Equalizing with Fractionally-spaced Constant Modulus and Second-order-statistics Blind Receivers

This dissertation is concerned with the blind, cold-start equalization of a closed-eye, fractionally-spaced channel, so that the error rate is suuciently reduced for transfer to a decision directed mode. First, a simulated comparison study of recently proposed second-order-statistics (SOS) algorithms and the constant modulus algorithm (CMA) shows a severe lack of robustness for the SOS algorithms to practical situations, while to the contrary, CMA appears quite robust. Next, a class of cyclic all-pass channels is shown to be the only channel class whose cascade with a core channel results in no change in the SOS indicators used by many SOS algorithms. This ambiguity raises robustness concerns for SOS algorithms due to the possibility of channel mis-identiication. The sequel focuses on the robustness properties of fractionally-spaced CMA. Though the literature contains reasonable treatment for CMA's robustness properties to violation of three of the four perfect equalization assumptions, essentially no analytical work exists for the undeniably practical case when the equalizer length is less than that needed for perfect equalization. Original algebraic analysis is presented for the constant modulus (CM) cost function, describing the deformation of the CM error surface due to undermodeling. The analysis is connected to previous work on CMA misadjustment, suggesting that similar to noisy LMS, a longer fractionally-spaced equalizer (FSE) is not always better than a shorter FSE. Next, a truncated Taylor series of the binary CM cost function is used to estimate the location of the undermodeled CM minima. A measure is proposed from this estimate to determine the proximity of CM and mean squared error (MSE) minima, suggesting that those CM minima with better MSE performance stay closer to their corresponding Wiener solutions than those CM minima with worse MSE performance. This dissertation can be used to determine design guidelines for length selection of a FSE updated by CMA (CMA-FSE) given speciic signalling formats and channel models. Together, this work and the recent work of others can be used to establish a cohesive behavioral theory of CMA-FSE describing the robustness properties of the CM criterion to practical situations. iii To Joe and Viv: my parents, my inspiration, my friends. To Jerry Garcia: Long ago under a hot Texas sun I heard the strangest sound emanating from my sister's room. What did I know, I thought that tone was normal and that everyone knew about it. It took a number of years (and a seventh grade math …