New blind equalisation for non-constant modulus signals using a segment cost function

Abstract

It is well known that for constant modulus (i.e., magnitude) signals the famous constant modulus (CM) blind equalisation algorithm implemented in a fractionally spaced equaliser can present a zero steady-state mean square error (MSE), which means completely eliminating the distortions introduced in transmitting signals through channels. But for non-constant modulus signals it suffers a large steady-state MSE. In order to overcome this defect, a segment cost function according to the CM criterion is suggested. The distinctive feature of the segment cost function is that the equalised signals (of the non-constant modulus signals) are divided into three segments to form a ⊓ shape where the ideal signals have a constant modulus instead of non-constant. And then a new blind equalisation algorithm seeks to minimise this segment cost function by applying a stochastic gradient method is proposed. When employing the proposed algorithm to equalise the 4-PAM or 16-QAM non-constant modulus signals, just as using the CM blind equalisation algorithm to equalise the 4-QAM constant modulus signal, a zero steady-state MSE can be obtained, which is derived. Compared to the classical bind equalisation algorithms, such as CMA, MMA, MCMA, or CMA+SDD, the proposed algorithm yields improved performance, especially for higher SNR.