无线通信中的中继功率分配技术研究
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摘要
中继协作通信已经成为无线通信研究的热点。本文对该论题中的功率资源优化分配问题做了一些研究,首先给出了两跳单AF型中继系统中,考虑直达径时的最优功率分配算法。然后给出了在频率选择性信道衰落情况下,两跳非并行双AF型中继系统中,考虑直达径时的最优功率分配算法。接着又给出了在频率选择性信道衰落情况下,两跳非并行多AF型中继系统,考虑直达径时的最优功率分配算法。最后针对频率平坦信道衰落情况下的两跳并行AF中继网络,提出了一种混合功率约束下的最优功率分配方法。其中,混合功率约束是指同时具有上下限约束的中继独立功率约束和中继和功率约束。本文所研究的两跳中继系统均只有一个源节点和一个目的节点。当信道为频率选择性衰落时,优化目标为最大化系统瞬时可靠通信速率;当信道为频率平坦性衰落时,优化目标为最大化系统瞬时输出信噪比。
Relay-based cooperative communication has attracted a great deal of attentions in wireless communication research community. This thesis includes some research on optimal power allocation for relay systems. First, this thesis gives optimal power allocation scheme for dual-hop single amplify-and-forward relay system in which the direct path is also considered. Then this thesis gives optimal power allocation scheme for dual-hop two amplify-and-forward relay system in which the direct path has been taken into consideration. And this thesis also gives optimal power allocation scheme for dual-hop mutiple amplify-and-forward relay system with direct path. Finally, this thesis proposes optimal power allocation scheme for dual-hop amplify-and-forward relay network, where an aggregate relay power constraint and independent power constraint with both upper bound and lower bound are imposed on all the relays, the channels are assumed to be frequency-flat fading. The dual-hop relay system this thesis study only contains one source node and one destination node. When the channel is frequency selective fading, the optimization objective is to maximize system instantaneous communication rate. When the channel is frequency flat fading, the optimization objective is to maximize instantaneous output SNR.
Relay-based cooperative communication has attracted a great deal of attentions in wireless communication research community. This thesis includes some research on optimal power allocation for relay systems. First, this thesis gives optimal power allocation scheme for dual-hop single amplify-and-forward relay system in which the direct path is also considered. Then this thesis gives optimal power allocation scheme for dual-hop two amplify-and-forward relay system in which the direct path has been taken into consideration. And this thesis also gives optimal power allocation scheme for dual-hop mutiple amplify-and-forward relay system with direct path. Finally, this thesis proposes optimal power allocation scheme for dual-hop amplify-and-forward relay network, where an aggregate relay power constraint and independent power constraint with both upper bound and lower bound are imposed on all the relays, the channels are assumed to be frequency-flat fading. The dual-hop relay system this thesis study only contains one source node and one destination node. When the channel is frequency selective fading, the optimization objective is to maximize system instantaneous communication rate. When the channel is frequency flat fading, the optimization objective is to maximize instantaneous output SNR.
引文
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[2] Hong Y W, Huang W J, Chiu F H, et al. Cooperative communications in resource-constr-ained wireless networks[J]. Signal Processing Magazine, IEEE, 2007, 24 (3):47-57.
[3] Bolcskei H, Nabar R U, Oyman O, et al. Capacity scaling laws in MIMO relay networks[J]. IEEE Transactions on Wireless Communications, 2006, 5 (6): 1433-1444.
[4] Munoz O, Vidal J, Agustin A. Linear transceiver design in nonregenerative relays with channel state information[J]. IEEE Transactions on Signal Processing, 2007, 55 (6):2593-2604.
[5] Tang X, Hua Y. Optimal design of non-regenerative MIMO wireless relays [J]. IEEE Transactions on Wireless Communications, 2007, 6 (4):1398-1407.
[6] Fan Y, Thompson J. MIMO congurations for relay channels: Theory and practice[J]. IEEE Transactions on Wireless Communications, 2007, 6 (5):1774-1786.
[7] Rong Y, Hua Y. Optimality of diagonalization of multi-hop MIMO relays[J]. IEEE Tranactions on Wireless Communications, 2009, 8 (12):6068-6077.
[8] Chen M, Serbetli S, Yener A. Distributed power allocation strategies for parallel relay networks[J]. IEEE Transactions on Wireless Communicaions, 2008, 7(2):552-561.
[9] Zhao Y, Adve R, Lim T J. Improving amplify-and-forward relay networks: optimal power allocation versus selection [J]. IEEE Transactions on Wireless Communications, 2007,6 (8):3114-3123.
[10] Tse D, Viswanath P. Fundamentals of Wireless Communication [M]. Cambridge, UK: Cam-bridge University Press, 2004.
[11] Larsson P. Large-scale cooperative relaying network with optimal coherent combining under aggregate relay power constraints[A]. in: Proc. of Future Telecomm. Conf.[C]. 2003.
[12] Quek T Q S, Win M Z, Shin H, et al. Optimal power allocation for amplify-and-forward relay networks via conic programming [A]. in: Proc. ICC[C]. 2007. 5058-5063.
[13] Ibrahim A, Sadek A, Su W, et al. Cooperative communications with partial channel stateinformation: When to cooperate?[A]. in: Global Telecommunications Conference, IEEE[C]. 2005. Vol. 5. 3068-3072.
[14] Ibrahim A S, Sadek A K, Su W, et al. Cooperative communications with relay-selection: when to cooperate and whom to cooperate with? [J]. IEEE Transactions on Wireless Communications, 2008, 7(7):2814-2827.
[15] Bletsas A, Khisti A, Reed D P, et al. A simple cooperative diversity method based on network path selection [J]., IEEE Journal on Selected Areas in Communications 2006, 24 (3):659-672.
[16] Ibrahim A S, Sadek A K, Su W, et al. Cooperative communications with relay-selection: when to cooperate and whom to cooperate with?[J]. IEEE Transactions on Wireless Communications, 2008, 7 (7):2814-2827.
[17] Beres E, Adve R. On selection cooperation in distributed networks[A]. in: Information Sciences and Systems, 2006 40th Annual Conference on[C]. 2006. 1056–1061.
[18] Michalopoulos D, Karagiannidis G. Performance analysis of single relay selection in Rayleigh fading[J]. IEEE Transactions on Wireless Communications, 2008, 7 (10): 37183724.
[19] Zhao Y, Adve R, Lim T J. Symbol error rate of selection amplify-and-forward relay systems [J]. Communications Letters, IEEE, 2006, 10 (11): 757–759.
[20] Michalopoulos D, Karagiannidis G, Tsiftsis T, et al. An optimized user selection method for cooperative diversity systems[A]. in: Global Telecommunications Conference,IEEE[C]. 2006.1-6.
[21] Jing Y, Jafarkhani H. Single and multiple relay selection schemes and their achievable IEEE Transactions on Wireless Communications, 2009, 8 (3): 1414-1423.
[22] Alamouti SM. A simple transmit diversity technique for wireless communications[J]. IEEE Journal on Selected Areas in Communications, 1998, 16 (8): 1451-1458.
[23] Jing Y, Hassibi B. Distributed space-time coding in wireless relay networks[J]. IEEE Transactions on Wireless Communications, 2006, 5 (12): 3524-3536.
[24] Jing Y, Jafarkhani H. Using orthogonal and quasi-orthogonal designs in wireless relay networks[J]. IEEE Transactions on Information Theory, 2007, 53 (11): 4106-4118.
[25] Zhao Q, Li H. Performance of differential modulation with wireless relays in rayleigh fading channels[J]. Communications Letters, IEEE, 2005 , 9 (4): 343-345.
[26] Yiu S, Schober R, Lampe L. Differential distributed space-time block coding[A]. in: Communications, Computers and signal Processing, 2005. PACRIM. 2005 IEEE Pacic Rim Conference on[C]. 2005. 3-56.
[27] Yiu S, Schober R, Lampe L. Distributed space-time block coding[J]. IEEE Transactions on Communications, 2006 , 54 (7): 1195-1206.
[28] Jing Y, Jafarkhani H. Distributed differential space-time coding for wireless relay networks[J], IEEE Transactions on Communications, 2008 , 56 (7): 1092-1100.
[29] Shang Y, Xia X G. Shift-full-rank matrices and applications in space-time trellis codes for relay networks with asynchronous cooperative diversity[J]. IEEE Transactions on Information Theory, 2006 , 52 (7): 3153–3167.
[30] Li Y, Zhang W, Xia X G. Distributive high-rate full-diversity space-frequency codes for asynchronous cooperative communications[A]. in: Information Theory, 2006 IEEE International Symposium on[C]. 2006. 2612-2616.
[31] Prasad N, Varanasi M. Diversity and multiplexing tradeoff bounds for cooperative diversity protocols[A]. in: Information Theory, 2004. ISIT 2004. Proceedings. International Symposiumon[C].2004.
[32] Azarian K, Gamal H E, Schniter P. On the achievable diversity-multiplexing tradeoff in half-duplex cooperative channels[J]. IEEE Transactions on Information Theory, 2005, 51 (12): 4152–4172.
[33] Yang S, Belore J C. Towards the optimal amplify-and-forward cooperative diversity scheme[J]. IEEE Transactions on Information Theory, 2007, 53 (9): 3114-3126.
[34] Yuksel M, Erkip E. Diversity-multiplexing tradeoff in cooperative wireless systems[A]. in: Information Sciences and Systems, 2006 40th Annual Conference on[C]. 2006.
[35] Elia P, Oggier F, Kumar P V. Asymptotically optimal cooperative wireless networks with reduced signaling complexity[J]. IEEE Journal on Selected Areas in Communicatio-ns, 2007, 25 (2): 258-267.
[36] Cover T M, Thomas J A. Elements of information theory[M]. John Wiley & Sons, Inc., NewYork, 1991.
[37] Gallager R G. Information theory and reliable communication[M]. New York: Wiley, 1968.
[38] Luo J, Blum R S, Cimini L J, et al. Decode-and-forward cooperative diversity with power allocation in wireless networks[J]. IEEE Transactions on Wireless Communications, 2007, 6(3): 793–799.
[39] Zhang X, Gong Y. Adaptive power allocation for regenerative relaying with multiple antennas at the destination[J]. IEEE Transactions on Wireless Communications, 2009,8 (6):2789–2794.
[40] Ramesh A, Pamela C C, Laurence B M. Statistical channel knowledge-based optimum power allocation for relaying protocols in the high snr regime[J]. Selected Areas in Communications, IEEE Journal on, 2007, 25 (2): 292-305.
[41] Gao F, Cui T, Nallanathan A. Optimal training design for channel estimation in decode and-forward relay networks with individual and total power constraints[J]. IEEE Transactions on Signal Processing, 2008, 56 (12): 5937–5949.
[42] Sirkeci-Mergen B, Scaglione A. On the power efciency of cooperative broadcast in dense wireless networks[J]. Selected Areas in Communications, IEEE Journal on, 2007 , 25 (2):497–507.
[43] Serbetli S, Yener A. Relay assisted F/TDMA ad-hoc networks: node classication, power allocation and relaying strategies[J]. IEEE Transactions on Communications, 2008, 56 (6):937–947.
[44] Truman C Y N, Yu W. Joint optimization of relay strategies and resource allocations in cooperative cellular networks[J]. Selected Areas in Communications, IEEE Journal on, 2007 ,25(2): 328–339.
[45] Dohler M, Gkelias A, Aghvami H. A resource allocation strategy for distributed MIMO multi-hop communication systems[J]. Communications Letters, IEEE, 2004,8 (2): 99–101.
[46] Cui Y, Lau V K N, Wang R. Distributive subband allocation, power and rate control for relay-assisted OFDMA cellular system with imperfect system state knowledge[J]. IEEE Transactions on Wireless Communications, 2009, 8 (10): 5096–5102.
[47] Li Y, Vucetic B, Zhou Z, et al. Distributed adaptive power allocation for wireless relay networks[J]. Wireless Communications, IEEE Transactions on, 2007 , 6 (3): 948-958.
[48] Gedik B, Amin O, Uysal M. Power allocation for cooperative systems with training-aided channel estimation[J]. IEEE Transactions on Wireless Communications, 2009 , 8 (9): 4773-4783.
[49] Hammerstrom I, Wittneben A.On the optimal power allocation for nonregenerative OFDM relay links[A]. in: Proc. ICC[C]. 2006. Vol. 10. 4463-4468.
[50] Hammerstrom I, Wittneben A. Power allocation schemes for amplify-and-forward MIMO-OFDM relay links[J]. IEEE Transactions on Wireless Communications, 2007, 6 (8): 2798-2802.
[51] Saito M,Athaudage C, Evans J. On power allocation for dual-hop amplify-and-forward OFDM relay systems[A]. in: Proc. GLOBECOM[C]. 2008. 1-6.
[52] Jing Y, Jafarkhani H. Network beamforming using relays with perfect channel information[J]. IEEE Transactions on Information Theory, 2009, 55 (6): 2499-2517.
[53] Jing Y, Jafarkhani H. Network beamforming using relays with perfect channel information[A]. in: Proc. ICASSP[C]. 2007. Vol. 3. III-473-III-476.
[54] Jing Y, Jafarkhani H. Beamforming in wireless relay networks[A]. in: Information Theory and Applications Workshop, 2008[C]. 2008. 142-150.
[55] Quek T Q S, Win M Z, Shin H, et al. Optimal power allocation for amplify-and-forward relay networks via conic programming[A]. in: Proc. ICC[C]. 2007. 5058-5063.
[56] Behbahani A S, Eltawil A M. Amplify-and-forward relay networks under received power constraint[J]. IEEE Transactions on Wireless Communications 2009, 8 (11): 5422-5426.
[57] Farhadi G, Beaulieu N C. Power-optimized amplify-and-forward multi-hop relaying systems[J]. IEEE Transactions on Wireless Communications 2009 , 8 (9): 4634-4643.
[58] Mesbah W, Davidson T. Joint power and channel resource allocation for two-user orthogonal amplify-and-forward cooperation[J]. IEEE Transactions on Wireless Communications 2008 , 7 (11): 4681-4691.
[59] Jafar S A, Gomadam K S, Huang C. Duality and rate optimization for multiple access and broadcast channels with amplify-and-forward relays[J]. IEEE Transactions on Information Theory, 2007, 53 (10): 3350-3370.
[60] Phan K T, Tho L N, Vorobyov S A, et al. Power allocation in wireless multi-user relay networks[J]. IEEE Transactions on Wireless Communications, 2009 , 8 (5): 2535-2545.
[61] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press,2004
[62] I. Hammerstr¨m and A. Wittneben,“On the optimal power allocation for nonregenerative ofdm relay links,”in Proc. ICC, June 2006, vol. 10, pp. 4463–4468.
[2] Hong Y W, Huang W J, Chiu F H, et al. Cooperative communications in resource-constr-ained wireless networks[J]. Signal Processing Magazine, IEEE, 2007, 24 (3):47-57.
[3] Bolcskei H, Nabar R U, Oyman O, et al. Capacity scaling laws in MIMO relay networks[J]. IEEE Transactions on Wireless Communications, 2006, 5 (6): 1433-1444.
[4] Munoz O, Vidal J, Agustin A. Linear transceiver design in nonregenerative relays with channel state information[J]. IEEE Transactions on Signal Processing, 2007, 55 (6):2593-2604.
[5] Tang X, Hua Y. Optimal design of non-regenerative MIMO wireless relays [J]. IEEE Transactions on Wireless Communications, 2007, 6 (4):1398-1407.
[6] Fan Y, Thompson J. MIMO congurations for relay channels: Theory and practice[J]. IEEE Transactions on Wireless Communications, 2007, 6 (5):1774-1786.
[7] Rong Y, Hua Y. Optimality of diagonalization of multi-hop MIMO relays[J]. IEEE Tranactions on Wireless Communications, 2009, 8 (12):6068-6077.
[8] Chen M, Serbetli S, Yener A. Distributed power allocation strategies for parallel relay networks[J]. IEEE Transactions on Wireless Communicaions, 2008, 7(2):552-561.
[9] Zhao Y, Adve R, Lim T J. Improving amplify-and-forward relay networks: optimal power allocation versus selection [J]. IEEE Transactions on Wireless Communications, 2007,6 (8):3114-3123.
[10] Tse D, Viswanath P. Fundamentals of Wireless Communication [M]. Cambridge, UK: Cam-bridge University Press, 2004.
[11] Larsson P. Large-scale cooperative relaying network with optimal coherent combining under aggregate relay power constraints[A]. in: Proc. of Future Telecomm. Conf.[C]. 2003.
[12] Quek T Q S, Win M Z, Shin H, et al. Optimal power allocation for amplify-and-forward relay networks via conic programming [A]. in: Proc. ICC[C]. 2007. 5058-5063.
[13] Ibrahim A, Sadek A, Su W, et al. Cooperative communications with partial channel stateinformation: When to cooperate?[A]. in: Global Telecommunications Conference, IEEE[C]. 2005. Vol. 5. 3068-3072.
[14] Ibrahim A S, Sadek A K, Su W, et al. Cooperative communications with relay-selection: when to cooperate and whom to cooperate with? [J]. IEEE Transactions on Wireless Communications, 2008, 7(7):2814-2827.
[15] Bletsas A, Khisti A, Reed D P, et al. A simple cooperative diversity method based on network path selection [J]., IEEE Journal on Selected Areas in Communications 2006, 24 (3):659-672.
[16] Ibrahim A S, Sadek A K, Su W, et al. Cooperative communications with relay-selection: when to cooperate and whom to cooperate with?[J]. IEEE Transactions on Wireless Communications, 2008, 7 (7):2814-2827.
[17] Beres E, Adve R. On selection cooperation in distributed networks[A]. in: Information Sciences and Systems, 2006 40th Annual Conference on[C]. 2006. 1056–1061.
[18] Michalopoulos D, Karagiannidis G. Performance analysis of single relay selection in Rayleigh fading[J]. IEEE Transactions on Wireless Communications, 2008, 7 (10): 37183724.
[19] Zhao Y, Adve R, Lim T J. Symbol error rate of selection amplify-and-forward relay systems [J]. Communications Letters, IEEE, 2006, 10 (11): 757–759.
[20] Michalopoulos D, Karagiannidis G, Tsiftsis T, et al. An optimized user selection method for cooperative diversity systems[A]. in: Global Telecommunications Conference,IEEE[C]. 2006.1-6.
[21] Jing Y, Jafarkhani H. Single and multiple relay selection schemes and their achievable IEEE Transactions on Wireless Communications, 2009, 8 (3): 1414-1423.
[22] Alamouti SM. A simple transmit diversity technique for wireless communications[J]. IEEE Journal on Selected Areas in Communications, 1998, 16 (8): 1451-1458.
[23] Jing Y, Hassibi B. Distributed space-time coding in wireless relay networks[J]. IEEE Transactions on Wireless Communications, 2006, 5 (12): 3524-3536.
[24] Jing Y, Jafarkhani H. Using orthogonal and quasi-orthogonal designs in wireless relay networks[J]. IEEE Transactions on Information Theory, 2007, 53 (11): 4106-4118.
[25] Zhao Q, Li H. Performance of differential modulation with wireless relays in rayleigh fading channels[J]. Communications Letters, IEEE, 2005 , 9 (4): 343-345.
[26] Yiu S, Schober R, Lampe L. Differential distributed space-time block coding[A]. in: Communications, Computers and signal Processing, 2005. PACRIM. 2005 IEEE Pacic Rim Conference on[C]. 2005. 3-56.
[27] Yiu S, Schober R, Lampe L. Distributed space-time block coding[J]. IEEE Transactions on Communications, 2006 , 54 (7): 1195-1206.
[28] Jing Y, Jafarkhani H. Distributed differential space-time coding for wireless relay networks[J], IEEE Transactions on Communications, 2008 , 56 (7): 1092-1100.
[29] Shang Y, Xia X G. Shift-full-rank matrices and applications in space-time trellis codes for relay networks with asynchronous cooperative diversity[J]. IEEE Transactions on Information Theory, 2006 , 52 (7): 3153–3167.
[30] Li Y, Zhang W, Xia X G. Distributive high-rate full-diversity space-frequency codes for asynchronous cooperative communications[A]. in: Information Theory, 2006 IEEE International Symposium on[C]. 2006. 2612-2616.
[31] Prasad N, Varanasi M. Diversity and multiplexing tradeoff bounds for cooperative diversity protocols[A]. in: Information Theory, 2004. ISIT 2004. Proceedings. International Symposiumon[C].2004.
[32] Azarian K, Gamal H E, Schniter P. On the achievable diversity-multiplexing tradeoff in half-duplex cooperative channels[J]. IEEE Transactions on Information Theory, 2005, 51 (12): 4152–4172.
[33] Yang S, Belore J C. Towards the optimal amplify-and-forward cooperative diversity scheme[J]. IEEE Transactions on Information Theory, 2007, 53 (9): 3114-3126.
[34] Yuksel M, Erkip E. Diversity-multiplexing tradeoff in cooperative wireless systems[A]. in: Information Sciences and Systems, 2006 40th Annual Conference on[C]. 2006.
[35] Elia P, Oggier F, Kumar P V. Asymptotically optimal cooperative wireless networks with reduced signaling complexity[J]. IEEE Journal on Selected Areas in Communicatio-ns, 2007, 25 (2): 258-267.
[36] Cover T M, Thomas J A. Elements of information theory[M]. John Wiley & Sons, Inc., NewYork, 1991.
[37] Gallager R G. Information theory and reliable communication[M]. New York: Wiley, 1968.
[38] Luo J, Blum R S, Cimini L J, et al. Decode-and-forward cooperative diversity with power allocation in wireless networks[J]. IEEE Transactions on Wireless Communications, 2007, 6(3): 793–799.
[39] Zhang X, Gong Y. Adaptive power allocation for regenerative relaying with multiple antennas at the destination[J]. IEEE Transactions on Wireless Communications, 2009,8 (6):2789–2794.
[40] Ramesh A, Pamela C C, Laurence B M. Statistical channel knowledge-based optimum power allocation for relaying protocols in the high snr regime[J]. Selected Areas in Communications, IEEE Journal on, 2007, 25 (2): 292-305.
[41] Gao F, Cui T, Nallanathan A. Optimal training design for channel estimation in decode and-forward relay networks with individual and total power constraints[J]. IEEE Transactions on Signal Processing, 2008, 56 (12): 5937–5949.
[42] Sirkeci-Mergen B, Scaglione A. On the power efciency of cooperative broadcast in dense wireless networks[J]. Selected Areas in Communications, IEEE Journal on, 2007 , 25 (2):497–507.
[43] Serbetli S, Yener A. Relay assisted F/TDMA ad-hoc networks: node classication, power allocation and relaying strategies[J]. IEEE Transactions on Communications, 2008, 56 (6):937–947.
[44] Truman C Y N, Yu W. Joint optimization of relay strategies and resource allocations in cooperative cellular networks[J]. Selected Areas in Communications, IEEE Journal on, 2007 ,25(2): 328–339.
[45] Dohler M, Gkelias A, Aghvami H. A resource allocation strategy for distributed MIMO multi-hop communication systems[J]. Communications Letters, IEEE, 2004,8 (2): 99–101.
[46] Cui Y, Lau V K N, Wang R. Distributive subband allocation, power and rate control for relay-assisted OFDMA cellular system with imperfect system state knowledge[J]. IEEE Transactions on Wireless Communications, 2009, 8 (10): 5096–5102.
[47] Li Y, Vucetic B, Zhou Z, et al. Distributed adaptive power allocation for wireless relay networks[J]. Wireless Communications, IEEE Transactions on, 2007 , 6 (3): 948-958.
[48] Gedik B, Amin O, Uysal M. Power allocation for cooperative systems with training-aided channel estimation[J]. IEEE Transactions on Wireless Communications, 2009 , 8 (9): 4773-4783.
[49] Hammerstrom I, Wittneben A.On the optimal power allocation for nonregenerative OFDM relay links[A]. in: Proc. ICC[C]. 2006. Vol. 10. 4463-4468.
[50] Hammerstrom I, Wittneben A. Power allocation schemes for amplify-and-forward MIMO-OFDM relay links[J]. IEEE Transactions on Wireless Communications, 2007, 6 (8): 2798-2802.
[51] Saito M,Athaudage C, Evans J. On power allocation for dual-hop amplify-and-forward OFDM relay systems[A]. in: Proc. GLOBECOM[C]. 2008. 1-6.
[52] Jing Y, Jafarkhani H. Network beamforming using relays with perfect channel information[J]. IEEE Transactions on Information Theory, 2009, 55 (6): 2499-2517.
[53] Jing Y, Jafarkhani H. Network beamforming using relays with perfect channel information[A]. in: Proc. ICASSP[C]. 2007. Vol. 3. III-473-III-476.
[54] Jing Y, Jafarkhani H. Beamforming in wireless relay networks[A]. in: Information Theory and Applications Workshop, 2008[C]. 2008. 142-150.
[55] Quek T Q S, Win M Z, Shin H, et al. Optimal power allocation for amplify-and-forward relay networks via conic programming[A]. in: Proc. ICC[C]. 2007. 5058-5063.
[56] Behbahani A S, Eltawil A M. Amplify-and-forward relay networks under received power constraint[J]. IEEE Transactions on Wireless Communications 2009, 8 (11): 5422-5426.
[57] Farhadi G, Beaulieu N C. Power-optimized amplify-and-forward multi-hop relaying systems[J]. IEEE Transactions on Wireless Communications 2009 , 8 (9): 4634-4643.
[58] Mesbah W, Davidson T. Joint power and channel resource allocation for two-user orthogonal amplify-and-forward cooperation[J]. IEEE Transactions on Wireless Communications 2008 , 7 (11): 4681-4691.
[59] Jafar S A, Gomadam K S, Huang C. Duality and rate optimization for multiple access and broadcast channels with amplify-and-forward relays[J]. IEEE Transactions on Information Theory, 2007, 53 (10): 3350-3370.
[60] Phan K T, Tho L N, Vorobyov S A, et al. Power allocation in wireless multi-user relay networks[J]. IEEE Transactions on Wireless Communications, 2009 , 8 (5): 2535-2545.
[61] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press,2004
[62] I. Hammerstr¨m and A. Wittneben,“On the optimal power allocation for nonregenerative ofdm relay links,”in Proc. ICC, June 2006, vol. 10, pp. 4463–4468.
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