Closed-form correlative coding (CFC2) blind identification of MIMO channels: Isometry fitting to second order statistics

We present a blind closed-form consistent channel estimator for multiple-in put multiple-output (MIMO) systems that uses only second-order statistics. We spectrally modulate the output of each source by correlative coding it w ith a distinct filter. The correlative filters are designed to meet the fol lowing desirable characteristics: No additional power or bandwidth is requi red; no synchronization between the sources is needed; the original data ra te is maintained, We first prove an identifiability theorem: Under a simple spectral condition on the transmitted random processes, the MIMO channel i s uniquely determined, up to a phase offset per user, from the second-order statistics of the received data. We then develop the closed-form algorithm that attains this identifiability bound. We show that minimum-phase finite impulse response filters with arbitrary memory satisfy our sufficient spec tral identifiability condition, This results in a computationally attractiv e scheme for retrieving the data information sequences after the MIMO chann el has been identified. We assess the performance of the proposed algorithm s by computer simulations. In particular, the results show that our techniq ue outperforms the recently introduced transmitter-induced conjugate cyclos tationarity approach when there are carrier frequency misadjustments.