Abstract
This paper deals with the analysis of adaptive Volterra filters, driven by the LMS algorithm, in the finite-alphabet inputs case. A tailored approach for the input context is presented and used to analyze the behavior of this nonlinear adaptive filter. Complete and rigorous mean square analysis is provided without any constraining independence assumption. Exact transient and steady-state performances expressed in terms of critical step size, rate of transient decrease, optimal step size, excess mean square error in stationary mode, and tracking nonstationarities are deduced.
Highlights
Adaptive systems have been extensively designed and implemented in the area of digital communications
The exact analysis of adaptive Volterra filters made for the finite-alphabet input case is illustrated
We have presented an exact and complete theoretical analysis of the generic LMS algorithm used for the identification of time-varying Volterra structures
Summary
Adaptive systems have been extensively designed and implemented in the area of digital communications. Nonlinear adaptive filters, such as adaptive Volterra filters, have been used to model nonlinear channels encountered in satellite communications applications [1, 2]. When dealing with land-mobile satellite systems, the channels are time varying and can be modeled by a general Mth-order Markovian model to describe these variations [4]. To take into account the effect of the amplifier’s nonlinearity and channel variations, one can model the equivalent baseband channel by a time-varying Volterra filter. The baseband model of the nonlinear time-varying channel is described as follows: q L−1 L−1 L−1 yk =. Im) is a complex number, referred to as the mth-order Volterra kernel. This latter complex number may be a time-varying parameter.
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