經由觀察得知基於半正定放寬(semidefinite relaxation)方法運用於高階正交振幅調變(quadrature amplitude modulation)之多輸入多輸出(multiple-input multiple-output)檢測法存在多樣性不足的問題，特別是在接收天線數目不夠大(小於八根)的時候情況特別明顯。另一方面，輔以晶格正交化(lattice reduction)的多輸入多輸出系統檢測方法被證實可以達到最大的接收多樣性(receive diversity)。因此，這裡提出了一個不一樣的半正定放寬輔以Lenstra, Lenstra, and Lovasz (LLL) 晶格正交方法去獲得系統檢測上的多樣性。由於使用一般常見的解半正定程式軟體去解半正定放寬輔以晶格正交問題的計算複雜度太高，所以我們提出了一個特殊的內點演算法(interior-point)去解此特定問題。除此之外，我們將基於通道特性的終止機制應用到此特殊內點演算法裡，不同的是，這是一個針對高階正交振幅調變延伸而得的機制。結果顯示，此機制亦可以減少內點演算法的重複次數使得整體的運算時間更加減少而不影響其錯誤機率的表現。

[1] M. O. Damen, H. E. Gamal, and G. Caire, “On maximum-likelihood detection and the
search for the closest lattice point,” IEEE Trans. Inform. Theory, vol. 49, no. 10, pp.
2389–2402, 2003.
[2] A. Wiesel, Y. C. Eldar, and S. Shamai, “Semidefinite relaxation for detection of 16-QAM
signaling in MIMO channels,” in IEEE Signal Process. Lett., vol. 12, no. 9, November
2005, pp. 653–656.
[3] Y. Yang, C. Zhao, P. Zhou, and W. Xu, “MIMO detection of 16-QAM signaling based
on semidefinite relaxation,” in IEEE Signal Process. Lett., vol. 14, no. 11, November
2007, pp. 797–800.
[4] N. D. Sidiropoulos and Z.-Q. Luo, “A semidefinite relaxation approach to MIMO detection
for higher-order constellations,” in IEEE Signal Process. Lett., vol. 13, no. 9,
September 2006, pp. 525–528.
[5] Z. Mao, X.Wang, and X.Wang, “Semidefinite programming relaxation approach for
multiuser detection of QAM signals,” IEEE Trans. Wireless Commun., vol. 6, no. 12,
pp. 4275–4279, December 2007.
[6] A. Mobasher, M. Taherzadeh, R. Sotirov, and A. K. Khandani, “A nearmaximumlikelihood
decoding algorithm for MIMO systems based on semi-definite programming,”
IEEE Trans. Inf. Theory, vol. 53, no. 11, pp. 3869–3886, November 2007.
[7] P. Tan and L. Rasmussen, “The application of semidefinite programming for detection
in CDMA,” IEEE J. Select. Areas Commun., vol. 19, no. 4, pp. 1442–1449, April 2001.
[8] W.-K. Ma, T. N. Davidson, K. M.Wong, Z.-Q. Luo, and P. C. Ching, “Quasi-maximumlikelihood
multiuser detection using semi-definite relaxation with application to synchronous
CDMA,” IEEE Trans. Signal Process., vol. 50, no. 4, pp. 912–922, April 2002.
[9] B. Steingrimsson, Z.-Q. Luo, and K. M. Wong, “Soft quasi-maximum-likelihood detection
for multiple-antenna wireless channels,” IEEE Trans. Signal Process., vol. 51,
no. 11, pp. 2710–2719, November 2003.
[10] W.-K. Ma, P. C. Ching, and Z. Ding, “Semidefinite relaxation based multiuser detection
for M-ary PSK multiuser systems,” IEEE Trans. Signal Process., vol. 52, no. 10, pp.
2862–2872, October 2004.
[11] J. Jalden and B. Ottersten, “The diversity order of the semidefinite relaxation detector,”
IEEE Trans. Inf. Theory, vol. 54, no. 4, pp. 1406–1422, April 2008.
[12] M. Kisialiou and Z.-Q. Luo, “Performance analysis of quasi-maximum-likelihood detector
based on semi-definite programming,” in Proc. IEEE Int. Conf. Acoustics and
Speech and Signal Process., pp. 433–436, March 2005.
[13] A. M.-C. So, “On the performance of semidefinite relaxation MIMO detectors for QAM
constellations,” In Proceedings of the 2009 IEEE International Conference on Acoustics
and Speech and Signal Processing (ICASSP 2009), pp. 2449–2452, 2009.
[14] M. Taherzadeh, A. Mobasher, and A. K. Khandani, “LLL reduction achieves the receive
diversity in MIMO decoding,” IEEE Trans. Inform. Theory, vol. 53, no. 12, pp. 4801–
4805, 2007.
[15] C. Helmberg, F. Rendl, R. Vanderbei, and H. Wolkowicz, “An interior-point method
for semidefinite programming,” SIAM J. Optim., vol. 6, no. 2, pp. 342–361, 1996.
[16] D. Wubben, R. Bohnke, V. Kuhn, and K.-D. Kammeyer, “MMSE-based latticereduction
for near-ML detection of MIMO systems,” ITG Workshop on Smart Antennas,
pp. 106–113, March 2004.
[17] A. K. Lenstra, H. W. Lenstra, and L. Lovssz, “Factoring polynomials with rational
coefficients,” Math. Ann., vol. 261, pp. 515–534, 1982.
[18] D. Seethaler, G. Matz, and F. Hlawatsch, “Low-complexity MIMO data detection using
Seysen’s lattice reduction algorithm,” in IEEE International Conference on Acoustics,
Speech and Signal Processing, 2007. ICASSP 2007., vol. 3, 15-20 2007, pp. III–53 –III–
56.
[19] W.-K. Ma, C.-C. Su, J. J., T.-H. Chang, and C.-Y. Chi, “The equivalence of semidefinite
relaxation MIMO detectors for higher-order QAM,” IEEE Journal of Selected Topics
in Signal Processing, vol. 3, pp. 1038–052, December 2009.
[20] J. F. Sturm, “Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric
cones,” Optimization Methods and Software, vol. 11-12, pp. 625–653, 1999.
[21] S. J. Benson and Y. Ye, “DSDP5 User GuideXThe Dual-Scaling Algorithm for Semidefinite
Programming,” Mathematics and Computer Science Division, Argonne National
Laboratory, Argonne, IL, 2004, [Online]. Available: http://www.mcs.anl.gov/ benson.
[22] W.-K. Ma, C.-C. Su, J. Jalden, and C.-Y. Chi, “Some results on 16-QAM MIMO detection
using semidefinite relaxation,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal
Process (ICASSP), pp. 2673–2676, April 2008.
[23] J. Jalden and B. Ottersten, “Channel dependent termination of the semidefinite relaxation
detector,” IEEE International Conference on Acoustics, Speech and Signal
Processing, vol. 4, May 2006.