Unilateral Left-Tail Anderson Darling Test Based Spectrum Sensing with Laplacian Noise

Abstract: This paper focuses on spectrum sensing under Laplacian noise. To remit the negative effects caused by heavy-tailed behavior of Laplacian noise, the fractional lower order moments (FLOM) technology is employed to pre-process the received samples before spectrum sensing. Via exploiting the asymmetrical difference between the distribution for the FLOM of received samples in the absence and presence of primary users, we formulate the spectrum sensing problem under Laplacian noise as a unilateral goodness-of-fit (GoF) test problem. Based on this test problem, we propose a new GoF-based detector which is called unilateral left-tail Anderson Darling (ULAD) detector. The analytical expressions for the theoretical performance, in terms of false-alarm and detection probabilities, of the ULAD are derived. Moreover, a closed-form expression for the optimal detection threshold is also derived to minimize the total error rate. Simulation results are provided to validate the theoretical analyses and to demonstrate the superior performance of the proposed detector than others.