DFT based optimal blind channel identification

Optimal solutions for channel identification from over-sampled Pulse Amplitude Modulated signals are presented. While (large sample) optimal identification derived in the time domain involves solution of matrix weighted linear systems of equations solved in a Least Squares sense, using Discrete Fourier Transforms of the received data, it is shown that optimal solutions are rather obtained through scalar weighted Least Squares. Since the matrix of weights is not a priori known, estimation is generally performed in two steps. Here, we describe a less computational demanding single step estimation procedure. In the small samples case, the single step estimation is slightly less accurate than two step procedures.