Performance analysis of the multiuser Shalvi-Weinstein algorithm

Abstract

Performance analyses of blind adaptive equalizers provide valuable insights on their behavior, thus being fundamental in the design process. In the literature, interesting theoretical results to predict the steady-state performance of well-known constant-modulus-based algorithms were obtained under rather idealized equalization conditions. In practice, however, the communication channel is often noisy and perfect equalization can be unachievable. In this paper, we employ a linear regression model, commonly used in supervised adaptive filtering, to consider imperfect equalization conditions in the steady-state analysis of constant-modulus-based algorithms. Due to the nonlinear nature of blind algorithms, this analysis extension is a rather challenging, but rewarding, task. In particular, we apply the extended analysis model to the multiuser Shalvi–Weinstein algorithm, chosen due to its inherent advantages in adaptive blind equalization, namely high convergence rate and numerical robustness. As a result, we obtain a theoretical expression for its excess mean-square error (EMSE) at steady state. Interestingly enough, the resulting EMSE expression allows for the identification of distinct performance degradation causes, such as effects due to high-order statistics of the transmitted constellation, imperfect equalization, and multiuser cross-correlation penalty. In spite of the many assumptions considered throughout the EMSE expression derivation, simulation results validate it under realistic operating conditions.