# On Optimizing Feedback Interval for Temporally Correlated MIMO Channels With Transmit Beamforming And Finite-Rate Feedback

## TL;DR

This paper analyzes the optimal feedback interval for MIMO channels with temporal correlation, demonstrating that proper timing of feedback significantly improves transmission rates with limited feedback.

## Contribution

It introduces a method to determine the optimal feedback interval for correlated MIMO channels, enhancing rate performance over existing schemes.

## Key findings

- Optimal feedback interval maximizes average received power.
- Large system approximation accurately predicts finite system performance.
- Quantized beamforming with optimal interval outperforms Kalman-filter scheme and frequent feedback.

## Abstract

A receiver with perfect channel state information (CSI) in a point-to-point multiple-input multiple-output (MIMO) channel can compute the transmit beamforming vector that maximizes the transmission rate. For frequency-division duplex, a transmitter is not able to estimate CSI directly and has to obtain a quantized transmit beamforming vector from the receiver via a rate-limited feedback channel. We assume that time evolution of MIMO channels is modeled as a Gauss-Markov process parameterized by a temporal-correlation coefficient. Since feedback rate is usually low, we assume rank-one transmit beamforming or transmission with single data stream. For given feedback rate, we analyze the optimal feedback interval that maximizes the average received power of the systems with two transmit or two receive antennas. For other system sizes, the optimal feedback interval is approximated by maximizing the rate difference in a large system limit. Numerical results show that the large system approximation can predict the optimal interval for finite-size system quite accurately. Numerical results also show that quantizing transmit beamforming with the optimal feedback interval gives larger rate than the existing Kalman-filter scheme does by as much as 10% and than feeding back for every block does by 44% when the number of feedback bits is small.