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

more »

... est, 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. The white Gaussian noise property of observations is one of the important theoretical bases in statistical inference, signal detection, estimation theory, and so on. The normality test has been well studied, [1] such as Pearson's 2 test, the D'Agostino test, the Lilliefors test and the Jarque-Bera test. Although these classical test methods are simple and matured, they are just suitable for cases of high signal-to-noise ratios (SNRs), and will miss low-SNR signals. Since it is logical to compare random data sets by way of the associated probability density function (PDF), and the Kullback-Leibler divergence (KLD) has been confirmed to be a powerful and accurate tool to measure the information of multivariate data, [2] Lu et al. [3] attempt to find a novel normality measure which uses the KLD between the fitted PDF and the generalized Gaussian PDF to test the white Gaussian noise property. However, this method needs some complex parameter estimations and is only suitable for high false alarm circumstances, and the detection performance still needs to be further improved. With the wide use of the random matrix theory (RMT), [4−10] it not only solves the problem of invalidation of the classical limiting theorems for large dimensional data, but also provides a completely new way of signal detection. [11] Therein, the maximum-minimum eigenvalue (MME) spectrum sensing technology [12] for cognitive radio is a recent and classical research result. However, the MME method only uses the ratio of the maximum eigenvalue to the minimum eigenvalue to detect the presence of signals, while it does not make use of the KLD information of PDFs. To further improve the detection performance, this study takes full advantage of KLD and RMT, and uses a numerical KLD of the empirical spectral cumulative distribution function (CDF) based on observations from the asymptotic spectral CDF of the Wigner matrices to test the white Gaussian noise property. Under the white Gaussian noise assumption, we re-