Eigenvalues-Based Universal Spectrum Sensing Algorithm in Cognitive Radio Networks

The eigenvalues of the sample covariance matrix can capture signal correlations and noise characteristics well, which are widely used for spectrum sensing in cognitive radio networks. Some totally blind spectrum sensing algorithms were proposed, such as maximum eigenvalue-to-arithmetic mean (ME-AM), maximum eigenvalue-to-geometric mean (ME-GM), and arithmetic-to-geometric mean of eigenvalues (AGM) methods. This article makes full use of the advantages of these algorithms and proposes a universal spectrum sensing algorithm based on maximum eigenvalue, arithmetic mean, and geometric mean of eigenvalues. The proposed algorithm takes the weighted geometric mean of the test statistics of the ME-AM and AGM algorithms as new test statistic and includes the ME-AM, ME-GM, and AGM algorithms as special cases. Following the random matrix theory framework, in a similar vein to the ME-AM and ME-GM algorithms, we derive the analytical expressions of false alarm probability, threshold, and detection probability of the proposed method using the Tracy-Widom distribution of maximum eigenvalue. In addition, we discuss the problem of designing the optimal weighting factor through theoretical analysis and simulation experiments. Finally, simulation results verify that the universal algorithm can effectively improve the detection performance.