The design of second order adaptive equalizers with reduced order implementation

We consider the design of equalizer for communication channels with unknown and time variable channel coefficients. The key feature of the proposed methodology is that the implementation is of fixed complexity. This is achieved even though the true bilinear nature of the problem is preserved. The problem we consider is an important one in the field of digital communications, the recovery of a message when intersymbol interference and noise are both difficulties. We consider the problem with randomly variable channel coefficients. The results are an important extension to the adaptive equalization work presented by Reynolds et al. (see Asilomar Conference on Circuits and Systems, 1994), because the keeping the second order terms in the Taylor series expansion allows us to keep all the terms there are in a bilinear problem. The theory is illustrated on a simple binary example with unknown channel parameters.