Wigner-Matrix-Based Normality Test and Application to Weak Signal Detection in SISO/SIMO Systems**Supported by the National Natural Science Foundation of China under Grant No 61371170, the Fundamental Research Funds for the Central Universities under Grant Nos NP2015404 and NS2016038, the Aeronautical Science Foundation of China under Grant No 20152052028, and the Funding of Jiangsu Innovation Program for Graduate Education under Grant

Abstract

Based on the asymptotic spectral distribution of Wigner matrices, a new normality test method is proposed via reforming the white noise sequence. In this work, the asymptotic cumulative distribution function (CDF) of eigenvalues of the Wigner matrix is deduced. A numerical Kullback—Leibler divergence of the empirical spectral CDF based on test samples from the deduced asymptotic CDF is established, which is treated as the test statistic. For validating the superiority of our proposed normality test, we apply the method to weak 8PSK signal detection in the single-input single-output (SISO) system and the single-input multiple-output (SIMO) system. By comparing with other common normality tests and the existing signal detection methods, simulation results show that the proposed method is superior and robust.