Wiener Filtering in PN Spread-Spectrum Systems

By reconfiguring an unrealizable and a realizable Wiener whitening filter in terms of an estimator-subtractor structure, the estimation of a signal in the presence of a colored noise is shown to be the dual to the estimation of a colored noise in the presence of a signal. The error in the estimate of a signal or a colored noise by an unrealizable Wiener filter is shown to be smaller than that by a realizable Wiener filter. For uniform spectrum of a PN signal, Gaussian spectrum of the colored noise is shown to be more difficult to filter than a bandlimited spectrum. Furthermore, the error in the estimate is worse for a second-order Butterworth spectrum than for Gaussian or bandlimited spectrum.