Novel underdetermined blind source separation algorithm based on compressed sensing and K‐SVD

Abstract

In this paper, a novel two‐stage underdetermined blind source separation (UBSS) algorithm based on eigenvalue decomposition and compressed sensing (CS) is proposed. UBSS techniques can separate the complex mixed signals into multiple single signal components, which are widely applied in the field of electronic surveillance, spectrum management, radar applications, etc. Our major contributions are summarized as follows: (1) deriving a single source points detection algorithm based on eigenvalue decomposition; (2) proposing a novel hierarchical coupling dictionary training method based on K‐means singular value decomposition; and (3) using the two‐stage method to realize the separation of radar signals under the condition of unknown prior information. In the first stage, we present a single source point detection method involving eigenvalue decomposition to estimate the unknown mixing matrix. In this method, the eigenvector corresponding to the maximum eigenvalue is estimated and clustered as a vector of mixing matrix. The second stage is the recovery of sources from the observed signals utilizing the mixing matrix estimated by the first step. In the second stage, we first build the unified model of UBSS and CS, thus the reconstruction algorithm in the CS field can be applied to UBSS. Then, a hierarchical coupling dictionary training method based on K‐means singular value decomposition is proposed. The dictionary training method obtains the prior training signals by pre‐separation and employs the hierarchical coupling idea to train the dictionary efficiently. Simulations illustrate the validity of the method and show that the proposed method outperforms the traditional methods in source separation, especially in real‐world noncooperative cases without prior knowledge.

Research on Mixed Matrix Estimation Algorithm Based on Improved Sparse Representation Model in Underdetermined Blind Source Separation System

“…The above analysis verifies the unified time-frequency characteristic of FrFT. The fractional Fourier domain can be understood as rotating the time-frequency plane obtained by FT by a certain angle [24]. This plane integrates the information of the time domain and frequency domain.…”