Optimization of training and feedback for beamforming over a MIMO channel

We examine the capacity of beamforming over a block Rayleigh fading Multi-Input/Multi-Output (MIMO) channel with finite training for channel estimation and limited feedback. A fixed-length packet is assumed, which is spanned by T training symbols, B feedback bits, and the data symbols. The training symbols are used to obtain a Minimum Mean Squared Error (MMSE) estimate of the channel matrix. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing 2^B i.i.d. random vectors, and relays the corresponding B-bit index back to the transmitter. We derive bounds on the large system capacity, i.e., as the number of transmit antennas N_t → ∞ and receive antennas N_r → ∞ with fixed ratio N_t/N_r. The bounds are used to show that the optimal T, which maximizes the capacity, increases as N _t/ log N_t, whereas the optimal B increases as N _t/ log² N_t.