Performance analysis of the multiuser Shalvi-Weinstein algorithm

• Published in: Signal processing Vol. 163; pp. 153 - 165
• Main Authors: Pavan, Flávio R.M., Silva, Magno T.M., Miranda, Maria D.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2019
• Subjects: Adaptive signal processing; Higher-order statistics; Multiuser blind equalization; Performance analysis; Shalvi–Weinstein algorithm; Adaptive signal processing; Higher-order statistics; Performance analysis; Shalvi–Weinstein algorithm; Multiuser blind equalization
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2019.05.012

•An extended analysis model is proposed to consider imperfect equalization conditions in the steady-state analysis of blind equalization constant-modulus-based algorithms.•This extended analysis model is applied to obtain a theoretical expression for the excess mean-square error of the multiuser Shalvi-Weinstein algorithm at steady state.•The proposed analysis expression agrees with simulated results in realistic operating conditions, even when perfect equalization is unachievable or channel noise is present.•The proposed analysis expression allows for the identification of distinct performance degradation causes in the multiuser Shalvi-Weinstein algorithm. 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.