Iterative Detection and Estimation of Coherent Narrowband Signals In Colored Noise

This paper proposes an algorithm to simultaneously estimate the presence, count, frequencies, amplitudes, and phases of coherent narrowband signals in unknown, correlated, Gaussian noise at a very low signal-to-noise ratio (SNR), without utilizing costly numerical/gradient search. Such a model is applicable to resolving radar multipath propagation with unknown, spatially-correlated corrupting environmental noise. The iterative method is a series of frequency estimation (using subspace decomposition), closed-form maximum likelihood amplitude estimation, signal reconstruction, noise isolation, and spectral pre-whitening, followed by Bayesian model order selection to detect the number of sources. We derive the closed-form Maximum Likelihood amplitude estimator for spatially-smoothed, forward-backward averaged data. Simulations show that at low -6 dB SNR, the method successfully detects the signal count where the method of Wax and Kailath (the random signal model) cannot, and it iteratively improves the accuracy of the estimated parameters.