A fundamental algorithm for power estimates of closely spaced spectral sources in high noise backgrounds

A relatively simple algorithm that can accurately determine the powers of closely separated line spectral sources at low signal-to-noise ratios (SNRs) is developed. The algorithm is based upon fundamental considerations of the effects of fluctuations due to finite data samples on the eigenstructure of the sample covariance matrix. The development uses a stochastic perturbation theoretic approach that mathematically parallels quantum mechanics perturbation theory. Statistical power estimation results are presented for simulated scenarios of two sources separated by sub-Rayleigh resolution and by source power differences of 40 dB at SNR levels of -5 and 0 dB measured relative to the power of the weaker source. Simulation experiments and theory are in complete accord