Bussgang-zero crossing equalization: An integrated HOS-SOS approach

In this paper, an integrated higher order statistics (HOS) and second order statistics (SOS) based equalization technique is presented as an extension of the Bussgang equalization algorithm. This extension allows the simultaneous taking into account of the statistical knowledge about the data source, as done in the conventional HOS approaches and, in particular, by Buss-gang-like equalization algorithms such as super exponential, constant modulus, etc., and the spectral redundancy usually present in pulse-amplitude modulation (PAM) and quadrature-amplitude modulation (QAM) modulated signals, exploited by SOS-based approaches. The technique presented here employs a new form of SOS equalization that naturally inserts into the Bussgang scheme. It is based on a zero crossing (ZC) property of the received signal when it is passed through a suitable filter. The novel equalization scheme is presented in a Bayesian estimation framework, after illustration of the general Bussgang paradigm and of the principles of the ZC approach. From simulated experiments, it results that the extended Bussgang-ZC equalizer not only outperforms conventional Bussgang equalizers but is also robust to situations where HOS and SOS approaches individually fail.