Robust Super-exponential methods for deflationary blind source separation of instantaneous mixtures

Robust super-exponential methods for blind deconvolution of MIMO-IIR systems with Gaussian noise

“…We considered an MIMO channel with two inputs and three outputs, and assumed that the length of channel is three (K = 3 ), that is H (k) s in (1) were set to be H(z) = The length of the deconvolver was chosen to be five (L = 5 ). We set the values of the tap coefficients to be zero expect for w (3) 11 = w (3) [2], [6]. The value of MISI becomes ;1, ifg l 's in (7) are obtained, and hence a minus large value of MISI indicates the proximity to the desired solution.…”

“…Suppose the index ji and ki are unique, that is, Since theorem 1 is proven by using the similar way as in [6], the proof of theorem 1 is omitted for page limit.…”

An adaptive super-exponential deflation algorithm for blind deconvolution of MIMO systems using the QR-factorization of matrix algebra

“…6 Calculatew l (t) using (26) and (8). 7 Carry out the deflationary process using the MSEDM with the higher-order correlations [9]. 8 If the subscript l is less than n, then set l = l + 1, and the procedures (from Step 3 through Step 7) are continued until l = n. 9…”

“…One of the attractive properties of the SEM is that it converges iteratively to desired solution regardless of initialization at a superexponential rate. Extensions of their idea to multichannel deconvolution were presented in [3], [4], [5], [6], [7], [9]. In particular, Inouye and Tanebe [3] proposed the multichannel super-exponential deflation method (MSEDM) using the second-order correlations.…”

“…In particular, Inouye and Tanebe [3] proposed the multichannel super-exponential deflation method (MSEDM) using the second-order correlations. Moreover, Kawamoto et al [7] and Kohno et al [9] proposed MSEDMs using the higher-order correlations instead of the second-order correlations in order to reduce the computational complexity and accelerate the performance of deconvolution. The MSEDMs are to deconvolve sequentially the source signals one by one.…”