Statistical efficiency study of blind identification/equalization of two-path channels with the constant-modulus-criterion

The statistical efficiency of a batch-processing constant-modulus blind equalizer for estimating a) the complex-valued tap weight within a two-path channel model and b) the equalized signal is investigated. Expanding the constant-modulus cost-function in a multidimensional Taylor series up to third order we derive closed-form expressions for the first-order bias and variance of the path weight and the equalized symbols as a function of the variance of the Gaussian distributed noise, the block length, and the actual channel parameters. We study random as well as deterministic symbol sequences. In the first case we compute the average of the bias and variance over zero-mean random (real-valued) signals of binary pulse amplitude modulation (PAM), and (complex-valued) signals of phase shift keying (PSK) modulation. We compare our analytical results with Monte-Carlo simulations and find good agreement for small to medium noise variance.