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<sup>B</sup> 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<sub>t</sub> rarr infin and receive antennas N<sub>r</sub> rarr infin with fixed ratio N<sub>t</sub>/N<sub>r</sub>. The bounds are used to show that the optimal T, which maximizes the capacity, increases as N<sub>t</sub>/ log N<sub>t</sub>, whereas the optimal B increases as N<sub>t</sub>/log<sup>2</sup> N<sub>t</sub>.

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