Some Results on the Blind Identifiability of Orthogonal Space-Time Block Codes from Second Order Statistics

In this paper, the conditions for blind identifiability from second order statistics (SOS) of multiple-input multiple-output (MIMO) channels under orthogonal space-time block coded (OSTBC) transmissions are studied. The main contribution of the paper is to show that, assuming more than one receive antenna, any OSTBC with a transmission rate higher than a given threshold, which is inversely proportional to the number of transmit antennas, permits the blind identification of the MIMO channel from SOS. Additionally, some previous identifiability results have been extended. The implications of these theoretical results include the explanation of previous simulation examples found in the literature and, from a practical point of view, they show that the only non-identifiable OSTBC codes with practical interest are the Alamouti codes and the real square orthogonal design with four transmit antennas. Further discussion and empirical analysis are also provided.