Optimization of Training and Feedback Overhead for Beamforming over Block Fading 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 $1/{\log }^2{N}_t$).

accepted for IEEE Trans. Info. Theory, 2010

References in corpus (1)

• Capacity of a Multiple-Antenna Fading Channel with a Quantized Precoding Matrix

Cited by in corpus (4)

• Downlink Training Techniques for FDD Massive MIMO Systems: Open-Loop and Closed-Loop Training with Memory
• Pilot Beam Pattern Design for Channel Estimation in Massive MIMO Systems
• On Optimizing Feedback Interval for Temporally Correlated MIMO Channels With Transmit Beamforming And Finite-Rate Feedback
• Signature Quantization in Fading CDMA With Limited Feedback