Optimization of Training and Feedback Overhead for Beamforming Over Block Fading Channels

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Abstract
We examine the capacity of beamforming over a single-user, multiantenna link taking into account the overhead due to channel estimation and limited feedback of channel state information. Multi-input-single-output (MISO) and multi-input-multi-output (MIMO) channels are considered subject to block Rayleigh fading. Each coherence block contains L symbols, and 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 estimate of the channel matrix. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing 2B i.i.d. random vectors, and sends the corresponding B bits back to the transmitter. We derive bounds on the beamforming capacity for MISO and MIMO channels and characterize the optimal (rate-maximizing) training and feedback overhead (T and B) as L and the number of transmit antennas Nt both become large. The optimal Nt is limited by the coherence time, and increases as L/logL. For the MISO channel the optimal T/L and B/L (fractional overhead due to training and feedback) are asymptotically the same, and tend to zero at the rate 1/log Nt. For the MIMO channel the optimal feedback overhead B/L tends to zero faster (as 1/log2 Nt).

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