New class of zero-forcing cost functions in blind equalization

The use of gradient descent recursive algorithms in blind adaptive equalization requires a cost function with a unique minimum such that the FIR equalizer setup removes sufficient intersymbol interference (ISI). A class of such cost functions is proposed. The newly proposed class is based on minimizing the difference between any two norms of the joint channel-equalizer impulse response, each raised to the same power, i.e., ||·||_p^ζ-||·|| ^ζ_q, where p<q. A set of implementable recursive online algorithms using the above cost functions is also derived for QAM inputs. Some examples show that the above class could be unimodal in equalizer weights. In addition, results of analysis of the effects of additive white Gaussian noise (AWGN) on the ISI for the ||·||⁴₂-||·||₄ ⁴ cost functions´ algorithm as well as the well-known CMA algorithm are presented. It is shown that for both of the above algorithms, the AWGN affects the residual ISI only in O(1/SNR²) under a high SNR assumption. Extensive simulations show that the performance of the newly proposed algorithms is comparable with the CMA algorithms´ performance without the misconvergence