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

TL;DR

This paper analyzes the capacity of beamforming in multi-antenna channels considering the overhead of channel estimation and limited feedback, deriving optimal training and feedback strategies as system parameters grow large.

Contribution

It provides bounds on beamforming capacity and characterizes optimal training and feedback overhead for large MISO and MIMO systems.

Findings

Optimal number of transmit antennas increases with coherence time.

Training and feedback overhead fractions tend to zero as system size grows.

Feedback overhead decreases faster in MIMO than in MISO channels.

Abstract

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 $2^B$ {\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 $N_t$ 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 $1/\log^2 N_t$).