Blind equalization of linear and nonlinear digital communication channels from second order statistics

In digital transmission systems the nonideal channel introduces distortion that must be compensated for to provide reliable communication, a process known as equalization. Recently there has been a great interest in the problem of blind equalization of digital communication channels, in which the equalizer is computed by the receiver without aid from the transmitter. This disposes of the need for sending training signals, leading to higher bandwidth efficiency.; Many real world channels distort signals in a nonlinear fashion. However, most of the literature on blind equalization is devoted to the linear case. This thesis addresses the blind equalization problem for nonlinear single-input multiple-output digital communication channels, based on the second order statistics (SOS) of the received signal. The required channel diversity can be obtained by using several sensors and/or by oversampling the received signal. In the latter case, the overall system can be cast in a multirate framework. We provide the basic elements of a theory of multirate nonlinear systems.; We consider the class of ‘linear in the parameters’ channels, which can be seen as multiple-input systems in which the additional inputs are nonlinear functions of the signal of interest. These models include (but are not limited to) polynomial approximations of nonlinear systems. Although any SOS-based method can only identify the channel to within a mixing matrix (at best), sufficient conditions are given to ensure that the ambiguity is at a level that still allows for the computation of linear finite impulse response equalizers from the received signal SOS, should such equalizers exist. These conditions involve only statistical characteristics of the input signal and the channel nonlinearities and can therefore be checked a priori . Based on these conditions, blind algorithms are developed for the computation of the linear equalizers in the case of independent sources. For correlated sources, a novel algorithm is also given for the linear channel case. The new algorithms compare favorably to previous approaches which do not fully exploit all the information available at the receiver.