On the use of kernel structure for blind equalization

Abstract—The mathematical theory of kernel (null space) struc-ture of Hankel and Hankel-like matrices is applied to the problem of blind equalization of cochannel signals. This approach provides a new perspective on the blind equalization problem and gives in-sights into the identifiability conditions already presented in the lit-erature. An algorithm is presented that tracks the exact null space of the symbol matrix even in the presence of noise. This work ex-ploits shift structure in the oversampled channel output and the finite alphabet property of the signals. Previously, these two prop-erties were used independently in a two-step (equalize then sepa-rate) process. A contribution of the new approach is that it allows simultaneous exploitation of both shift structure and the finite al-phabet property of the signals. Index Terms—Adaptive equalizers, communications channels, deconvolution, equalizers, Hankel matrices, intersymbol interfer-ence, multipath channels, Toeplitz matrices