is synchronous.>

It is shown that the stochastic error gradient cannot be computed exactly for adaptive recursive filters because of parameter time variations. The usual pseudogradient, (G), which recursively filters the increment, is based on the assumption of slow variations, which is false when the stability boundary is crossed. In the example of adaptive prediction with narrowband inputs, it is shown that (G) may eventually yield an unbounded output. The recursive LMS suppresses the increment filtering and ensures a bounded output, due to the self-stabilization phenomenon, without external stabilization procedures although the adaptive poles may momentarily go outside the unit circle.>

The author deals with array processing using a flexible antenna whose shape is time-varying. The purpose is to improve the techniques of beamforming and source-bearing estimation by estimating the array shape in real time. The original contribution of this paper is the use of the capability of the LMS (least-mean-squares) algorithm in adapting a nonstationary environment in association with the knowledge of a pilot signal. Limitations concerning the variations that can be tracked are established and performance gains on beamforming and source-bearing estimation techniques are shown.>

In a previous correspondence [1], we have studied an echo canceller (EC) compensating far-end echos affected by frequency offset. It has been shown that the sensitivity of the loop gain versus the powerPof the echo and the powerSof the signal, can be reduced by adoption of a normalized gain multiplied by the echo power. In this correspondence a novel and very simple algorithm is described that further reduces this sensitivity and yields an optimum phase loop gain proportional to(S/ p)^{1/6}.

In an echo canceller (EC) compensating far-end echos affected by frequency offset, the phase loop gain is highly dependent on the echo and signal powers. Adoption of a normalized gain multiplied by the echo power yields an improved robustness. It is shown that the latter gain depends only on the echo-to-signal ratio. Practical implementation of this idea is realized by generating a first unitary echo replica, on which the DPLL will act, and then controlling the output power. The system has the additional advantage of a reduced binary size for the canceller taps.

In digital adaptive echo cancellation, the sign algorithm is very attractive since it is multiplication free. However, when the residual echo undercrosses the useful signal level, the error sign is no longer significant of the canceller quality and the convergence stops. Introduction of extra noise into the error can eliminate this drawback. The system performances regarding the residual echo and the computational complexity are shown to be competitive with those of the classical gradient algorithm (not using the function sign).

It is well known that implementation of adaptive digital filters for echo cancellation in full-duplex transmission over telephone lines requires a large number of bits for the tap representation. This is due to the large dynamic ranges of the echo and far-end signal. In this paper, we introduce a new echo canceller: the "controlled gain echo canceller" (CGEC) which uses an adaptive gain control at the output of the classical echo canceller (CEC). A feedback loop permits approximate regulation of the front-edge CEC output power at a nominal level, independently of the echo and far-end signal levels. By this means, the precision required for adaptation is reduced to a minimum value. The analysis of adaptation, convergence, residual echo power, and computational complexity is given for the CGEC and compared to the similar quantities in a CEC; computer simulation results are presented. As an example, a 64 taps CGEC with only 16 bits instead of 20 can achieve secure binary data transmission (with bit error rate less than10 ^{-6}) for a far-end signal-to-noise ratio of 16 dB and for an echo to far-end signal ratio of 20 dB, independently of the echo and far-end signal powers.

A theoretical analysis of self-adaptive equalization for data-transmission is carried out starting from known convergence results for the corresponding trained adaptive filter. The development relies on a suitable ergodicity model for the sequence of observations at the output of the transmission channel. Thanks to the boundedness of the decision function used for data recovery, it can be proved that the algorithm is bounded. Strong convergence results can be reached when a perfect (noiseless) equalizer exists: the algorithm will converge to it if the eye pattern is initially open. Otherwise convergence may take place towards certain other stationary points of the algorithm for which domains of attraction have been defined. Some of them will result in a poor error rate. The case of a noisy channel exhibits limit points for the algorithm that differ from those of the classical (trained) algorithm. The stronger the noise, the greater the difference is. One of the principal results of this study is the proof of the stability of the usual decision feedback algorithms once the learning period is over.

This paper presents a new equalizer for rapidly time varying selective fading without an apriori information about the shape of that fading in frequency domain. The basic idea is to analyze the output of the channel by a set of adjacent filters covering the band of channel. Then, a gradient algorithm is used to identify frequency bands at which fading takes place and an other gradient algorithm is used to adapt only the gains of filters lying in vicinity of fading. This idea enables a high tracking speed for the equalizer and enables equalization of rapid fadings that are beyond the capabilities of presently existing equalizers.

The problem of simultaneously estimating phase and decoding data symbols from baseband data is posed. The phase sequence is assumed to be a random sequence on the circle, and the symbols are assumed to be equally likely symbols transmitted over a perfectly equalized channel. A dynamic programming algorithm (Viterbi algorithm) is derived for decoding a maximum {\em a posteriori} (MAP) phase-symbol sequence on a finite dimensional phase-symbol trellis. A new and interesting principle of Optimality for simultaneously estimating phase and decoding phase-amplitude coded symbols leads to an efficient two-step decoding procedure for decoding phase-symbol sequences. Simulation results for binary,8-ary phase shift keyed (PSK), and 16-quadrature amplitude shift keyed (QASK) symbol sets transmitted over random walk and sinusoidal jitter channels are presented and compared with results one may obtain with a decision-directed algorithm or with the binary Viterbi algorithm introduced by Ungerboeck. When phase fluctuations are severe and when occasional large phase fluctuations exist, MAP phase-symbol sequence decoding on circles is superior to Ungerboeck's technique, which in turn is superior to decision-directed techniques.

In this paper we consider the problem of estimation and detection of Weak optical signals formulated as a problem in point process theory. Indeed at very low light intensity the only information available from an intensity detector is the random distribution of time instants\{t_i \}at which photons of the field are absorbed and photoelectrons emitted. There is also a noise due to thermoelectrons or to a background optical field. Starting from the statistical properties of the point process\{t_i\}, we formulate for various kinds of optical fields the problem of estimation of the light intensity of a modulated beam. We show that in some cases the number of photoelectrons is a sufficient statistic. In general, theoretical results are complex and we formulate the problem in the case of linear estimation, which is solved by means of the resolvent of an integral equation using the covariance function of the field. Some detection problems are also considered.

In this paper stochastic point processes (PP) are studied by means of coincidence probabilities (CP). After a definition and short review of these CP, it is shown that they provide a complete statistical description of the PP. All the statistics of the resulting shot noise are derived and time intervals between successive occurrences are studied and related to CP. Some new applications, including the "generalized" renewal process, illustrate the coincidence approach. The method applies very well to such cases as nonstationary or multidimensional PP.