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Underdetermined blind source separation (UBSS) is an important issue for sparse signals, and a novel two-step approach for UBSS based on the law of large numbers and minimum intersection angle rule (LM method) is presented. In the first step, an estimation of the mixed matrix is obtained by using the law of large numbers, and the number of source signals is displayed graphically. In the second step, a method of estimating the source signals by the minimum intersection angle rule is proposed. The significance of this step is that the minimum intersection rule is better than the shortest path method, and the decomposition components can be found optimally by the former. The simulation results illustrate the effectiveness of the LM method. It has a simple principle, has good transplantation capability and may be widely applied in various fields of digital signal processing.

Underdetermined Blind Source Separation for Sparse Signals Based on the Law of Large Numbers and Minimum Intersection Angle Rule