Detection of phase- or frequency-modulated signals in reverberation noise

This paper is devoted to the detection of phase- or frequency-modulated signals corrupted by the reverberation noise they have created. When the reverberation is modeled as a time-varying stochastic filtering of the emitted signal, the optimal detector consists of prewhitening the observation before applying a matched filter. This theory is very difficult to implement because of the nonstationarity of the reverberation noise. In this paper, a suboptimal detector proposed by Kay and Salisbury in 1990 is generalized to phase or frequency modulated signals. The reverberation is assumed locally stationary; the signal is cut into blocks and the whitening is performed as follows: An autoregressive (AR) modeling of one block allows the whitening of the following block. After whitening, an appropriate matched filter is applied. This scheme is explained in detail. The local stationarity assumption of the reverberation noise is discussed in light of the Itakura spectral distance. Performance of the proposed approach is evaluated theoretically when all parameters are known, and experimentally using three different real-data sets.