On the relaxed maximum-likelihood blind MIMO channel estimation for orthogonal space-time block codes

This paper concerns the maximum-likelihood channel estimation for MIMO systems with orthogonal space-time block codes when the finite alphabet constraint of the signal constellation is relaxed. We study the estimation subspace for the channel coefficients that this approach generates. We provide an algebraic characterisation of this subspace which turns the optimization problem into a purely algebraic one and more importantly, leads to several interesting analytical proofs. We prove that the dimension of the estimation subspace for the channel coefficients is almost surely deterministic and it almost surely decreases with increasing the number of receive antennas up to a certain critical number of receive antennas after which the dimension remains constant. In fact, we show that over-passing this critical number of receive antennas, the estimation subspace for channel coefficients stabilizes to a fixed deterministic space which possesses very rich algebraic structure. This structure could be utilized in designing signal constellations that render the channel coefficients identifiable.