Worst-case design for optimal channel equalization in filterbank transceivers

A worst-case approach is adopted to tackle optimal channel equalization for multirate filterbank transceivers, which are widely used in data communication networks, such as discrete wavelet multitone (DWMT) systems in digital subscriber lines (DSL), orthogonal frequency multiplexing division (OFMD) in frequency division multiple access (FDMA) systems, applicable to direct-sequence/spread-spectrum (DS/SS) code division multiple access (CDMA) networks. It is assumed that the observation noise is nonwhite with bounded power-norm or root-mean-squared (RMS) value. Our objective is to design the optimal receiving filterbanks that not only achieve the zero-forcing (ZF) condition or channel equalization but also minimize the RMS error between the transmitted symbols and the received symbols in the presence of the worst-case nonwhite noise. All ZF receiving filterbanks will be parameterized, and optimal design for channel equalization will be converted into an equivalent optimal H_∞ filtering problem for the augmented receiving filterbanks with RMS error preserved. Our main results cover computation of the optimal RMS error achievable for the worst-case noise and an explicit design algorithm for suboptimal channel equalizers with the performance index arbitrarily close to the optimal one. A simulation example is used to illustrate the proposed optimal channel equalization algorithm.