Unified analysis of certain coherent and noncoherent binary communications systems

A general result is presented for the error-rate performance of common binary signaling-detection techniques for reception in additive Gaussian noise, including {\em all} possible conditions of nonorthogonality of signal, and correlations in the noise processes. These forms include frequency-shift keying with non-coherent detection, generalized to {\em all} noncoherent detection systems utilizing two basic waveforms, and phase-shift keying with a noisy reference signal, generalized to {\em all} coherent detection systems utilizing a single basic waveform. The unified result is achieved by exploiting a fundamental relationship between noncoherent and coherent operation. Also, some useful and not widely-known mathematical techniques involving the Q function are presented and utilized in the derivations.