Search

This letter develops theoretical analysis of the normalized LMS algorithm (NLMSA) for use in complex-domain adaptive filters in the presence of impulse noise at filter input. We propose a new "stochastic" model for such impulse noise, and assume that filter reference input process is a white process, e.g., digital QAM data, White & Gaussian process, etc. In the analysis, we derive a simple difference equation for mean square tap weight misalignment (MSTWM). Experiment is carried out to demonstrate effectiveness of the NLMSA in robust filtering in the presence of the impulse noise at the filter input. Good agreement between simulated and theoretically calculated filter convergence, in a transient phase as well as in a steady-state, proves the validity of the analysis.

The paper presents an adaptive algorithm named adaptive threshold nonlinear algorithm for use in adaptive filters in the complex-number domain (c-ATNA) in applications to digital QAM systems. Although the c-ATNA is very simple to implement, it makes adaptive filters highly robust against impulse noise and at the same time it ensures filter convergence as fast as that of the well-known LMS algorithm. Analysis is developed to derive a set of difference equations for calculating transient behavior as well as steady-state performance. Experiment with simulations and theoretical calculations for some examples of filter convergence in the presence of Contaminated Gaussian Noise demonstrates that the c-ATNA is effective in combating impulse noise. Good agreement between simulated and theoretical convergence proves the validity of the analysis.

This letter develops convergence analysis of normalized sign-sign algorithm (NSSA) for FIR-type adaptive filters, based on an assumption that filter tap weights are Gaussian distributed. We derive a set of difference equations for theoretically calculating transient behavior of filter convergence, when the filter input is a White & Gaussian process. For a colored Gaussian input and a large number of tap weights, approximate difference equations are also proposed. Experiment with simulations and theoretical calculations of filter convergence demonstrates good agreement between simulations and theory, proving the validity of the analysis.

In this letter, we derive a probability density function (PDF) for a modulus of product of two complex-valued Gaussian random variables. The PDF is expressed using Modified Bessel Functions, and the probability distribution is named Gaussian Product Modulus Distribution. Some examples of expectation calculation are provided.