CMA adaptive equalization in subspace pre-whitened blind receivers

Abstract

In blind channel equalization, the use of whitening transformation (WT) preceding the constant modulus algorithm (CMA), referred to as the pre-whitened CMA, may accelerate the rate of convergence of using the CMA alone. In this work, we develop a novel subspace pre-whitened CMA (SP-CMA) using the subspace WT. By allowing the channel matrix to be non-square, this approach for the subspace WT offers greater flexibility in the design of the WT than the conventional per-whitened CMA does. The similarities and differences between the SP-CMA and the conventional CMA were first examined and analyzed in terms of their convergence behaviors from a theoretical viewpoint. The convergence behavior of the SP-CMA was analyzed under the whiteness assumption in which the input of the blind equalizer has been whitened beforehand by the subspace WT. The upper bound of the improvement in convergence of the SP-CMA over its CMA counterpart was developed. This analysis can be readily extended to other existing pre-whitened CMA schemes. Computer simulations using two highly dispersive multipath channels confirmed the superior convergence of the SP-CMA.