Convergence and performance analysis of Godard family and multimodulus algorithms for blind equalization

Abstract

We obtain the convergence of the Godard family [including the Sato and constant modulus (CM) algorithms] and the multimodulus algorithms (MMA) in a unified way. Our analysis also works for CMA fractionally spaced equalizer (FSE). Our assumptions are quite realistic: The channel input can be asymptotically stationary and ergodic, the channel impulse response is finite and can be stationary and ergodic (this models fading channels), and the equalizer length is finite. The noise is independent and identically distributed (i.i.d.). The channel input can be discrete or continuous. Our approach allows us to approximate the whole trajectory of the equalizer coefficients. This provides estimates of the rate of convergence, and the system performance (symbol error rate) can be evaluated under transience and steady state.