Performance analysis of a family of adaptive blind equalization algorithms for square-QAM

Multimodulus algorithms (MMA) based adaptive blind equalizers mitigate inter-symbol interference and recover carrier-phase in communication systems by minimizing dispersion in the in-phase and quadrature components of the received signal using the respective components of the equalized sequence in a decoupled manner. These equalizers are mostly incorporated in bandwidth-efficient digital receivers which rely on quadrature amplitude modulation (QAM) signaling. The nonlinearities in the update equations of these equalizers tend to lead to difficulties in the study of their steady-state performance. This paper presents originally the steady-state excess mean-square-error (EMSE) analysis of different members of multimodulus equalizers MMAp-q in a non-stationary environment using energy conservation arguments, and thus bypassing the need for working directly with the weight error covariance matrix. In doing so, the exact and approximate expressions for the steady-state mean-square-error of several MMA based blind equalization algorithms are derived, including MMA2-2, MMA2-1, MMA1-2, and MMA1-1. The accuracy of the derived analytical results is validated using Monte-Carlo experiments and found to be in close agreement.