有限群表現理論在複數時空編碼上之設計及應用

Designing Complex Space-Time Block Codes via Representation Theory on Finite Groups

陳明揚(Ming-Yang Chen)

指導教授 ： 貝蘇章

國立臺灣大學/電機資訊學院/電信工程學研究所/碩士(2005年)

https://doi.org/10.6342/NTU.2005.03053

摘要

無資料

關鍵字

群表現 ； 時空編碼

並列摘要

The designing potential of using quaternionic numbers to identify a 4 × 4 real orthogonal space-time block code has been exploited in various communication articles. Although it has been shown that orthogonal codes in full rate exist only for 2 Tx-antennas in complex constellations, a series of complex quasi-orthogonal codes for 4 Tx-antennas is still proposed to have good performance recently. This quasi-orthogonal scheme enables the codes reach the optimal non-orthogonality, which can be measured by taking the expectation over all transmitted signals of the ratios between the powers of the off-diagonal and diagonal components. In Chapter 1 of this thesis, we extend the quaternionic identification to the above encoding methods. Based upon tensor product for giving the quaternionic space a linear extension, a complete necessary and sufficient condition of identifying any given complex quasi-orthogonal code with the extended space is generalized by considering every possible 2-dimensional R-algebra.

In Chapter 2, a new set of quasi-orthogonal space-time block codes for 4 Txantennas derived by a group-theoretic methodology on the generalized quaternion group of order 16 is presented. We show that these new codes achieve full diversity whenever a square lattice constellation is adopted. From the simulation results, the new designs perform very closely to quasi-orthogonal codes with constellation rotations and admit high coding gains (in fact we prove their coding gains are optimal among those codes whose diagonal entries are all within z1, z1†, or multiples of them by a uni-power coefficient). Without a search of the optimal rotation angle and any constellation expansion, our new codes yield an advantageous transmission scheme for QPSK and 16-QAM modulations.

並列關鍵字

Representations of Finite Groups ； Space-Time Block Codes ； Generalized Quaternion Groups

參考文獻

[1] S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE Journal on Selected Areas in Communications, Vol.16, No.8, pp. 1451–1458, October 1998.

[2] J.-C. Belfiore and G. Rekaya, “Quaternionic lattices for space-time coding,” in Proceedings of the 2003 IEEE Information Theory Workshop, ITW 2003, pp. 267–270, Paris, France, March-April 2003.

[3] M.-Y. Chen, C.-Y. Chen, H.-C. Li, S.-C. Pei, and John M. Cioffi, “Deriving new quasi-orthogonal space-time block codes and relaxed designing viewpoints with full transmit diversity,” to appear in Proceedings of the 2005 IEEE International Conference on Communications, ICC 2005, Seoul, Korea, May 2005.

[4] M.-Y. Chen, H.-C. Li, and S.-C. Pei, “Algebraic identification for optimal nonorthogonality 4 × 4 complex space-time block codes using tensor product on quaternions,” IEEE Transactions on Information Theory, Vol.51, No.1, pp. 324–330, January 2005.

[8] J. Hou, M. H. Lee, and J. Y. Park, “Matrices analysis of quasi-orthogonal space-time block codes,” IEEE Communications Letters, Vol.7, No.8, pp. 385–387, August 2003.