Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 56, Issue 12, Pages 6103-6115Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2010.2081150
Keywords
Block fading; channel capacity; channel estimation; limited feedback; multiple-input multiple-output (MIMO)
Funding
- U.S. Army Research Office [W911NF-07-1-0028]
- National Science Foundation [CCR-0310809]
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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 2(B) 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 N-t both become large. The optimal N-t is limited by the coherence time, and increases as L/log L. 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 N-t. For the MIMO channel the optimal feedback overhead B/L tends to zero faster (as 1/log(2) N-t).
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