Detection of signals by information theoretic criteria: general asymptotic performance analysis

Detecting the number of sources is a well-known and a well-investigated problem. In this problem, the number of sources impinging on an array of sensors is to be estimated. The common approach for solving this problem is to use an information theoretic criterion like the minimum description length (MDL), or the Akaike information criterion (AIC). Although it has been gaining much popularity and has been used in a variety of problems, the performance of information theoretic criteria-based estimators for the unknown number of sources has not been sufficiently studied, yet. In the context of array processing, the performance of such estimators were analyzed only for the special case of Gaussian sources where no prior knowledge of the array structure, if given, is used. Based on the theory of misspecified models, this paper presents a general asymptotic analysis of the performance of any information theoretic criterion-based estimator, and especially of the MDL estimator. In particular, the performance of the MDL estimator, which assumes Gaussian sources and structured array when applied to Gaussian sources, is analyzed. In addition, it is shown that the performance of a certain MDL estimator is not very sensitive to the actual distribution of the source signals. However, appropriate use of prior knowledge about the array geometry can lead to significant improvement in the performance of the MDL estimator. Simulation results show a good fit between the empirical and the theoretical results.