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Conventional tools in array signal processing have traditionally relied on the availability of a large number of samples acquired at each sensor or array element (antenna, hydrophone, microphone, etc.). Large sample size assumptions typically guarantee the consistency of estimators, detectors, classifiers and multiple other widely used signal processing procedures. However, practical scenario and array mobility conditions, together with the need for low latency and reduced scanning times, impose strong limits on the total number of observations that can be effectively processed. When the number of collected samples per sensor is small, conventional large sample asymptotic approaches are not relevant anymore. Recently, large random matrix theory tools have been proposed in order to address the small sample support problem in array signal processing. In fact, it has been shown that the most important and longstanding problems in this field can be reformulated and studied according to this asymptotic paradigm. By exploiting the latest advances in large random matrix theory and high dimensional statistics, a novel and unconventional methodology can be established, which provides an unprecedented treatment of the finite sample-per-sensor regime. In this talk, we will see that random matrix theory establishes a unifying framework for the study of array signal processing techniques under the constraint of a small number of observations per sensor, which has radically changed the way in which array processing methodologies have been traditionally established. We will show how this unconventional way of revisiting classical array processing has lead to major advances in the design and analysis of signal processing techniques for multidimensional observations.