基于不完全信道状态信息的多用户MIMO中继系统预编码算法
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摘要
针对上行多用户MIMO中继系统,在信道存在反馈延迟及估计误差的条件下,以误比特率(Bit error rate,BER)为优化目标,提出了基于最小均方误差(Minimum mean?squared error,MMSE)准则的预编码算法。所提算法将求解发射端、中继节点、接收端矩阵的复杂非凸问题分解为3个独立的子优化问题,发射端的用户配备单天线且服从空间独立分布,先确定发射端预编码矩阵,将求解中继矩阵的凸优化问题转化为半正定规划(Semi?definite programming,SDP)问题,采用CVX工具箱求解,接收端处理矩阵通过线性搜索法求解,最后采用联合迭代法得到各节点矩阵的最优解。仿真结果表明,所提算法能有效改善系统的误比特率性能。
For up?link multi?user multiple?input multiple?output relay systems,with the aim of minimizing the bit error rate,a linear precoding scheme design is proposed based on the minimum mean?squared error(MMSE)rule in the presence of the feedback delay and channel estimation error. The proposed precoding algorithm decomposes the constrained optimization problem into three sub?convex optimization problems that are solved separately. The transmitter equipped with single antenna is subject to independent distribution,and it can be assumed that the precoding matrix is a diagonal matrix. The convex optimization problem of relay matrix is transformed into semi?definite programming problem(SDP),which can be solved by CVX toolbox. The equalizer matrix can be introduced by the gradient?based line search algorithms. Then the optimal solution is obtained by using joint iteration. The simulation results show that the proposed scheme can achieve better system performance.
For up?link multi?user multiple?input multiple?output relay systems,with the aim of minimizing the bit error rate,a linear precoding scheme design is proposed based on the minimum mean?squared error(MMSE)rule in the presence of the feedback delay and channel estimation error. The proposed precoding algorithm decomposes the constrained optimization problem into three sub?convex optimization problems that are solved separately. The transmitter equipped with single antenna is subject to independent distribution,and it can be assumed that the precoding matrix is a diagonal matrix. The convex optimization problem of relay matrix is transformed into semi?definite programming problem(SDP),which can be solved by CVX toolbox. The equalizer matrix can be introduced by the gradient?based line search algorithms. Then the optimal solution is obtained by using joint iteration. The simulation results show that the proposed scheme can achieve better system performance.
引文
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[13]Au E K S,Jin S,Mckay M R,et al.Analytical performance of MIMO?SVD systems in ricean fading channels with channel estimation error and feedback delay[J].IEEE Transactions on Wireless Communications,2008,7(4):1315?1325.
[14]Chu T M C,Duong T Q,Zepernick H.Outage probability and ergodic capacity for MIMO?MRT systems under co?channel interference and imperfect CSI[C]//Communication Technologies Workshop(Swe?CTW).[S.l.]:IEEE,2011:46?51.
[15]Chu T M C,Duong T Q,Zepernick H J.Performance analysis for multiple?input multiple?output?maximum ratio transmission systems with channel estimation error,feedback delay and co?channel interference[J].IET Communications,2013,7(4):279?285.
[16]Zhao C,Champagne B.A unified approach to optimal transceiver design for non?regenerative MIMO relaying[J].IEEETransactions on Vehicular Technology,2015,64(7):2938?2951.
[17]Xu W,Dong X,Lu W S.Joint precoding optimization for multiuser multi?antenna relaying downlinks using quadratic programming[J].IEEE Transactions on Communications,2011,59(5):1228?1235.
[18]Grant M,Boyd S P.CVX:MATLAB software for disciplined convex programming[EB/OL].(2015?13?01)[2017?04?13].http://cvxr.com/cvx.
[19]Song C,Ling C.On the diversity of linear transceivers in MIMO AF relaying systems[J].IEEE Transactions on Information Theory,2016,62(1):272?289.
[2]Zhang R,Chai C C,Liang Y C.Joint beamforming and power control for multi?antenna relay broadcast channel with QoSconstraints[J].IEEE Transactions on Signal Processing,2009,57(2):726?737.
[3]Xu W,Dong X,Lu W S.Joint precoding optimization for multiuser multi?antenna relaying downlinks using quadratic programming[J].IEEE Transactions on Communications,2011,59(5):1228?1235.
[4]He Z,Guo S,Ou Y,et al.Multiuser multi?hop MIMO relay system design based on mutual information maximization[J].IEEE Transactions on Signal Processing,2014,62(21):5725?5733.
[5]Khandaker M R A,Rong Y.Precoding design for MIMO relay multicasting[J].IEEE Transactions on Wireless Communications,2013,12(7):3544?3555.
[6]Li J,Zhang J,Zhang Y,et al.A comparison of TDMA,dirty paper coding,and beamforming for multiuser MIMO relay networks[J].Journal of Communications&Networks,2008,10(2):186?193.
[7]Gopal L,Rong Y,Zang Zhuquan.Simplified robust design for nonregenerativemm multicasting MIMO relay systems[C]//International Conference on Telecommunications(ICT).[S.l.]:[s.n.],2015:289?293.
[8]Shu F,Tong J,You X,et al.Adaptive robust max?SLNR precoder for MU?MIMO?OFDM systems with imperfect CSI[J].Science China,2016,59(6):1?14.
[9]Wang J,Shu F,Chen R Q,et al.Adaptive robust beamformer for multi?pair two?way relay networks with imperfect channel state information[J].Frontiers of Information Technology&Electronic Engineering,2016,17(3):265?280.
[10]Liu G,Ji H,Yu F R,et al.MMSE?based transceiver design in multi?user MIMO relay systems with channel correlation and estimation errors[C]//IEEE Wireless Communications and NETWORKING Conference.[S.l.]:IEEE,2014:1182?1187.
[11]谭伟,陈小敏,朱益民,等.存在信道相关及估计误差时V?BLAST系统的功率分配算法[J].数据采集与处理,2015,30(3):571?577.Tan Wei,Chen Xiaomin,Zhu Yimin,et al.Power allocation algorithm for correlated V?BLAST system with channel estima?tion error[J].Journal of Data Acquisition and Processing,2015,30(3):571?577.
[12]Sanguinetti L,Amico A A D,Rong Y.A tutorial on the optimization of amplify?and?forward MIMO relay systems[J].IEEEJournal on Selected Areas in Communications,2012,30(8):1331?1346.
[13]Au E K S,Jin S,Mckay M R,et al.Analytical performance of MIMO?SVD systems in ricean fading channels with channel estimation error and feedback delay[J].IEEE Transactions on Wireless Communications,2008,7(4):1315?1325.
[14]Chu T M C,Duong T Q,Zepernick H.Outage probability and ergodic capacity for MIMO?MRT systems under co?channel interference and imperfect CSI[C]//Communication Technologies Workshop(Swe?CTW).[S.l.]:IEEE,2011:46?51.
[15]Chu T M C,Duong T Q,Zepernick H J.Performance analysis for multiple?input multiple?output?maximum ratio transmission systems with channel estimation error,feedback delay and co?channel interference[J].IET Communications,2013,7(4):279?285.
[16]Zhao C,Champagne B.A unified approach to optimal transceiver design for non?regenerative MIMO relaying[J].IEEETransactions on Vehicular Technology,2015,64(7):2938?2951.
[17]Xu W,Dong X,Lu W S.Joint precoding optimization for multiuser multi?antenna relaying downlinks using quadratic programming[J].IEEE Transactions on Communications,2011,59(5):1228?1235.
[18]Grant M,Boyd S P.CVX:MATLAB software for disciplined convex programming[EB/OL].(2015?13?01)[2017?04?13].http://cvxr.com/cvx.
[19]Song C,Ling C.On the diversity of linear transceivers in MIMO AF relaying systems[J].IEEE Transactions on Information Theory,2016,62(1):272?289.
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