MIMO Systems with Limited Rate Differential Feedback in Slowly Varying Channels

Abstract

Abstract-In this paper, an adaptive limited feedback linear precoding technique for temporally correlated multiple-input multiple-output (MIMO) channels is proposed, where the receiver has perfect channel knowledge but the transmitter only receives a quantized channel direction. To perform adaptation to the time correlation structure, we employ a differential feedback, where the "amount" of the perturbation added to the previous precoder is determined by the statistics of the directional variation. Based on random matrix quantization analysis, we develop a spherical cap codebook approach, where the cap is centered at the previous precoder and the radius of the cap is determined proportional to the identified directional variation. If the channel is highly correlated in time, the proposed differential feedback scheme can achieve a throughput improvement in the large codebook size regime. The rest of the paper is devoted to developing a systematic spherical cap codebook generation method. The developed approach employs a feedback scheme that uses a differential rotation of the previously used precoder. Our codebook adaptation is based on generating a perturbation in Euclidean space and projecting the perturbation onto the unitary space. Simulation results show that the proposed adaptation scheme accurately tracks the channel using only a small rate of feedback.Index Terms-Multiple-input multiple-output (MIMO) channel, adaptive linear precoding, limited feedback, differential feedback, temporal correlation.

An Adaptive Differential Equal Gain Transmission Technique using M-PSK Constellations

“…[13] 에서 정규화된 구면 캡   의 반경은 채널 방향의 변 화 및 누적된 양자화 오차의 영향을 적분함으로써 연속 적으로 결정된다. 적응형 계획 기반의 섭동 및 투영의 코 드북 업데이트 프로세스는 다음과 같이 나타낼 수 있다.…”

“…[12] 에서 연속된 MIMO 채널은 차분 선부호기가 준 대각 행렬이 되도록 매우 느리게 변화한다고 가정한 다. [13] 에서 차분 회전 피드백 기술은 구면 캡 반경 최 , long term evolution advanced (LTE-A)는 최근 차분 코드북과 유 사성을 가지는 듀얼 코드북 구조를 논의한 바 있다 [16] .…”

Variable-Rate Transmission for MIMO Time-Correlated Channels With Limited Feedback

“…Also shown in Fig. 6(a) is the BER of the differential precoder systems in [17] and [20], and the bit allocation (BA) system in [6] for the same transmission rate . All of these three are fixed-rate systems.…”

“…The design of polar-cap differential codebooks is addressed in [19] for beamforming systems. A feedback scheme that uses a differential rotation of the precoder is proposed in [20]. Based on random matrix quantization analysis, a spherical cap codebook can be generated systematically.…”

A Limited Feedback Algorithm Sacred from Feedback Error for Slowly Time-varying Channel

“…If the channel temporal correlation can be utilized fully, it is possible to reduce the amount of feedback. To benefit from the temporal correlation, the Grassmannian Predictive Codebook (GPC) algorithm was considered in [4,5]. In GPC, both transmitter and receiver predict the forthcoming CSI based on the previous one.…”