Research Of Algorithms And Applications Of Blind Signal Separation Under Underdetermined Condition

Blind Signal Separation is the separation of a set of signals from a set of mixed signals, without any information of transmission channel, only relying on the assumption of the independence and little prior knowledge. Currently, most of the BSS algorithms assume the number of sources is smaller than the number of observers. However, in fact, in real world the underdetermined condition is much common which means the number of sources is larger than the number of observers. Thus research of BSS algorithms under underdetermined conditions is of great significance. This dissertation focuses on BSS problems of simultaneous linear mixed signals, and makes some progress based on available algorithms in the following aspects:(1) This dissertation does some research on FastICA algorithm based on kurtosis measurements and negentropy approximation, respectively, and ICA algorithm based on maximum likelihood estimation. Furthermore, FastICA algorithm based on maximum likelihood estimation is deduced. Compared to ICA algorithm based on gradient decent algorithm, this new FastICA algorithm enhances its robustness and converge speed. Then, simulations in MATLAB using typical biological signals with the purpose to validate these three FastICA algorithms are carried out, based on which another 11 sets of test signals are used to test the performance under different circumstances of these three FastICA algorithms. The results could be referred for selection of algorithms. (2) This dissertation also researches on BSS algorithms based on over-complete representation under underdetermined condition which turns underdetermined model into determined model using the sparsity among signals. Then, simulation in MATLAB which tries to separate a set of 2-channel sources into 3 channels is done to verify the algorithm. Besides, the prerequisite that sources should follow super-Gaussian distribution is proposed.(3) This paper builds an experimental system on DSK 6713 platform to realize the FastICA algorithm based on maximum likelihood estimation and the ICA algorithm based on over-complete representation. The separated signals are played through headphone and at the same time transmitted to PC through serial port for further analysis of performance in MATLAB.