Iterative Detection and Estimation of Coherent Narrowband Signals In Colored Noise
Radu S. Matei, Налини Равишанкер, Peter Willett, J.S. Bergin · 2024
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.