This paper applies wavelet transform methods to the detection of continuous wave (cw) radar signals in Gaussian white noise. The method applies to radar signal processing in typical, semi-active missile systems. The usual detection procedure consists of Fourier transforming the sampled data using the FFT, performing a CFAR operation, and thresholding. However, a detection loss occurs when the signal Doppler exists near the FFT bin center. This loss results from the spectral spreading of the signal, due to mismatch between the signal and FFT basis functions. The spectral spreading causes the signal to appear as a larger scale fluctuation relative to the small scale fluctuations of the white noise. It is shown that application of the single-level wavelet transform captures the signal through exploitation of these scale differences. Furthermore, it is shown that improved detection performance may be obtained by first applying the single-level wavelet transform to the amplitude spectrum. Then, the CFAR process is performed in the wavelet domain, followed by thresholding. A family of wavelet- based detectors is presented, which offer a trade-off between peak detection performance, and average detection performance over Doppler frequencies. That is, a slight detection performance loss near the FFT basis frequencies is traded for a significant detection performance gain near the FFT bin center. ROC curves, generated by Monte-Carlo simulation, are presented which sweep out detector performance. The computational complexity of the proposed detectors is discussed. The design of wavelets matched to this application, using Vaidyanathan's lattice decomposition, is also presented.

Date Published: 6 April 1995
PDF: 10 pages
Proc. SPIE 2491, Wavelet Applications II, (6 April 1995); doi: 10.1117/12.205402

Published in SPIE Proceedings Vol. 2491:
Wavelet Applications II
Harold H. Szu, Editor(s)