Wigner-Matrix-Based Normality Test and Application to Weak Signal Detection in SISO/SIMO Systems

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.

Extended Target Echo Detection Based on KLD and Wigner Matrices

“…L represents the number of signals in additive noise. The KLD between the empirical spectral CDF (F † (x)) and the finite dimensional spectral CDF (F (x)) is used as an airborne radar RFS performance indicator [23,24]. Its calculation process is depicted in Figure 1.…”