On Optimizing Feedback Interval for Temporally Correlated MIMO Channels With Transmit Beamforming and Finite-Rate 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 finitesize 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.Index Terms-MIMO, transmit beamforming, temporally correlated channels, Gauss-Markov process, finite-rate feedback, random vector quantization (RVQ), feedback interval.

Ergodic capacity of antenna selection aided massive multi‐user MIMO systems with imperfect CSI in correlated time‐varying channels

“…where R t (u) and R r (u) are the submatrics extracted from the 1st to uth rows and columns of R t and R r , respectively, whereas D = M − M s , and u is varied from 1 to N. In our study, (23) and (24) will have a comparison to prove the correction of our derivation.…”

On Optimizing Feedback-Rate Allocation for Downlink MIMO-NOMA With Quantized CSIT

“…In this section, we analyze the achievable rate in a large system limit in which system parameters (N t , M 1 , M 2 , B 1 , and B 2 ) tend to infinity with fixed ratios. Previous work [22], [24], [36] has shown that analysis in a large system limit in some MIMO channels is tractable and predicts the performance of finitesize systems well.…”

“…On the other hand, the amount of feedback can be reduced if the channels are temporally correlated. If the correlation coefficients are sufficiently high, clusters do not have to feed back their CDI to the base station for every fading block [24]. In our previous work [24], we modeled the time evolution of MIMO channels by a Gauss-Markov process parameterized by a temporal-correlation coefficient, and proposed the feedback scheme that maximizes the spectral efficiency for a given feedback rate.…”

“…Many studies [4], [15], [19]- [21, and references therein] assume perfect CSIT at the base station. However, imperfect channel state information (CSI) with significant error or quantized CSI with a limited number of quantizing bits can severely affect the rate performance of multiple-antenna channels [22]- [24]. Reference [16] assumed that the channel estimation errors were not negligible and hence, CSI fed back from the receiver contained some errors.…”

“…Thus, we propose to find the optimal feedback allocation for a large system limit in which SINR becomes deterministic. Our past work [22], [24], [31] has shown that the large-system performance with RVQ feedback can predict the finite-size system accurately.…”