A fast wavelet packet based blind signal separation

It is well known that, signal separation algorithms based on second order statistics alone, are not always sufficient of achieving signal separation of mixed digital modulation signals. Methods based on higher order eigenvalue or more efficiently singular value decompositions of the received sensor´s covariance matrix, only work satisfactorily when the received mixed signals are linear combination of each others. In this paper, it has been shown that it is possible to retain the simplicity of the 2^nd order-based methods and still be able to successfully separate mixed digital signals, by designing the decoupling system to maximize the output normalized kurtosis functions. Next, it is proposed that in order to reduce computations and speeded up signal separation, we should perform wavelet packet decomposition of the outputs of the de-coupling network. The parameters of this network are optimally chosen through minimizing the cross correlations between wavelet packet coefficients of its outputs, at various nodes and a specific depth. Illustrative examples are given to verify these results, and demonstrate that the proposed approaches work when other methods fail.