The Least Mean Square (LMS) algorithm, introduced by Widrow and Hoff in 1959 [12] is an adaptive algorithm, which uses a gradient-based method of steepest decent [10]. LMS algorithm uses the estimates of the gradient vector from the available data. LMS incorporates an iterative procedure that makes successive corrections to the weight vector in the direction of the negative of the gradient vect...

In wireless communication system, a Decision Feedback Equalizer (DFE) to cancel the intersymbol interference (ISI) is required. In this paper, an exact convergence analysis of the (DFE) adapted by the Least Mean Square (LMS) algorithm during the training phase is derived by taking into account the finite alphabet context of data transmission. This allows us to determine the shortest training se...

Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...

This paper proposes a new regularized transform domain normalized LMS (R-TDNLMS) algorithm and studies its mean and mean square convergence performances. The proposed algorithm extends the conventional TDNLMS algorithm by imposing a regularization term on the filter coefficients to reduce the variance of estimators due to the lacking of excitation in a certain frequency band or in the presence ...

Regression models are used in many areas of signal processing, e.g., spectral analysis and speech LPC, where block processing methods have typically been used to estimate the unknown coefficients. Iterative methods for adaptive estimation fall into two categories: the least-mean-square (LMS) algorithm and the recursive-least-squares (RLS) algorithm. The LMS algorithm offers low complexity and s...

We extend the use of the least squares method to develop a recursive algorithm for the design of adaptive transversal filters such that, given the least-square estimate of a vector of a filter at iteration, we may compute the updated estimate of this vector at iteration upon the arrival of new data. In this paper, we propose a new tap-weight-updated RLS algorithm for an adaptive transversal fil...