Parametric joint detection-estimation of the number of sources in array processing

Detection of the number of signals and estimation of their directions of arrival (DOAs) are fundamental problems in array processing. We present three main contributions to these problems, under the conditional model, where signal amplitudes are assumed deterministic unknown. First, we show that there is an explicit relation between model selection and the breakdown phenomena of the Maximum Likelihood estimator (MLE). Second, for the case of a single source, we provide a simple approximate formula for the location of the breakdown of the MLE, using tools from the maxima of stochastic processes. This gives an explicit formula for the source strength required for reliable detection. Third, we apply these results and propose a new joint detection-estimation algorithm with state-of-the-art performance. We demonstrate via simulations the improved detection performance of our algorithm, compared to other popular source enumeration methods.