Finite dictionary techniques for MSER equalization in RKHS

Abstract

Adaptive channel equalization is a signal processing technique to mitigate inter-symbol interference in a time dispersive channel. For adaptive equalization, minimum mean square error (MMSE) criterion-based reproducing kernel Hilbert spaces (RKHS) approaches such as the kernel least mean squares (KLMS) algorithm and its variants have been suggested in the literature for nonlinear channels. Another optimality criterion, based on minimum bit/symbol error rate (MBER/MSER), is a better choice for adapting an equalizer as compared to MMSE criterion. A kernel-based minimum symbol error rate (KMSER) equalization algorithm combines minimum symbol error rate (MSER)-based approaches with RKHS techniques. However, most algorithms in RKHS such as KMSER/KLMS require infinite storage requirement and hence cannot be practically implemented. To curtail the infinite memory requirement, and make adaptive algorithm suitable for implementation with finite memory and processing power, we propose quantized KMSER (QKMSER) and fixed-budget quantized KMSER (FBQKMSER)-based equalizers in this paper. In this paper, we derive the dynamical equation for MSE evolution of the QKMSER and FBQKMSER and find their performance to be asymptotically close to the MSE behavior of the KMSER. Also, it is found via simulations that the tracking performance of FBQKMSER is better than all the compared algorithms in this paper which is particularly useful for non-stationary channels.