本篇論文針對中繼站協助之多用戶多輸入單輸出(multiple-input single-output, MISO)下行(downlink)無線通訊系統，考慮高效能(energy-efficient)的預編碼矩陣(precoding matrix)設計。此問題一般是非凸(nonconvex)且複雜的問題，目前已經受到廣泛的關注，不過並沒有強而有效的演算法被提出。在此篇論文中，考慮分別在單天線用戶的服務品質(Quality of Service, QoS)，以及在基地台(base station)和中繼站(relay station)的傳輸功率限制下，設計多根天線的基地台和中繼站之預編碼矩陣以使傳輸的能量效率(energy efficiency) (此傳輸能量效率定義為系統傳輸速率總和對消耗總功率之比值)最大化。有鑑於此最佳化問題是一個非凸分式問題(nonconvex fractional programming)，我們提出了一個可以保證收斂的連續丁克爾巴赫凸近似(successive Dinkelbach and convex approximation, SDCA )演算法用以處理此問題。模擬結果驗證所提出的SDCA演算法之效能，以及當基地台和中繼站天線個數增加時(亦即，更多的空間自由度)，SDCA會顯著地改善傳輸能量效率。最後，我們總結此篇論文。

This thesis considers the energy-efficient precoding matrix design for a relay-aided multiuser
downlink multiple-input single-output (MISO) wireless system. This problem is nonconvex
and complicated in general and has drawn extensive attention, but few effective and efficient
algorithms have been reported. In this thesis, the precoders of the base station (BS) and
the relay station (RS) both equipped with multiple antennas are designed to maximize the
transmit energy efficiency (EE), defined as the ratio between the system sum rate and the
total power consumption, under respective quality-of-service (QoS) constraints of singleantenna
users and the transmit power constraints on the BS and the RS. In view of the fact
that the associated optimization problem is a nonconvex fractional programming, a successive
Dinkelbach and convex approximation (SDCA) algorithm with convergence guaranteed is
proposed to cope with the problem. Some simulation results are provided to demonstrate
the effectiveness of the proposed SDCA algorithm, and significant EE improvement as the
number of antennas at the BS and the RS increases (i.e., more spatial degrees of freedom).
Finally, some conclusions are provided.

[1] H. Zhang, A. Gladisch, M. Pickavet, Z. Tao, and W. Mohr, “Special issue on energy
efficiency in communications,” IEEE Commun. Mag., vol. 48, no. 11, pp. 48–49, Nov.
2010.
[2] S. Betz and H. V. Poor, “Energy efficient communications in CDMA networks: A game
theoretic analysis considering operating costs,” IEEE Trans. Signal Process., vol. 56,
no. 10, pp. 5181–5190, Oct. 2008.
[3] G. Miao, N. Himayat, G. Y. Li, and S. Talwar, “Distributed interferenceaware energyefficient
power optimization,” IEEE Trans. Wireless Commun., vol. 10, no. 4, pp. 1323–
1333, Apr. 2011.
[4] C. Isheden and G. P. Fettweis, “Energy-efficient multi-carrier link adaptation with sum
rate-dependent circuit power,” in Proc. IEEE GLOBECOM, Miami, FL, Dec. 6-10,
2010, pp. 1–6.
[5] Z. Chong and E. A. Jorswieck, “Energy-efficient power control for MIMO time-varying
channels,” in Proc. IEEE GreenCom, New York, NY, Sept. 26-29, 2011, pp. 92–97.
[6] E.-V. Belmega and S. Lasaulce, “Energy-efficient precoding for multiple-antenna terminals,”
IEEE Trans. Signal Process., vol. 59, no. 1, pp. 329–340, Jan. 2011.
[7] M. Le Treust and S. Lasaulce, “A repeated game formulation of energy efficient decentralized
power control,” IEEE Trans. Wireless Commun., vol. 9, no. 9, pp. 2860–2869,
Sept. 2010.
[8] J. Cho and Z. J. Haas, “On the throughput enhancement of the downstream channel in
cellular radio networks through multihop relaying,” IEEE J. Sel. Areas Commun., vol.
22, no. 7, pp. 1206–1219, Sept. 2004.
[9] S. Zhou, A. J. Goldsmith, and Z. Niu, “On optimal relay placement and sleep control
to improve energy efficiency in cellular networks,” in IEEE ICC, Kyoto, June 2011, pp.
1–6.
[10] A. Zappone, Z. Chong, E. A. Jorswieck, and S. Buzzi, “Energy-aware competitive power
control in relay-assisted interference wireless networks,” IEEE Trans. Wireless Com-
mun., vol. 12, no. 4, pp. 1860–1871, Apr. 2013.
[11] A. Zappone, P. Cao, and E. A. Jorswieck, “Energy efficiency optimization in relayassisted
MIMO systems with perfect and statistical CSI,” IEEE Trans. Signal Process.,
vol. 62, no. 2, pp. 443–457, Jan. 2014.
[12] C. Li, F. Sun, J. M. Cioffi, and L. Yang, “Energy efficient MIMO relay transmissions
via joint power allocations,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 61, no. 7,
pp. 531–535, Jul. 2014.
[13] C. Li, H. J. Yang, F. Sun, J. M. Cioffi, and L. Yang, “Approximate closed-form energy
efficient PA for MIMO relaying systems in the high SNR regime,” IEEE Commun. Lett.,
vol. 18, no. 8, pp. 1367-1370, Aug. 2014.
[14] X. Zhou, B. Bai, and W. Chen, “A low complexity energy efficiency maximization
method for multiuser amplify-and-forward MIMO relay systems with a holistic power
model,” in IEEE Commun. Lett. vol. 18, no. 8, pp. 1371–1374, Aug. 2014.
[15] W. Dinkelbach, “On nonlinear fractional programming,” Manag. Sc., vol. 13, no. 7, pp.
492–498, 1967.
[16] D. Bertsekas, Nonlinear Programming. Nashua, NH, USA: Athena Scientific, 1999.
[17] J. Xu, and L. Qiu, “Energy efficiency optimization for MIMO broadcast channels,”
IEEE Trans. Wireless Commun., vol. 12, no. 2, pp. 690–701, Feb. 2013.
[18] C. Hellings and W. Utschick, “Energy effiiency optimization in MIMO broadcast channels
with fairness constraints,” in Proc. IEEE 14th Int. Workshop Signal Process. Adv.
Wireless Commun. (SPAWC), Jun. 2013, pp. 594–598.
[19] G. Miao, N. Himayat, and G. Y. Li, “Energy-efficient link adaptation in frequencyselective
channels,” IEEE Trans. Wireless Commun., vol. 58, no. 2, pp. 545–554, Feb.
2010.
[20] W.-C. Li, T.-H. Chang, C. Lin, and C.-Y. Chi, “Coordinated beamforming for multiuser
MISO interference channel under rate outage constraints,” IEEE Trans. Signal Process.,
vol. 61, no. 5, pp. 1087–1103, 2013.
[21] F. You, P. M. Castro, and I. E. Grossmann, “Dinkelbach’s algorithm as an efficient
method to solve a class of MINLP models for large-scale cyclic scheduling problems,”
Computers & Chemical Engineering, vol. 33, no. 11, pp. 1879–1889, 2009.
[22] R. Zhang, C. C. Chai, and Y.-C. Liang, “Joint beamforming and power control for multiantenna
relay broadcast channel with QoS constraints,” IEEE Trans. Signal Process.,
vol. 57, no. 2, pp. 726–737, 2009.
[23] M. Grant and S. Boyd, “CVX: Matlab software for disciplined convex programming,
version 1.21,” http://cvxr.com/cvx, Apr. 2011.