Blind identification and order estimation of FIR communications channels using cyclic statistics

We address the problem of the blind joint identification and order estimation of a non-minimum phase FIR communication channel by exploiting the cyclo-stationarity of the received signal sampled at a rate greater than the symbol rate. We show that the identification can be formulated as a "subspace fitting" problem; this allows for using the subspace distance as a test statistic to detect the correct channel length (among different hypotheses). Moreover, mimicking estimation procedures proposed in the framework of DOA estimation, an asymptotically efficient procedure is proposed which obtains the channel estimate in two steps: the channel estimate obtained in the first step determines optimal weights which are then employed in the second step to refine the channel estimate. The accuracy of the identification is comparable with other methods described in the literature (e.g. the subspace method) while the test for order detection performs quite well also in the presence of channel disparity outperforming commonly used tests based on the eigenvalues of the covariance matrix.