  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 channel
coefficients estimation subspace generated by this method. 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 with probability one, the
dimension of the estimation subspace for the channel coefficients is
deterministic and it decreases by 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 beyond this critical number of receive
antennas, the estimation subspace for the channel coefficients is isometric to
a fixed deterministic invariant space which can be easily computed for every
specific OSTB code.
