A time-frequency formulation of optimum detection

A time-frequency formulation is proposed for the optimum detection of Gaussian signals in white Gaussian noise. By choosing the Wigner-Ville distribution as the basic time-frequency tool, it is shown that the corresponding receivers generally take the form of a correlation between time-frequency structures, matching mathematical optimality with a physically meaningful interpretation. The case of low SNR is examined and various examples are considered: deterministic signal, Rayleigh fading signal, random jitter, and random time-varying channel. A general class of time-frequency receivers is proposed which admits as limiting cases different known structures, and its suboptimum performance is evaluated. Possible extensions to more elaborate situations (including parameter estimation) are mentioned.>