Multiple User Limited Feedback
Wireless communication systems can make use of channel state information at the transmitter to improved throughput and reliability. Channel state information can be provided at the transmitter practically using the concept of limited feedback. In brief, key features of the channel state are quantized at the receiver and fed back to the transmitter over a finite rate feedback channel. Multiple user systems can make special use of channel state information. On the downlink, the transmitter can send information to multiple users through multiuser beamforming, also known as spatial division multiple access (SDMA) or the MIMO broadcast channel. Unfortunately, multiple user systems generally require high-resolution channel state information at the transmitter. This makes the problem of multiuser limited feedback challenging because feedback requirements increased due to the increasing codebook size and the number of users sending back information.
With collaborators, my research group has tackled several problems in multiuser MIMO limited feedback from different perspectives. We have looked at joint beamforming and scheduling together, where the scheduler includes quantization error. We have also proposed threshold-based feedback techniques in which only users with good channels feedback, thus reducing the overall feedback load. More recently we have proposed high resolution codebooks with low search complexity. We have also developed some important predictive quantizers that exploiting temporal correlation to further reduce feedback requirements.
T. Inoue and R. W. Heath, Jr., “Geodesic Prediction for Limited Feedback Multiuser MIMO Systems in Temporally Correlated Channels” IEEE Radio & Wireless Symposium, pp. 167-170, Jan. 18-22, 2009.
Many multiuser limited feedback problems can be restated as a quantization problem on the Grassmann manifold. In this paper we proposed a new prediction framework, which exploits temporal correlation in the channel. The idea is to use geodesics to define a predictor on the Grassmann manifold, allowing the system to leverage the benefits of predictive quantization. Substantial reductions in throughput overheads are observed with the proposed technique.
J. Zhang, R. W. Heath, Jr., M. Kountouris, and J. G. Andrews, “Mode Switching for the MIMO Broadcast Channel Based on Delay and Channel Quantization,” EURASIP Journal on Advances in Signal Processing, special issue on Multiuser Limited Feedback, vol. 2009, Article ID 802548, 15 pages, doi:10.1155/2009/802548, 2009.
In this paper we analyzed the impact of mode switching, adaptive the number of transmit streams, in a multiuser MIMO system with limited feedback. We considered the impact of delay as well as quantization in the switching algorithm. A general conclusion is that when there is significant delay and course quantization it may be preferable to serve fewer users and send fewer data streams to those users.
R. W. Heath, Jr., T. Wu, and A. C. K. Soong, “Progressive Refinement for High Resolution Limited Feedback Beamforming,” EURASIP Journal on Advances in Signal Processing, special issue on Multiuser Limited Feedback, vol. 2009, Article ID 463823, 13 pages, doi:10.1155/2009/463823, 2009.
In his paper we propose a structured beamforming codebook design, which permits high resolution limited feedback beamforming. The idea is to first quantize the beamformers using a nonlocal codebook. Then a local codebook is successively applied, with smaller and smaller size, to progressively refine the quantized value. Several specific codebooks are proposed that have low storage requirements. A number of algorithmic tricks are proposed to reduce complexity of the algorithm and avoid rescaling the local codebook.
D. J. Ryan, I. B. Collings, I. V. L. Clarkson, and R. W. Heath, Jr., “Performance of Vector Perturbation Multiuser MIMO Systems with Limited Feedback” IEEE Trans. on Communications, vol. 57, no. 9., pp. 2633-2644, Sept. 2009.
Vector perturbation is a nonlinear precoding technique that avoids the power penalty due to zero forcing. The idea is to perturb the direction of the transmitted vector by perturbing the transmit vector with another vector that can be subtracted by a modulo operation. In this paper we analyzed the impact of limited feedback and training on vector perturbation, using the results to propose a limited feedback approach for nonlinear precoding.
K. Huang, J. G. Andrews, and R. W. Heath, Jr., “Performance of Orthogonal Beamforming for SDMA with Limited Feedback,” IEEE Trans. on Veh. Tech., vol. 57, no. 5, pp. 1959-1975, May 2009. Earlier version at at ArXiv.
In this paper we analyze a type of feedback-based transmission technique known as user unitary and rate control (PU2RC). We derive scaling laws for zero forcing and PU2RC transmission techniques as a function of the amount of feedback. One interesting result is that PU2RC outperforms zero forcing, giving higher throughput and more robustness, if the number of users is sufficiently large.
C. B. Chae, D. Mazzarese, N. Jindal and R. W. Heath, Jr., “Coordinated Beamforming with Limited Feedback in the MIMO Broadcast Channel” IEEE Journal on Sel. Areas in Comm., Special Issue on Exploiting Limited Feedback in Tomorrow’s Wireless Communication Networks, vol. 26, no. 8, pp. 1505-1515, Oct. 2008.
Many multiuser limited feedback techniques only work for subscriber stations with a single receive antenna. In this paper we proposed a limited feedback technique for use in coordinated beamforming systems, where the transmit beamformers and receiver combiners are designed jointly. An interesting feature of this paper is that the limited feedback problem involves quantizing parameters of a normalized Hermittian matrix, as opposed to a variation of a Grassmannian beamforming as in the single antenna case.
K. Huang, R. W. Heath, Jr., and J. G. Andrews, “Uplink SDMA with Limited Feedback: Throughput Scaling,” EURASIP Journal on Advances in Signal Processing, special issue on Limited Feedback, vol. 2008, Article ID 479357, 17 pages, doi:10.1155/2008/479357, 2008.
In this paper we consider multiuser MIMO on the uplink. Feedback on the uplink is used primarily for scheduling. We deriving scaling laws that show how throughput scales with users, codebook size, and number of antennas on the uplink. One interesting result is that at high SNR, the scheduler should select users with low quantization error.
Best Student Paper Award at the 2009 IEEE Radio and Wireless Symposium given to Takao Inoue for the paper:T. Inoue and R. W. Heath, Jr., “Geodesic Prediction for Limited Feedback Multiuser MIMO Systems in Temporally Correlated Channels” IEEE Radio & Wireless Symposium, pp. 167-170, Jan. 18-22, 2009.
We have been fortunate to have several current and past sponsors of our work including the National Science Foundation, Motorola, Samsung, Freescale, and Huawei Technologies. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of any sponsors of this work.