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 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 {\em 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 Ntβ both become large. The optimal Ntβ 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/logNtβ. For the MIMO channel the optimal feedback overhead B/L tends to zero
faster (as 1/log2Ntβ).Comment: accepted for IEEE Trans. Info. Theory, 201