達到分集與多工最佳取捨的時空編碼之峰均值減低方法

Peak to Average Ratio Reduction of Space-Time Codes That Achieve Diversity-Multiplexing Gain Tradeoff

李崇丕(Chung-Pi Lee)

指導教授 ： 蘇炫榮

國立臺灣大學/電機資訊學院/電信工程學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.00412

摘要

在參考文獻[1]裡指出在類似靜止的通道下，存在一個多工與分集的最佳取捨，之後有許多研究在設計可達到最佳取捨的時空編碼，然而，這些時空編碼往往導致相當高的峰均比，高的峰均比會使傳送端的放大器設計困難，所以我們將探討如果加上峰均比的限制，多工與分集的最佳取捨會有怎樣的影響。結果顯示最佳取捨仍然是不變的，但是那些原本設計可達到多工與分集最佳取捨的時空編碼需要作適當的調整使其符合峰均比的限制。因此，我們提供了二種方法來降低峰均比並維持時空編碼本身的結構，所以仍然可以達到多工與分集的最佳取捨並有較低的峰均比。第一種方法利用Hermite Normal Form分解來達成，第二種方法則是利用可逆整數對應來完成，在時空編碼個數足夠大時，二者皆可漸近的降低峰均比到3

關鍵字

分集,多工,峰均比

並列摘要

A result of Zheng and Tse [1] states that over a quasi-static channel, there exists a fundamental tradeoff, known as diversity-multiplexing gain (D-MG) tradeoff. The quest for space-time codes that achieve D-MG tradeoff has generated numerous work [2-7],etc. However, these space-time codes generally have a pretty high peak to average power ratio (PAR) value on each antenna. In a realistic system, to avoid inefficiently operating the power amplifier, one should put constraints on PAR value. In the following context, we investigate D-MG tradeoff with PAR constraints. The results show D-MG tradeoff remains the same even with PAR constraints, but space-time codes devised to achieve D-MG tradeoff need some modifications to meet the PAR constraints. Therefore, we propose two general ways to reduce PAR without affecting codes structure and without any side information being transmitted. They are both based on constellation shaping, that is, a constellation is used such that the transmitted signals have low PAR values. The first method is similar as [8] except we choose the Hermite Normal Form (HNF) decomposition instead of Smith Normal Form (SNF); the second one takes the idea of integer reversible mapping [9], [10]. If the approximately cubic shaping is used, both techniques would lead to an asymptotical PAR value equalto 3 when SNR is large.

並列關鍵字

diversity,multiplexing,par

參考文獻

[1] L. Zheng and D. N. C. Tse, “Diversity and multiplexing: A fundamental tradeoff in multiple antenna channels,” IEEE Trans. Inform. Theory,vol. 49, no. 5, pp. 1073–1096, May. 2003.

[2] P. Elia, B. Sethuraman, and P. V. Kumar, “Perect space time codes with minimum and non-minimum delay for any number of antennas,”preprint, submited to arXiv:cs.IT, Dec 2005.

[3] P. Elia, S. A. Pawar, K. R. Kumar, P. V. Kumar, and H. Lu, “Explicit space-time codes achieving the diversity-multiplexing gain tradeoff,”IEEE Trans. Inform. Theory, vol. 52, no. 9, Sep 2006.

[5] H. E. Gamal, G. Caire, and M. Damen, “Lattice coding and decoding achieve the optimal diversity-multilpexing tradeoff of mimo channels,”IEEE Trans. Inform. Theory, vol. 50, pp. 968–985, June 2004.56

[6] P. Dayal and M. K. Varanasi, “An optimal two transmit antenna spacetime code and its stacked extension,” in Asilomar Conf. on Signals,Systems and Computers, Monterey, CA, Nov 2003.