大规模MIMO系统中基于Lanczos方法的低复杂度预编码
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摘要
针对大规模MIMO系统中因基站天线数与用户数过大导致迫零(ZF)预编码矩阵求逆复杂度较高的问题,提出一种基于迭代子空间投影算法的Lanczos方法低复杂度预编码方案。根据大规模MIMO系统信道矩阵具有对角占优特性,将信道大矩阵求逆诺依曼级数的第1项作为迭代的初始值,从而加快算法的收敛速度,使得ZF预编码的复杂度从O(K~3)降低到O(K~2)。仿真结果表明,该算法以较快的收敛速度逼近传统ZF预编码方案的信道容量与误码率性能。
Aiming at the problem that the computational complexity of the required matrix inversion of Zero Forcing(ZF)precoding matrix is very high due to the large number of antennas and users in large-scale MIMO systems,a low complexity ZF precoding scheme based on Lanczos Method( LM) is proposed. In the proposed iterative algorithm,according to the channel matrix of massive MIMO systems which has diagonally dominant characteristics,the first term of the Neumann series of the inverse of the channel large matrix is taken as the initial value of the iteration,that speeds up the convergence rate of the algorithm,and the complexity of ZF precoding can be reduced from O( K~3) to O( K~2).Simulation results show that the algorithm approaches the channel capacity and Bit Error Rate(BER) of traditional ZF precoding scheme with fast convergence speed.
Aiming at the problem that the computational complexity of the required matrix inversion of Zero Forcing(ZF)precoding matrix is very high due to the large number of antennas and users in large-scale MIMO systems,a low complexity ZF precoding scheme based on Lanczos Method( LM) is proposed. In the proposed iterative algorithm,according to the channel matrix of massive MIMO systems which has diagonally dominant characteristics,the first term of the Neumann series of the inverse of the channel large matrix is taken as the initial value of the iteration,that speeds up the convergence rate of the algorithm,and the complexity of ZF precoding can be reduced from O( K~3) to O( K~2).Simulation results show that the algorithm approaches the channel capacity and Bit Error Rate(BER) of traditional ZF precoding scheme with fast convergence speed.
引文
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[15]NGO H Q,LARSSON E.No downlink pilots are needed in TDD massive MIMO[J].IEEE Transactions on Wireless Communications,2017(16):2921-1935.
[16]MAWATWAL K,SEN D,ROY R.A semi-blind channel estimation algorithm for massive MIMOsystems[J].IEEE Wireless Communications Letters,2017,6(1):70-73.
[17]TULINO A M.Random matrix theory and wireless communications[M].[S.1.]:Now Publishers Inc.,2004.
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[19]QIN X,YAN Z,HE G.A Near-optimal detection scheme based on joint steepest descent and jacobi method for uplink massive MIMO systems[J].IEEE Communications Letters,2016,20(2):276-279.
[2]PATCHARAMANEEPAKORN P,WU S,WANG C X,et al.Spectral,energy,and economic efficiency of 5Gmulticell massive MIMO systems with generalized spatial modulation[J].IEEE Transactions on Vehicular Technology,2016,65(12):9715-9731.
[3]RUSEK F,PERSSON D,LAU B K,et al.Scaling up MIMO:opportunities and challenges with very large arrays[J].IEEE Signal Processing Magazine,2012,30(1):40-60.
[4]BOGALE T E,LE L B.Massive MIMO and mmWave for 5G wireless HetNet:potential benefits and challenges[J].IEEE Vehicular Technology Magazine,2016,11(1):64-75.
[5]COSTA M H M.Writing on dirty paper[J].IEEETransactions on Information Theory,1983,29(3):439-441.
[6]LU Z,NING J,ZHANG Y,et al.Richardson method based linear precoding with low complexity for massive MIMOsystems[C]//Proceedings of Vehicular Technology Conference.Glasgow,UK:[s.n.],2015:1-4.
[7]SONG W,CHEN X,WANG L,et al.Joint conjugate gradient and Jacobi iteration based low complexity precoding for massive MIMO systems[C]//Proceedings of International Conference on Communications in China.Chengdu,China:[s.n.],2016:1-5.
[8]XIE T,LU Z,HAN Q,et al.Low-complexity LSQR-based linear precoding for massive MIMO systems[C]//Proceedings of Vehicular Technology Conference.Boston,USA:[s.n.],2015:1-5.
[9]REN Y,XU G X,WANG Y M,et al.Low-complexity ZF precoding method for downlink of massive MIMOsystem[J].Electronics Letters,2015,51(5):421-423.
[10]XIE T,HAN Q,XU H,et al.A Low-complexity linear precoding scheme based on SOR method for massive MIMO systems[C]//Proceedings of Vehicular Technology Conference.Glasgow,UK:[s.n.],2016:11-25.
[11]龙恳,卿瑞强,涂斯宇,等.一种基于SSOR的大规模MIMO线性预编码方案[J].无线互联科技,2016(3):123-124.
[12]ZHANG H,PENG G,LIU L.Low complexity signal detector based on Lanczos method for large-scale MIMOsystems[C]//Proceedings of International Conference on Electronics Information and Emergency Communication.Beijing,China:[s.n.],2016:6-9.
[13]KOMZSIK L.Lanczos方法演变与应用[M].张伟,廖本善,译.北京:清华大学出版社,2011.
[14]ROSARIO F,MONTEIRO F A,RODRIGUES A.Fast matrix inversion updates for massive MIMO detection and precoding[J].IEEE Signal Processing Letters,2015,23(1):75-79.
[15]NGO H Q,LARSSON E.No downlink pilots are needed in TDD massive MIMO[J].IEEE Transactions on Wireless Communications,2017(16):2921-1935.
[16]MAWATWAL K,SEN D,ROY R.A semi-blind channel estimation algorithm for massive MIMOsystems[J].IEEE Wireless Communications Letters,2017,6(1):70-73.
[17]TULINO A M.Random matrix theory and wireless communications[M].[S.1.]:Now Publishers Inc.,2004.
[18]冉瑞生,黄廷祝,刘兴平,等.三对角矩阵求逆的算法[J].应用数学和力学,2009,30(2):238-244.
[19]QIN X,YAN Z,HE G.A Near-optimal detection scheme based on joint steepest descent and jacobi method for uplink massive MIMO systems[J].IEEE Communications Letters,2016,20(2):276-279.