Nonparametric detection of FM signals using time-frequency ridge energy

In many practical applications, signals to be detected are unknown nonlinear frequency modulated (FM) and are corrupted by strong noise. The phase histories of signals are assumed to be unknown smooth functions of time and these functions are poorly modeled or unmodeled by a small number of parameters. Thus, the conventional parametric-based detection methods are invalid in these cases. This paper proposes a nonparametric detection method using the ridge energy of observations.. The detection process consists of three steps, TF ridge detection, ridge energy extraction, and decision. First, the directionally smoothed-pseudo-Wigner-Ville distribution (DSPWVD) is introduced to highlight the instantaneous frequency (IF) points along a special direction on the IF curve of a signal from noise. Further, an angular maximal distribution (AMAD) is constructed from a set of DSPWVDs to highlight the entire IF curve. As a result, the TF ridge of an observation can be estimated well from its AMAD by the maxima position detector. Second, the ridge energy, the total energy along the TF ridge on the pseudo-Wigner-Ville distribution (PWVD), is extracted. A noisy signal has larger ridge energy than a pure noise does, with a large probability, because pure noise energy is randomly distributed throughout the TF plane while the signal energy in a noisy signal is concentrated along the estimated TF ridge. Third, the ridge energy of an observation is used as the test statistic to decide whether or not a signal of interest is present in the observation, where the decision threshold is determined by a large number of Monte Carlo simulations using pure noise. Finally, the simulation experiments to two test signals are made to verify the effectiveness of the proposed method.