This paper proposes a forecasting method for uni-variate time series based on a combination of Long-Short-Term-Memory (LSTM) Neural Network and Empirical Mode Decomposition (EMD) with envelope extraction. The basic steps of the method are 1) to split each Intrinsic Mode Function (IMF) into its envelope and detail, 2) to forecast separately these two components for each IMF, using LSTM and 3) to recombine the different forecasts. As already proven, the use of EMD in a forecast setting improves the accuracy. In this paper, we show that the splitting step on each IMF provides further significant improvement on the forecast. This is developed to be applied to treasury transactions forecast. The method relies on well known and easily implementable techniques and is usable with most forecasting algorithms. We experimented it on 3 non-stationary time series, showing its portability to a wide variety of univariate time series.

This paper considers time-domain beamforming in MIMO convolutive systems, using the classical LU-based (Gauss elimination) polynomial matrix decomposition. As the pre- and postfilters are not paraunitary, the output signal-to-noise ratio is degraded compared to QR-based beamforming. We investigate the role of the postfilter on the noise enhancement and propose a simple and efficient solution. We show that a simple normalisation of the postfilter, using row balancing, is sufficient to significantly improve the conditioning of the system and thereby, the performance of the system. With the resulting performance increase, the LU-based polynomial matrix decomposition for MIMO beamforming becomes competitive as compared to its QR-based counterparts, in terms of bit error rate, for medium input SNR.

We attack the problem of perfect equalizability of multiuser channels, in which the usual linear time-invariant assumption is dismissed. In the linear, time-invariant case, the condition for perfect equalizability is plain and expressed in terms of the column rank of the channel's transfer matrix. Using the module-theoretic approach developed by M. Fliess (see System and Control Letters, vol.15, p.391-6, 1990; Linear Algebra and its Application, no.203-204, p.429-42, 1994; Forum Math, vol.2, p.212-32, 1990), in which the transfer matrix of a time-varying channel as well as the rank of a nonlinear channel are clearly defined, we show how the condition obtained in the linear time-invariant case naturally extends to the time-varying and the nonlinear cases.

This article reviews the super-exponential algorithm proposed by Shalvi and Weinstein (1993) for blind channel equalization. The principle of this algorithm-Hadamard exponentiation, projection over the set of attainable combined channel-equalizer impulse responses followed by a normalization-is shown to coincide with a gradient search of an extremum of a cost function. The cost function belongs to the family of functions given as the ratio of the standard l/sub 2p/ and l/sub 2/ sequence norms, where p>1. This family is very relevant in blind channel equalization, tracing back to Donoho's (1981) work on minimum entropy deconvolution and also underlying the Godard (1980) (or constant modulus) and the earlier Shalvi-Weinstein algorithms. Using this gradient search interpretation, which is more tractable for analytical study, we give a simple proof of convergence for the super-exponential algorithm. Finally, we show that the gradient step-size choice giving rise to the super-exponential algorithm is optimal.

This paper reviews the super-exponential algorithm proposed by Shalvi and Weinstein (1993) for blind channel equalization. We show that the algorithm coincides with a gradient search of a maximum of a cost function, which belongs to a family of functions very relevant in blind channel equalization. This family traces back to Donoho's (1981) work on minimum entropy deconvolution, and also underlies the Godard (1980) (or constant modulus) and the Shalvi-Weinstein algorithms. Using this gradient search interpretation, we give a simple proof of convergence for the super-exponential algorithm. Finally, we show that the gradient step-size choice giving rise to the super-exponential algorithm is optimal.

In this paper we present a new robust adaptive algorithm. It is derived from the standard QR decomposition based RLS (QRD-RLS) algorithm by introducing a non-orthogonal transform into the update recursion. Instead of updating an upper triangular matrix, as it is the case for the QRD-RLS, we adapt an upper triangular block diagonal matrix. The complexity of the algorithm, thus obtained, varies from O(N/sup 2/) to O(N) when the size of the diagonal blocks decreases. Simulations of the new algorithm have shown a better robustness than the standard QRD-based algorithm in the context of multichannel adaptive filtering with highly inter-correlated channels.

We establish the existence of asymptotic stationary points for a class of adaptive IIR filtering algorithms, including (S)HARF, the Feintuch (1996) algorithm, and Landau's (1976) algorithm, for reduced-order cases. We show first that the nonlinear equations characterizing a stationary point admit a solution giving rise to a stable transfer function, when the input is white noise. We then show that an analytic procedure to construct the solution may be reduced to the Nevanlinna-Pick interpolation problem. The white noise assumption on the input simplifies the mathematics of an already difficult problem, although the existence proof appears extendable to correlated inputs as well.

A significant drawback of the least mean square (LMS) algorithm is slow convergence speed when the input covariance matrix is ill-conditioned. Two structures are presented and studied for increasing the convergence speed for this case. The structures incorporate a prewhitening filter prior to the usual LMS adaptation. When the prewhitening filter is also adaptive the input to the LMS algorithm is nonstationary. An analysis of the coupling effect between the two adaptive algorithms show that the adaptive prewhitener has the capability of significantly speeding up to LMS adaptation as compared to a system without prewhitening. When the prewhitening filter is fixed (nonadaptive), the structure is shown to be equivalent to the filtered-X LMS algorithm. Stability conditions and transient means behavior are given in the time domain, in terms of the parameters of the pre-whitening filter.>

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.>