Source Enumeration in Sensor Array Processing: A Model Order Selection Problem

In this PhD thesis, one of the most fundamental problems in sensor array processing is investigated, namely, determining the number of source signals impinging on a sensor array, which is referred to as source enumeration. As a problem of model order selection, source enumeration can be addressed using the information carried in the observed data at the array output, e.g., the sample covariance matrix of the observed data, or equivalently, its sample eigenvalues and eigenvectors. In the last three decades, this problem has received a large amount of attention and numerous approaches have been developed for it. It is shown that the distribution of the sample eigenvalues contains statistical information which is critical for the problem of source enumeration. However, such information is not taken into account by most of the existing approaches. As a result, these approaches yield unsatisfactory performance in terms of correctly detecting the number of sources in some practical situations such as very small sample size, very low signal-to-noise ratio, close spacing and high correlation of source signals. Here, distinct distributions of the sample eigenvalues are used to construct new approaches for source enumeration. The distributions are either estimated by computer-intensive resampling algorithms, such as bootstrap techniques, or derived from classical multivariate statistical theory and modern random matrix theory. As a consequence, four novel approaches are developed in a framework of hypothesis testing or information theoretic criteria. Firstly, the bootstrap-based test is improved in order to adapt itself to the case of impulsive noise or very small sample sizes. Secondly, based on random matrix theory, a two-step test procedure is developed for the case of extremely small sample sizes, including the case when the sample size is smaller than the array size. Thirdly, inspired by the performance analysis of the Bayesian information criterion (BIC), a flexible detection criterion is proposed by incorporating an extra parameter. Finally, a generalized BIC is proposed using the distributions of the sample eigenvalues and observations to construct the log-likelihood function, in contrast to the conventional BIC which contains only the distribution of the observations. Note that the last two approaches are more flexible and general than the conventional BIC. Theoretical analysis and numerical simulations show that the proposed approaches outperform significantly most of the existing approaches