A Design Method of Noncoherent Unitary Space-Time Codes

Li Peng, Qiuping Peng, Lingling Yang

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DOI: 10.4236/ijcns.2011.47051                

Abstract

We generalized an constructing method of noncoherent unitary space time codes (N-USTC) over Rayleigh flat fading channels. A family of N-USTCs with T symbol peroids, M transmit and N receive antennas was constructed by the exponential mapping method based on the tangent subspace of the Grassmann manifold. This exponential mapping method can transform the coherent space time codes (C-STC) into the N-USTC on the Grassmann manifold. We infered an universal framework of constructing a C-STC that is designed by using the algebraic number theory and has full rate and full diversity (FRFD) for t symbol periods and same antennas, where M, N, T, t are general positive integer. We discussed the constraint condition that the exponential mapping has only one solution, from which we presented a approach of searching the optimum adjustive factor α_opt that can generate an optimum noncoherent codeword. For different code parameters M, N, T, t and the optimum adjustive factor α_opt, we gave the simulation results of the several N-USTCs.

Keywords

Noncoherent Uintary Space-Time Codes (N-USTC), Coherent Space-Time Codes (C-STC), Grassmann Manifold, Degree of Freedom, Exponenatial Map, Full Rate and Full Diversity (FRFD)

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	T. L. Marzetta and B. M. Hochwald, “Capacity of a Mobile Multiple-Antenna Communication Link in Rayleigh flat Fading,” IEEE Transactions on Information Theory, Vol. 45, No. 1, January 1999, pp. 139-157. doi:10.1109/18.746779
[2]	B. M. Hochwald and T. L. Marzetta, “Unitary Space- Time Modulation for Multiple-Antenna Communication in Rayleigh Flat Fading,” IEEE Transactions on Information Theory, Vol. 46, No. 2, March 2000, pp. 543-564. doi:10.1109/18.825818
[3]	L. Zheng and D. N. C. Tse, “Communication on the Grassmann Manifold: A Geometric Approach to the Noncoherent Multiple-Antenna Channel,” IEEE Transactions on Information Theory, Vol. 48, No. 2, February 2002, pp. 359-383. doi:10.1109/18.978730
[4]	R. H. Gohary and T. N. Davidson, “Noncoherent MIMO Communication: Grassmannian Constellations and Efficient Detection,” IEEE Transactions on Information Theory, Vol. 55, No. 3, March 2009, pp. 1176-1205. doi:10.1109/TIT.2008.2011512
[5]	I. Kammoun and J. C. Belfiore, “A New Family of Grassmannian Space-Time Codes for Noncoherent MIMO Systems,” IEEE Communication Letters, Vol. 7, No. 11, November 2003, pp. 528-530. doi:10.1109/LCOMM.2003.820081
[6]	I. Kammoun and A. M. Cipriano and J. C. Belfiore, “Noncoherent Codes over the Grassmannian,” IEEE Transactions on Wireless Communications, Vol. 6, No. 10, October 2007, pp. 3657-3667. doi:10.1109/TWC.2007.06059
[7]	S. M. Alamouti, “A Simple Transmit Diversity Technique for Wireless Communications,” IEEE Journal on Selected Areas in Communications, Vol. 16, No. 8, October 1998, 1451-1458. doi:10.1109/49.730453
[8]	M. O. Damen, A. Tewfik and J. C. Belfiore, “A Construction of a Space-Time Code Based on the Theory of Numbers,” IEEE Transactions on Information Theory, Vol. 48, No. 3, March 2002, pp. 753-760. doi:10.1109/18.986032
[9]	J. C. Belfiore, G. Rekaya and E. Viterbo, “The Golden Code: A 2*2 Full-Rate Space—Time Code with Nonvanishing Determinants,” IEEE Transactions on Information Theory, Vol. 51, No. 4, April 2005, pp. 1432-1436. doi:10.1109/TIT.2005.844069
[10]	H. E. Gamal and M. O. Damen, “Universal Space-Time Coding,” IEEE Transactions on Information Theory, Vol. 49, No. 5, May 2003, pp. 1097-1119. doi:10.1109/TIT.2003.810644
[11]	F. Oggier, G. Rekaya, J. C. Belfiore and E. Viterbo, “Perfect Space-Time Block Codes,” IEEE Transactions on Information Theory, Vol. 52, No. 9, September 2006, pp. 3885-3902. doi:10.1109/TIT.2006.880010
[12]	J. H. Conway, R. H. Hardin and N. J. A. Sloane, “Packing Lines, Planes, etc.: Packings in Grassmannian Spaces,” Experimental Mathematics, Vol. 5, No. 2, 1996, pp. 139-159.
[13]	Z. Utkovski, P. C. Chen and J. Lindner, “Some Geometric Methods for Construction of Space-Time Codes in Grassmann Manifolds,” Proceedings of the 46th Annual Allerton Conference on Communication, Urbana-Cham- paign, September 2008, pp. 111-118.