Approximating the constellation constrained capacity of the MIMO channel with discrete input

In this paper the capacity of a Multiple Input Multiple Output (MIMO) channel is considered, subject to average power constraint, for multi-dimensional discrete input, in the case when no channel state information is available at the transmitter. We prove that when the constellation size grows, the QAM constrained capacity converges to Gaussian capacity, directly extending the AWGN result from [1]. Simulations show that for a given constellation size, a rate close to the Gaussian capacity can be achieved up to a certain SNR point, which can be found efficiently by optimizing the constellation for the equivalent orthogonal channel, obtained by the singular value decomposition. Furthermore, lower bounds on the constrained capacity are derived for the cases of square and tall MIMO matrix, by optimizing the constellation for the equivalent channel, obtained by QR decomposition.