Spectral Distribution of Wigner Matrices in Finite Dimensions and Its Application to LPI Performance Evaluation of Radar Waveforms

Abstract

Recent research on the assessment of low probability of interception (LPI) radar waveforms is mainly based on limiting spectral properties of Wigner matrices. As the dimension of actual operating data is constrained by the sampling frequency, it is very urgent and necessary to research the finite theory of Wigner matrices. This paper derives a closed-form expression of the spectral cumulative distribution function (CDF) for Wigner matrices of finite sizes. The expression does not involve any derivatives and integrals, and therefore can be easily computed. Then we apply it to quantifying the LPI performance of radar waveforms, and the Kullback-Leibler divergence (KLD) is also used in the process of quantification. Simulation results show that the proposed LPI metric which considers the finite sample size and signal-to-noise ratio is more effective and practical.