Eigenvalue-based spectrum sensing using the exact distribution of the maximum eigenvalue of a Wishart matrix

Maximum-eigenvalue-detection (MED) and maximum-eigenvalue geometric-mean (ME-GM) are attractive eigenvalue-based spectrum sensing (EBSS) schemes for cognitive radio (CR). The first objective of this paper is to present an analytical probability of detection (PD) expression for MED. The evaluated expression matches the simulation results well. Many of the existing analytical results for EBSS schemes are based on the asymptotic Tracy-Widom (TW) distribution; however, for small or moderate sample length, N and secondary users, M the distribution lacks accuracy. Recently, adjusted centring and scaling parameters have been presented to improve the accuracy of the TW distribution for this practical scenario; thus, the second objective is to present the adjusted-TW expressions (probability of false alarm (PFA), threshold and PD) for MED and ME-GM. The proposed results show an improved accuracy for moderate N when M is small. To improve the accuracy for small N the authors propose to use an exact cumulative distribution function of the maximum eigenvalue. Hence the third objective of the paper is to present the exact analytical expressions for MED. The exact approach is then applied to ME-GM, where an asymptotic expression for the GM is employed. The exact analysis exhibits a higher accuracy for both MED and ME-GM.