Design of CFAR detector combining with frequency estimation

An optimal detector is presented in this paper for simultaneously detecting and estimating an unknown sinusoidal signal in Gaussian noise. The detector is based on generalized likelihood ratio test (GLRT) and the frequency of the sinusoidal signal is obtained by maximum likelihood (ML) estimation. Considering the leakage effect, the tonal detector does not only use the amplitude information of the discrete Fourier transform (DFT) of observations, but also uses its phase information to compensate the leakage. Theoretical performance analysis shows that it is a constant false alarm rate (CFAR) detector and its detection performance approaches the uniformly most powerful invariant (UMPI) test bound. The processor can also be generalized for multiple sinusoids detection.