Determining the Number of Discrete Alphabet Sources from Sensor Data

Determining the number of sources in a received wave field 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. Under the assumption that the transmitted signals are Gaussian, the MDL estimator takes both a simple and an intuitive form. Therefore this estimator is commonly used even when the signals are known to be non-Gaussian communication signals. However, its ability to resolve signals (resolution capacity) is limited by the number of sensors minus one. In this paper, we study the MDL estimator that is based on the correct, non-Gaussian signal distribution of digital signals. We show that this approach leads to both improved performance and improved resolution capacity, that is, the number of signals that can be detected by the resulting MDL processor is larger than the number of array sensors. In addition, a novel asymptotic performance analysis, which can be used to predict the performance of the MDL estimator analytically, is presented. Simulation results support the theoretical conclusions.