Coding on Flag Manifolds for Limited Feedback MIMO Systems
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School of Electrical Engineering |
Doctoral thesis (article-based)
| Defence date: 2014-01-31
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Authors
Date
2013
Major/Subject
Mcode
Degree programme
Language
en
Pages
161
Series
Aalto University publication series DOCTORAL DISSERTATIONS, 211/2013
Abstract
The efficiency of the physical layer in modern communication systems using multi-input multi-output (MIMO) techniques is largely based on the availability of channel state information (CSI) at the transmitter. In many practical systems, CSI needs to be quantized at the receiver side before transmission through a limited rate feedback channel. This is typically done using a codebook-based precoding transmission, where the receiver transmits the index of a codeword from a pre-designed codebook shared with the transmitter. To construct such codes one has to discretize complex flag manifolds. For single-user MIMO with a maximum likelihood receiver, the spaces of interest are Grassmann manifolds. With a linear receiver and network MIMO, the codebook design is related to discretization of Stiefel manifolds and more general flag manifolds. In this thesis, coding in flag manifolds is studied. In a first part, flag manifolds are defined as metric spaces corresponding to subsurfaces of hyperspheres. The choice of distance defines the geometry of the space and impacts clustering and averaging (centroid computation) in vector quantization, as well as coding theoretical packing bounds and optimum constructions. For two transmitter antenna systems, the problem reduces to designing spherical codes. A simple isomorphism enables to analytically derive closed-form codebooks with inherent low-implementation complexity. For more antennas, the concept of orbits of symmetry groups is investigated. Optimum codebooks, having desirable implementation properties as described in industry standardization, can be obtained using orbits of specific groups. For large antenna systems and base station cooperation, a product codebook strategy is also considered. Such a design requires to jointly discretize the Grassmann and Stiefel manifolds. A vector quantization algorithm for joint Grassmann-Stiefel quantization is proposed. Finally, the pertinence of flag codebook design is illustrated for a MIMO system with linear receiver.Description
Supervising professor
Tirkkonen, Olav, Prof., Aalto University, Department of Communications and Networking, FinlandThesis advisor
Tirkkonen, Olav, Prof., Aalto University, Department of Communications and Networking, FinlandKeywords
MIMO systems, quantization, coding, flag, Stiefel, Grassmann, manifolds
Other note
Parts
- [Publication 1]: R.-A. Pitaval, O. Tirkkonen and S. D. Blostein. Density and Bounds for Grassmannian Codes with Chordal Distance. In Proceedings of the IEEE International Symposium on Information Theory (ISIT), Saint Petersburg, Russia, pp. 2298-2302, Aug. 2011.
- [Publication 2]: R.-A. Pitaval and O. Tirkkonen. Volume of Ball and Hamming-type Bounds for Stiefel Manifold with Euclidean Distance. In Proceedings of the 46th Annual Asilomar Conference on Signals, Systems, and Computers (ACSSC), Pacific Grove, California, pp. 483-487, Nov. 2012.
- [Publication 3]: R.-A. Pitaval, H.-L. Määttänen, K. Schober, O. Tirkkonen, and R. Wichman. Beamforming Codebooks for Two Transmit Antenna Systems based on Optimum Grassmannian Packings. IEEE Transactions on Information Theory, vol.57, no.10, pp. 6591-6602, Oct. 2011.
- [Publication 4]: R.-A. Pitaval, O. Tirkkonen and S. D. Blostein. Low Complexity MIMO Precoding Codebooks from Orthoplex Packings. In Proceedings of the IEEE International Conference on Communications (ICC), Kyoto, Japan, pp. 1-5, June 2011.
- [Publication 5]: R.-A. Pitaval and O. Tirkkonen. Grassmannian Packings from Orbits of Projective Group Representations. In Proceedings of the 46th Annual Asilomar Conference on Signals, Systems, and Computers (ACSSC), Pacific Grove, California, pp. 478-482, Nov. 2012.
- [Publication 6]: R.-A. Pitaval and O. Tirkkonen. Flag Orbit Codes and Their Expansion to Stiefel Codes. In Proceedings of the IEEE Information Theory Workshop (ITW), Seville, Spain, pp. 360-364, Sep. 2013.
- [Publication 7]: R.-A. Pitaval and O. Tirkkonen. Joint Grassmann-Stiefel Quantization for MIMO Product Codebooks. Accepted for publication in IEEE Transactions on Wireless Communications, 13 pp., Oct. 2013.
- [Publication 8]: R.-A. Pitaval, A. Srinivasan and O. Tirkkonen. Codebooks in Flag Manifolds for Limited Feedback MIMO Precoding. In Proceedings of the 9th International ITG Conference on Systems, Communications and Coding (SCC), Munich, Germany, pp. 1-5, Jan. 2013.