Compressive sensing based energy detector

While most of research in Compressive Sensing (CS) has been focused on reconstruction of the sparse signal from very fewer samples than the ones required by the Shannon-Nyquist sampling theorem, recently there has been a growing interest in performing signal processing directly in the measurement domain. This new area of research is known in the literature as Compressive Signal Processing (CSP). In this paper, we consider the detection problem using a reduced set of measurements focusing on the Energy Detector (ED), which is the optimal Neyman-Pearson (NP) detector for random signals in Gaussian noise. In particular, we provide simple closed form expressions for evaluating the detection performance of ED when considering compressive measurements. The resulting equations reflect the loss due to CS and allow to determine the minimum number of samples to achieve certain detection performance.