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A simple proof of a known blind channel identifiability result

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2 Author(s)
Serpedin, E. ; Dept. of Electr. Eng., Virginia Univ., Charlottesville, VA, USA ; Giannakis, G.B.

An alternative simple proof for a well-known result encountered in blind identification and equalization of communication channels is derived. It is shown that the coprimeness condition of a number of FIR channels is equivalent to the full column rank condition of a certain block Sylvester matrix, whose entries are the channel coefficients. As a corollary, it is also shown that in general, the null space of a block Sylvester matrix is spanned by the set of (generalized) Vandermonde vectors associated with the common zeros present in all the channels

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Signal Processing, IEEE Transactions on  (Volume:47 ,  Issue: 2 )