New Proof for a Blind Equalization Result: a Module Theory Approach

In the blind equalization problem, one can recently observe that the sought unknown filter can be performed from the sole knowledge of second order statistics of the received signal. According to this fact, a powerful algorithm which is the socalled subspace method has been developed. The subspace method was previously described in rational spaces framework which seemed to be unappropriated. Indeed, the filter to identify is polynomial. In this paper, we show how the module theory over the polynomial ring C [z] and, in particular, the duality of modules can highlight the previous proof of the subspace method and lead to generalize its results.