Blind Separation Using Characteristic Function Based Criterion

We propose a novel method for blind separation of statistically independent sources. The objective function used in the separation is based on the fact that the joint characteristic function factors to a product of the characteristic functions of the in- dependent marginals. New algorithm for minimizing the above criterion is derived as well. It estimates the separating matrix by ensuring that the sources are pairwise independent. The theoretical character- istic functions in the objective function are replaced by their empirical counterparts. Simulation studies demonstrating the reliable performance of the pro- posed method in separating many dierent types of sources are presented. In particular, distributions of- ten encountered in wireless communication applica- tions are employed in the examples. This paper introduces a novel approach to the Blind Source Separation (BSS). It is an Independent Component Analysis (ICA) method that assumes that the source signals are sta- tistically independent. We propose a method that exploits an alternative definition of the independence expressed in terms of characteristic functions: the joint characteristic function may be factored to a product of the characteristic functions of the independent marginals. A novel algorithm for mini- mizing the criterion based on this factorization is proposed as function always exists and consequently the method has the potential to separate wider class of source distributions than conventional methods. In the process of estimating the sep- arating matrix, the characteristic functions in the definition are just replaced by empirical characteristic functions. We also introduce a BSS algorithm that minimizes the proposed objective function by processing the sources pairwise. This is justified since it is enough for the separated sources to be pairwise independent. The algorithm employs a Jacobi type of processing. This paper is organized as follows. Section II describes briefly the ICA model. In Section III, the definition of inde- pendence is given in terms of characteristic functions, and the estimation is briefly discussed. An objective function which employs characteristic functions is derived in Section IV. An algorithm for finding the independent source signals is pro- posed in Section V. Examples illustrating the reliable perfor- mance of the proposed method are presented in Section VI. In the simulation studies, we consider skewed source distribu- tions such as Rayleigh that occur frequently in telecommuni- cations and biomedical applications. Conventional methods using fixed zero-memory nonlinearities perform poorly in sep- arating such sources. Finally, Section VII concludes the paper. II. ICA system model