Single User Limited Feedback
For single user MIMO systems, the transmitter can use information about the channel state information to implement transmit precoding. The idea of precoding is to couple the transmitted signal more efficiently into the MIMO channel. Precoding is most efficient when it uses precoders designed based on instantaneous channel state information at the transmitter. A practical method for informing the transmitter about the current channel state is to quantize channel state information and send it from the receiver back to the transmitter through a finite rate feedback link. The concept is broadly known as limited feedback.
In single user MIMO systems, limited feedback involves determining the index of a quantized precoding matrix from a predetermined codebook of precoding matrices (known at both the transmitter and receiver), is determined at the receiver and sent back to the transmitter. Limited feedback is challenging because high efficiency quantization is required to minimize the amount of overhead incurred by the feedback channel.
We have investigated many aspects of limited feedback wireless communication. Our earliest work was to connect the problem of limited feedback in MIMO wireless systems to a problem found in applied mathematics known as Grassmannian packing. The Grassmann manifold is the collection of all subspaces of a particular dimension. Packing is the problem of squeezing a bunch of subspaces together while at the same time keeping them as far apart as possible. Under some assumptions we showed that optimum codebooks maximize some form of minimum subspace distance. We call this Grassmannian beamforming or Grassmannian precoding. In later work we developed efficient implementations of limited feedback beamforming and precoding for MIMO-OFDM, exploiting correlation in the frequency domain. Most recently, we have exploited temporal correlation to further reduce feedback requirements. We have investigated the impact of various practical factors such as channel temporal correlation and feedback delay on limited feedback delay and performance.
Here we review select publications in limited feedback; more publications are listed in other sections on this web page as well as in my CV.
Grassmannian Beamforming and Precoding
B. Mondal and R. W. Heath, Jr., “A Diversity Guarantee and SNR Performance for Quantized Precoded MIMO Systems,”EURASIP Journal on Advances in Signal Processing, special issue on Limited Feedback, vol. 2008, Article ID 594928, 15 pages, doi:10.1155/2008/594928, 2008.
B. Mondal and R. W. Heath, Jr., “Performance Analysis of Quantized Beamforming MIMO Systems,” IEEE Trans. on Signal Processing, vol. 54, no. 12, pp. 4753-4766, December 2006.
D. J. Love and R. W. Heath, Jr., “Limited Feedback Unitary Precoding for Spatial Multiplexing,” IEEE Trans. on Info. Theory, vol. 51, no. 8, pp. 2967 – 2976, August 2005.
D. J. Love and R. W. Heath, Jr., “Diversity Performance of Precoded Orthogonal Space-Time Block Codes Using Limited Feedback”,” IEEE Communication Letters, vol. 8, pp. 305-307, May 2004.
D. J. Love, R. W. Heath, Jr., and T. Strohmer, “Grassmannian Beamforming for Multiple-Input Multiple-Output Wireless Systems,” IEEE Trans. on Info. Theory special issue on MIMO Communication, vol. 49, pp. 2735-2747, Oct. 2003.
A. Y. Panah, R. G. Vaughan, and R. W. Heath, Jr., “Optimizing Pilot Locations Using Feedback in OFDM Systems” IEEE Trans. on Veh. Tech., vol. 58, no. 6, pp. 2803-2814, July 2009.
J. Choi, B. Mondal, and R. W. Heath, Jr., “Interpolation Based Unitary Precoding for Spatial Multiplexing MIMO-OFDM with Limited Feedback,” IEEE Trans. on Signal Processing, vol. 54, no. 12, pp. 4730-4740, December 2006.
J. Choi and R. W. Heath, Jr., “Interpolation Based Transmit Beamforming for MIMO-OFDM with Limited Feedback,” IEEE Trans. on Signal Processing, vol. 53, no. 11, pp. 4125-4135, Nov. 2005.
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.
T. Inoue and R. W. Heath, Jr., “Kerdock Codes for Limited Feedback Precoded MIMO Systems” IEEE Trans. on Signal Processing, vol. 57, no. 9, pp. 3711-3716, September 2009. Prior draft available at ArXiv.
V. Raghavan, R. W. Heath, Jr., and A. Sayeed, “Systematic Codebook Designs for Quantized Beamforming in Correlated MIMO Channels,” IEEE Journal on Sel. Areas in Comm., Special Issue on Optimization of MIMO Transceivers for Realistic Communication Networks: Challenges and Opportunities, vol. 25, no. 7. pp. 1298-1310, Sept. 2007.
Exploiting Temporal Correlation
K. Huang, R. W. Heath, Jr., and J. G. Andrews, “Limited Feedback Beamforming Over Temporally-Correlated Channels,” IEEE Trans. on Signal Processing, vol. 57, no. 5, pp. 1959-1975, May 2009. Older version available on ArXiv.
B. Mondal and R. W. Heath, Jr., “Channel Adaptive Quantization for Limited Feedback MIMO Beamforming systems,” IEEE Trans. on Signal Processing, vol. 54, no. 12., pp. 4741-4740, December 2006.
D. J. Love and R. W. Heath, Jr., “Limited Feedback Diversity Techniques for Correlated Channels,” IEEE Trans. on Veh. Tech., vol. 55, no. 2, pp. 718-722, March 2006.
D. J. Love and R. W. Heath, Jr., “Necessary and Sufficient Conditions for Full Diversity Order in Correlated Rayleigh Fading Beamforming and Combining Systems,” IEEE Trans. on Wireless, vol. 4, no. 1, pp. 20-23, Jan. 2005.
Received the best student paper award at GLOBECOM 2006 in the category of Communication Systems, given to Kaibin Huang, for the paper:
K. Huang, B. Mondal, R. W. Heath, Jr., and J. G. Andrews, “Multi-Antenna Limited Feedback for Temporally-Correlated Channels: Feedback Compression,” Proc. of IEEE Global Telecommunications Conf., pp. 1-5, San Francisco, CA, USA, Nov. 27 – Dec. 1, 2006.
We have been fortunate to have several sponsors of our work on limited feedback including at present the National Science Foundation through grant NSF-CCF-0830615 and previously NSF-CCF-0514194. We have also had several industrial sponsors in the past including Motorola, Samsung, and Freescale. 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 the National Science Foundation.