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-input multiple-output (MIMO) systems that uses only second order statistics. We spectrally modulate the output of each source by correlative coding it with a distinct filter. The correlative filters are designed to meet the following desirable characteristics: no additional power or bandwidth is required; no synchronization between the sources is needed; the original data rate is maintained. We first prove an identifiability theorem: under a simple spectral condition on the transmitted random processes, the MIMO channel is 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 spectral identifiability condition. This results in a computationally attractive scheme for retrieving the data information sequences after the MIMO channel has been identified. We assess the performance of the proposed algorithms by computer simulations. In particular, the results show that our technique outperforms the previously introduced transmitter-induced conjugate cyclostationarity approach when there are carrier frequency misadjustments.