Adaptive Complex Singular Spectrum Analysis with Application to Modern Superresolution Methods

Abstract

The adaptive variant of the Singular Spectrum Analysis (SSA) approach for complex-valued signal model is obtained. It is related with the estimation of the noise variance using the results of the random matrix theory. Application of the adaptive complex SSA approach as preprocessing (denoising) step to modern methods of spectral analysis (subspace-based methods) is considered in the paper. The data sequence obtained after adaptive SSA approach is used as the input information for the superresolution method. The results of simulation demonstrate the performance improvement of the subspace-based methods in the conditions of low signal-to-noise ratio (SNR) when using the proposed approach. The performance of the subspace-based methods without and with the use of the adaptive SSA is comparable at high SNR. Furthermore, the performance of adaptive SSA approach depends on the quality of the noise variance estimate. The application of extended data matrix with specific structure obtained from the filtered data matrix is proposed. The directions of further investigations and possible applications of presented approach in communication systems are considered.