Optimum time–frequency distribution for detecting a discrete-time chirp signal in noise

Abstract

In the continuous-time domain, maximum-likelihood (ML) detection of a chirp signal in white Gaussian noise can be done by maximising (with respect to signal parameter arguments) the line-integral transform (LIT) of the classical Wigner distribution (of the observed signal). The LIT 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 independent and identically distributed (i.i.d.) Gaussian noise can be done by maximising the LIT of the Wigner–Claasen–Mecklenbrauker distribution (WCMD). This belief is false and results in loss of performance. The authors derive a Wigner-type distribution for discrete-time signals such that ML detection of a discrete-time chirp signal in i.i.d. Gaussian noise can be done by maximising the LIT of this distribution. Simulated receiver operating curves showing the performance advantage of the new method over the WCMD-based method are provided. The signal parameter values that maximise the LIT are taken as estimates of the actual parameters. The authors provide simulation results showing that the parameter estimates obtained using the new method are more accurate than those obtained using the WCMD-based method. For the WCMD-based method, the range of unambiguously measurable frequencies (RUMF) is [−π/2, π/2]. For the new method, the RUMF is [−π, π].