Source enumeration via GBIC with a statistic for sphericity test in white Gaussian and non-Gaussian noise

We propose a source enumeration method via the generalised Bayesian information criterion (GBIC) based on a statistic for sphericity test in the white Gaussian and non-Gaussian noise under a large array with few samples. Instead of joint probability of observations or sample eigenvalue distribution, the proposed method is based on a statistic for testing the sphericity of a positive definite covariance matrix, to overcome the limitation of the Gaussian observations assumption. Under the white noise assumption, the covariance matrix of the noise subspace components of the observations is proportional to an identity matrix, and this identity structure can be tested by a statistic for sphericity test. The observations are decomposed into signal and noise subspace components under a presumptive number of sources. When the presumptive noise subspace components do not contain signals, the corresponding statistic for sphericity test will have a certain Gaussian distribution, and the number of sources can be estimated via the GBIC with the test statistic. Simulation results demonstrate that the proposed method provides high detection probability in both the Gaussian and the non-Gaussian noise, and performs better when the number of samples is less than the number of array sensors compared with other methods.