Sequential Likelihood Ratio Test under Incomplete Signal Model for Spectrum Sensing

Abstract

Detecting the existence of the transmitter emitting signals is an important mechanism in many applications, e.g., the spectrum sensing in the cognitive radio. In conventional detection schemes, the predefined number of samples is taken for detection and the statistics of the signals are assumed to be available in the signal model. However, under the ubiquitous fading effects and the non-cooperation of the targets, the signal statistics are not accurately obtainable at the detector. In this paper, we propose a sequential detector operating on the signal model described by the autoregressive moving average (ARMA) process without assuming known coefficients. The sequential detector for the ARMA model is derived by using the likelihood ratio test framework and the predictive distributions of the ARMA process. The novelties the proposed sequential detector include: 1) performing detection without requiring complete knowledge of the signal; 2) using smaller number of samples to reach the decision on average; and 3) allowing user-specified probabilities of detection and false alarm. We derive the approximate average number of samples required to reach the decision. The energy detector and sequential energy detector are compared with the proposed sequential detector by simulations. The results show the sequential detector uses the smaller average number of samples than the energy detector and sequential energy detector to termination.