An Accelerated Underdetermined Blind Source Separation Algorithm Based on Tensor Decomposition

‍ ‍When the source signal and the mixed model are unknown， Blind Source Separation （BSS） can recover the source signal from the observed signal only according to the statistical characteristics of the source signal. BSS has become a key technology in the field of signal processing by virtue of this technical advantages. It has been widely used in wireless communication， biomedicine， industrial machinery， and other fields. Underdetermined blind source separation （the number of observed signals is less than the number of source signals） is an important branch of blind source separation， which is more suitable for practical application scenarios. The traditional underdetermined blind source separation technology utilizes the sparsity of the observed signal for cluster solving. However， in a complex communication environment， the sparsity of the signal is easily disturbed by noise， destructing the signal sparsity. It is difficult to realize the underdetermined blind source separation under the condition of low signal-to-noise ratio， which greatly limits the application range of this algorithm. To solve these problems， an accelerated， underdetermined blind source separation algorithm based on tensor decomposition is proposed in this paper. The algorithm first constructs a fourth-order tensor using the third-order cumulant of the observed signal at different time delays as statistical information， and compresses the fourth-order tensor by using High Order singular value decomposition （HOSVD） to reduce the tensor dimension， which reduces the computational complexity while fully characterizing the signal. The mixed matrix estimation problem is transformed into a tensor decomposition problem， and the search space is decomposed into multiple planes using the Enhanced Plane Search （EPS） algorithm and searched on each plane， which enhances the search space during the search process to accelerate the convergence of the Alternating Least Squares （ALS） method while avoiding the convergence into a “bottleneck” state. The experimental results show that the relative error of the algorithm is -22.41 dB for estimating 3 × 4 mixed matrices when the signal-to-noise ratio is 25 dB， which is better than that of the existing algorithms for estimating mixed matrices and faster than the existing algorithms in terms of convergence speed.