A simple proof of a known blind channel identifiability result

  • Authors:
  • E. Serpedin;G.B. Giannakis

  • Affiliations:
  • Dept. of Electr. Eng., Virginia Univ., Charlottesville, VA;-

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 1999

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Abstract

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