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Optimization of Training and Feedback Overhead for Beamforming over Block Fading Channels
We examine the capacity of beamforming over a single-user, multi-antenna 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 symbols, and is spanned by training
symbols, 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 {\em i.i.d.} random vectors, and sends the
corresponding 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 ( and ) as and the
number of transmit antennas both become large. The optimal is
limited by the coherence time, and increases as . For the MISO
channel the optimal and (fractional overhead due to training and
feedback) are asymptotically the same, and tend to zero at the rate . For the MIMO channel the optimal feedback overhead tends to zero
faster (as ).Comment: accepted for IEEE Trans. Info. Theory, 201
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