Simplified Robust Adaptive Detection and Beamforming for Wireless Communications

6Robust Constant Modulus Algorithms

6.1 Introduction

Blind equalization of intersymbol interference (ISI) in communications channels and blind separation of multiple users are crucial signal processing techniques in particular communications systems design. Because of the similarity between ISI and multiple access interference (MAI), many researchers have attempted to use blind equalization techniques, such as the constant modulus algorithm (CMA) to suppress MAI [1]. In addition to blind equalization and blind beamforming [2], the CMA can be used also for code acquisition in the context of DS‐CDMA systems [3, 4]. One of the earliest blind receiver designs is the Godared algorithm [5–7]. Godared [5] observed from simulations that blind receivers that minimize the CM cost function have similar mean‐squared error (MSE) performance to non‐blind Wiener receivers. Similar observations were also made by Treichler and Agee [6]. However, due to the complexity of the CM cost function, the performance of CM receivers has primarily been evaluated using numerical simulations or using Monte Carlo simulations [7]. Theoretical analysis is typically based on either the noiseless case or approximations of the cost function [8]. Zeng et al. presented a geometrical approach that relates the CM to Wiener (or minimum MSE) receivers [9]. The authors provided a generalization of this geometrical approach [10] using a subspace constraint imposed on the CM cost function during the optimization. The analysis ...