An optimum generalized cross-spectrum symbol-rate detector

The optimal design of a precorrelation filtering system for use in cross-spectrum symbol-rate detectors in the presence of additive Gaussian noise is described. This approach generalizes practical cross-spectrum symbol-rate detectors, and derives a necessary condition which achieves the maximum processed signal-to-noise ratio at an integer multiple of the symbol rate. The resultant optimum condition depends on the transfer functions of precorrelation filters and fixed signal model parameters. As a by-product, a performance measure applicable to any quadrature amplitude modulation format and including the effects of self-noise and intersymbol interference is derived. An algorithm for constructing physically realizable precorrelation filters that satisfy the optimum condition is given to complete the design process