Source Number Estimation in 2D Uniform Circular and L-Shaped Arrays With Unknown Nonuniform Noise

Classical source number estimators are usually derived under the assumption of uniform white noise, which may degrade substantially with unknown nonuniform sensor noise. Advanced estimators designed for nonuniform noise are however computationally expensive with limited performance in unfavorable conditions, such as low signal-to-noise ratio, small number of snapshots, close angular separations and sources with different transmitter powers. This brief proposes a new likelihood ratio statistics-based method for source number estimation under uncorrelated nonuniform noise. Using the asymptotic theory, it is shown that the likelihood ratio follows a chi-square distribution. Hence, the number of sources can be estimated via a sequence of hypothesis tests using maximum likelihood estimators (MLEs) of the covariance matrix with different assumed source numbers. The low complexity subspace algorithm is proposed to obtain the ML estimates. Theoretical analysis demonstrates that the proposed estimator is consistent in the general asymptotic regime. Simulation results on 2D arrays such as uniform circular and L-shaped arrays show that the proposed estimator achieves a higher correct detection probability in unfavorable conditions and is more robust against nonuniformity of noise than state-of-the-art estimators.