Rank-deficient APES filter for complex spectral estimation

In this paper, a new spectral estimation method, which is based on the rank-deficient sample covariance matrix, is proposed. The new method applies the amplitude and phase estimation (APES) filter and the Capon weight simultaneously on the data matrix to obtain the complex amplitude estimate of the spectral line of interest. Because the sample covariance matrix is singular, a rank-deficient version of the APES filter is derived. For obtaining the unique filter, an additional constraint is under considered, which minimizes the noise gain of the design filter. Also considering only fewer snapshots available, the traditional Fourier weight can not sufficiently suppressed the components of the interference plus noise. By minimizing the norm of the weighted snapshot, the Capon weight is selected as the optimal weight. The simulation results demonstrate that the new method has excellent estimation performance for estimating the spectrum in case of sample covariance matrix singular.