Detection-recognition algorithm based on the Gabor transform for unknown signals embedded in unknown noise

In this paper we present the CFAR (Constant False Alarm Rate) two-step detection-recognition algorithm for unknown, non-stationary signals embedded in unknown noise, based on the discrete Gabor transform. In the detection step, the decision about the absence or the presence of a signal of interest in a background of noise should be taken. The term ‘recognition’ means recovering the signal waveform from a noisy signal after the detection step. The recognition can be reformulated as the non-stationary, time-varying filtering problem in a time–frequency domain. In this paper the Gabor time–frequency domain is taken into account and the Gabor transform is used both in the detection and the in the filtering step. The discrete Gabor transform (DGT) is under intensive study of mathematicians, what results in a number of new, efficient computational algorithms for long time series. The Gabor frame approach is used for computation analysis and synthesis windows. Data-driven approach to develop the detection-recognition algorithm is based on the assumption, that disturbing noise signal after the Gabor transform, can be successfully approximated by the Weibull distribution regardless noise distribution before the transformation. It is shown by intensive simulations, that a two-parameter model like the Weibull distribution is really appropriate. Scale and shape parameters of the Weibull distribution are easily estimated and the CFAR threshold used in detection, based on estimated parameters, can be computed. The case of a low SNR ratio, with additional assumption about a signal, is also considered. It is shown that the iterative form of the time-varying filtering, significantly improves the quality of the whole detection-recognition CFAR algorithm. This approach is successfully investigated on a real-life radar signal.