多输入多输出单载波频分多址系统的鲁棒波束赋形算法

A Robust Beamforming Algorithm for Multiple Access Systems with Multiple-Input Multiple-Output and Single-Carrier Frequency Division

针对多输入多输出(MIMO)单载波频分多址(SC-FDMA)系统中现有波束赋形算法在非理想信道状态信息下性能下降以及对信道信息误差敏感的问题,提出了一种鲁棒波束赋形算法。该算法利用谱范数对信道状态信息误差进行建模,并基于均方误差和准则将波束赋形优化问题建模为一个极小极大化问题,然后利用优超理论以及奇异值不等式理论证明该优化问题的鞍点特性并得出最优的波束赋形结构,最后利用凸优化得到最优的功率分配算法。仿真结果表明:与非鲁棒波束赋形和等功率分配算法相比,该鲁棒波束赋形算法在误码率以及频谱效率方面都能获得更好的性能,信道状态信息误差增大时,该鲁棒波束赋形算法与非鲁棒波束赋形算法相比在高信噪比时误码率性能约有1dB增益,频谱效率约提升6%。

A robust beamforming algorithm for multiple access systems with multiple-input multiple-output （MIMO） and single carrier frequency division （SC-FDMA） is proposed to solve the problems of performance degradation and sensitivity to channel state information （CSI） errors of conventional beamforming algorithms under scenarios of imperfect CSI.The algorithm establishes a model for the imperfect CSI by using a spectral norm,and the beamforming optimization is formulated as a min-max problem based on the criterion of sum of mean-squared errors.Then,the saddle point property of the min-max problem is established and the optimal beamforming structure is obtained by using majorization theory and singular value inequalities.An optimal power allocation algorithm is derived by employing convex optimization.Simulation results and comparisons with the non-robust beamforming and equal power allocation algorithms show that the proposed algorithm has better performance in bit error rate （BER） and spectral efficiency.When the CSI errors increase,a comparison with the non-robust beamforming algorithm in the high SNR regime show that the proposed algorithm obtains 1 dB gain in bit error rate,and the spectral efficiency improves by about 6 %.