Blind identification of MIMO channels using optimal periodic precoding

Abstract

We propose a method for blind identification of multiple-input mutiple-out (MIMO) finite-impulse response (FIR) channels that exploits cyclostationarity of the received data induced at the transmitters by periodic precoding. It is shown that, by properly choosing the precoding sequence, the MIMO FIR transfer functions, with M-t inputs and M-r outputs, can be identified up to a unitary matrix ambiguity. The transfer functions need not be irreducible or column reduced, and there can be more outputs (M-r >= M-t) or more inputs (M-r < M-t). The method exploits the linear relation between the covariance matrix of the received data and the "channel product matrices". The method is shown to be robust with respect to channel-order overestimation. The proposed algorithm requires solving linear equations and computing the nonzero eigenvalues and eigenvectors of a Hermitian positive, semidefinite matrix. The performance of the algorithm, and indeed the identifiability, depends on the choice of the precoding sequence. We propose a method for optimal selection of the precoding sequence which takes into account the effect of additive channel noise and numerical error in covariance matrix estimation. Simulation results are used to demonstrate the performance of the algorithm.