Time-frequency-based detection using discrete-time discrete-frequency Wigner distributions

During the last decade, a comprehensive theory for optimum time-frequency (TF)-based detection has been developed. This was originally proposed in the continuous-time continuous-frequency case. This paper deals with detectors operating on discrete-time discrete-frequency Wigner distributions (WDs). The purpose is to discuss some existing definitions of this distribution within the context of TF-based detection and selecting those that do not affect the performance of the decision device with which they are associated. This question is of interest since there exist several approches for discretizing the WD, sometimes resulting in a loss of fundamental properties. First, the discrete-time discrete-frequency formulations of optimum detection are investigated. Next, the problem of the design of TF-based detectors from training data, keeping in mind severe effects of the curse of dimensionality, is considered.