Optimum Time-Frequency Distribution for Detecting a Discrete-Time Chirp Signal in White Gaussian Noise

In the continuous-time domain, Maximum-Likelihood (ML) detection of a chirp signal in white Gaussian noise can be done via the line-integral transform of the classical Wigner distribution. The line-integral transform is known variously as the Hough transform and the Radon transform. For discrete-time signals, the Wigner-type distribution defined by Claasen and Mecklenbrauker has become popular as a signal analysis tool. Moreover, it is commonly believed that ML detection of a discrete-time chirp signal in white Gaussian noise can be done via the line-integral transform of the Wigner-Claasen-Mecklenbrauker distribution. This belief is false and results in loss of performance. We derive a Wigner-type distribution for discrete-time signals whose line-integral transform can be used for ML detection of discrete-time chirp signals in white Gaussian noise. We provide simulated Receiver Operating Curves for the WignerClaasen-Mecklenbrauker distribution based method and the new ML-equivalent method and demonstrate the suboptimality of the former.