Junyu 1998

Abstract of PhD Dissertation
Electrical Engineering Department, UCLA, September 1998
Advisor: Prof. Ali H. Sayed

Steady-State Performance of Fractionally-Spaced Blind Adaptive Algorithms

Junyu, UCLA

Constant Modulus algorithms (CMA) are among the most popular adaptive schemes for blind equalization. Nevertheless, only a handful of results are available in the literature regarding the steady-state performance of this class of algorithms. This is mainly due to the fact that CM algorithms involve nonlinear update equations for the weight error vector, and classical approaches to steady-state performance evaluation often require, as an intermediate step, that a recursion be determined for the covariance matrix of the weight error vector. This step becomes a burden for CM algorithms due to their inherent nonlinear updates.

In this thesis we propose a new approach to the analysis of the steady-state performance of blind adaptive algorithms. The approach bypasses the need for the aforementioned intermediate step and works directly with the variance of the a-priori estimation error. The derivation is based on a fundamental relation that in fact holds for a general class of adaptive filters, not just CM algorithms. It corresponds to an energy-preserving relation that allows us to avoid working directly with the nonlinear update that is characteristic of CM algorithms. The energy relation is established by showing how a generic adaptive scheme can be represented as an interconnection of two subsystems: a lossless feedforward block and a feedback path.

The main contribution of this thesis is to apply this mathematical framework to the analysis of the mean square error of several CM algorithms. The thesis is organized as follows. Chapters 1 and 2 review the blind equalization problem and introduce the CM algorithms. The steady-state analysis of CM algorithms is in Chapters 3, 4, and 5. Chapter 6 concludes this thesis.

Acknowledgment This work was supported in part by the National Science Foundation under grants MIP-9796147 and CCR-9732376. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.