Open Access Research Article

Efficient Near Maximum-Likelihood Detection for Underdetermined MIMO Antenna Systems Using a Geometrical Approach

Kai-Kit Wong1* and Arogyaswami Paulraj2

Author Affiliations

1 Adastral Park Research Campus, University College London, Martlesham IP5 2BS, UK

2 Information Systems Laboratory, Stanford University, Stanford, CA 94305, USA

For all author emails, please log on.

EURASIP Journal on Wireless Communications and Networking 2007, 2007:084265 doi:10.1155/2007/84265


The electronic version of this article is the complete one and can be found online at: http://jwcn.eurasipjournals.com/content/2007/1/084265


Received:9 January 2007
Revisions received:21 May 2007
Accepted:10 October 2007
Published:9 December 2007

© 2007 Wong and Paulraj

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Maximum-likelihood (ML) detection is guaranteed to yield minimum probability of erroneous detection and is thus of great importance for both multiuser detection and space-time decoding. For multiple-input multiple-output (MIMO) antenna systems where the number of receive antennas is at least the number of signals multiplexed in the spatial domain, ML detection can be done efficiently using sphere decoding. Suboptimal detectors are also well known to have reasonable performance at low complexity. It is, nevertheless, much less understood for obtaining good detection at affordable complexity if there are less receive antennas than transmitted signals (i.e., underdetermined MIMO systems). In this paper, our aim is to develop an effcient detection strategy that can achieve near ML performance for underdetermined MIMO systems. Our method is based on the geometrical understanding that the ML point happens to be a point that is "close" to the decoding hyperplane in all directions. The fact that such proximity-close points are much less is used to devise a decoding method that promises to greatly reduce the decoding complexity while achieving near ML performance. An average-case complexity analysis based on Gaussian approximation is also given.

References

  1. GJ Foschini, MJ Gans, On limits of wireless communications in a fading environment when using multiple antennas. Wireless Personal Communications 6(3), 311–335 (1998). Publisher Full Text OpenURL

  2. V Tarokh, N Seshadri, AR Calderbank, Space-time codes for high data rate wireless communication: performance criterion and code construction. IEEE Transactions on Information Theory 44(2), 744–765 (1998). Publisher Full Text OpenURL

  3. U Fincke, M Phost, Improved methods for calculating vectors of short length in a lattice, including a complexity analysis. Mathematics of Computation 44(170), 463–471 (1985). Publisher Full Text OpenURL

  4. WH Mow, Maximum likelihood sequence estimation from the lattice viewpoint. IEEE Transactions on Information Theory 40(5), 1591–1600 (1994). Publisher Full Text OpenURL

  5. O Damen, A Chkeif, J-C Belfiore, Lattice code decoder for space-time codes. IEEE Communications Letters 4(5), 161–163 (2000). Publisher Full Text OpenURL

  6. B Hassibi, H Vikalo, On the sphere-decoding algorithm—I: expected complexity. IEEE Transactions on Signal Processing 53(8), 2806–2818 (2005)

  7. H Vikalo, B Hassibi, On the sphere-decoding algorithm—II: generalizations, second-order statistics, and applications to communications. IEEE Transactions on Signal Processing 53(8), 2819–2834 (2005)

  8. E Viterbo, J Boutros, A universal lattice code decoder for fading channels. IEEE Transactions on Information Theory 45(5), 1639–1642 (1999). Publisher Full Text OpenURL

  9. ND Sidiropoulos, Z-Q Luo, A semidefinite relaxation approach to MIMO detection for high-order QAM constellations. IEEE Signal Processing Letters 13(9), 525–528 (2006)

  10. Z Guo, P Nilsson, Algorithm and implementation of the -best Sphere decoding for MIMO detection. IEEE Journal on Selected Areas in Communications 24(3), 491–503 (2006)

  11. Y Xie, Q Li, CN Georghiades, On some near optimal low complexity detectors for MIMO fading channels. IEEE Transactions on Wireless Communications 6(4), 1182–1186 (2007)

  12. D Tse, P Viswanath, On the capacity of the multiple antenna broadcast channel. in Proceedings of the DIMACS Workshop on Signal Processing for Wireless Transmission, October 2002, Piscataway, NJ, USA, Series Discrete Math, ed. by . and Theoretical Computer Science (American Mathematical Society)

  13. S Vishwanath, N Jindal, A Goldsmith, Duality, achievable rates, and sum-rate capacity of Gaussian MIMO broadcast channels. IEEE Transactions on Information Theory 49(10), 2658–2668 (2003). Publisher Full Text OpenURL

  14. H Vikalo, B Hassibi, T Kailath, Iterative decoding for MIMO channels via modified sphere decoding. IEEE Transactions on Wireless Communications 3(6), 2299–2311 (2004). Publisher Full Text OpenURL

  15. MO Damen, K Abed-Meraim, J-C Belfiore, Generalized sphere decoder for asymmetrical space-time communication architecture. Electronics Letters 36(2), 166–167 (2000). Publisher Full Text OpenURL

  16. Z Yang, C Liu, J He, A new approach for fast generalized sphere decoding in MIMO Systems. IEEE Signal Processing Letters 12(1), 41–44 (2005)

  17. AM Chan, I Lee, A new reduced-complexity sphere decoder for multiple antenna systems. Proceedings of IEEE International Conference on Communications (ICC '02), April-May 2002, New York, NY, USA 1, 460–464

  18. K-K Wong, A Paulraj, On the decoding order of MIMO maximum-likelihood sphere decoder: linear and non-linear receivers. Proceedings of IEEE 59th Vehicular Technology Conference (VTC '04), May 2004, Milan, Italy 2, 698–702