Cyclic Wiener filtering: theory and method

Conventional time and space filtering of stationary random signals, which amounts to forming linear combinations of time translates and space translates, exploits the temporal and spatial coherence of the signals. By including frequency translates as well, the spectral coherence that is characteristic of cyclostationary signals can also be exploited. Some of the theoretical concepts underlying this generalized type of filtering, called frequency-shift (FRESH) filtering, are developed. The theory of optimum FRESH filtering, which is a generalization of Wiener filtering called cyclic Wiener filtering, is summarized, and the theory is illustrated with specific examples of separating temporally and spectrally overlapping communications signals, including AM, BPSK, and QPSK. The structures and performances of optimum FRESH filters are presented, and adaptive adjustment of the weights in these structures is discussed. Also, specific results on the number of digital QAM signals that can be separated, as a function of excess bandwidth, are obtained