A simple proof of a known blind channel identifiability result

An alternative simple proof for a well-known result encountered in blind id entification and equalization of communication channels is derived, It is s hown that the coprimeness condition of a number of FIR channels is equivale nt to the full column rank condition of a certain block Sylvester matrix, w hose 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 zer os present in all the channels.