Uniform blind equalization of two-path channels with zeros on the unit circle

Blind equalization of channels with z-transform having zeros on the unit circle or even just close-by is a very difficult task as the equalizer length tends to infinity. We propose a new blind equalizer for constant-modulus (CM) signals that uniformly equalizes inter-symbol interference caused by two-path propagations with arbitrary position of the zeros of the channel transfer function in the z-domain. The equalizer achieves perfect signal recovery in the noise-free case. It avoids the divergence of the inverse of the channel by truncating the zero-forcing equalizer filter at a certain order and uses the observation that the remainder is proportional to a single unknown transmitted symbol. A CM cost function is then optimized with respect to the unknown parameters of a two-path channel and that one symbol. We investigate our new equalizer theoretically and in numerical Monte-Carlo simulations and present results for the variance of the path parameters and the equalized symbols. Furthermore, we compare our algorithm with the classical parametric CMA.