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arXiv 1606.06408cs.ITmath.IT
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大规模MU-MIMO系统中高斯消息传递迭代检测器的收敛性分析与保证

Convergence Analysis and Assurance for Gaussian Message Passing Iterative Detector in Massive MU-MIMO Systems

Lei Liu, Chau Yuen, Yong Liang Guan, Ying Li, Yuping Su

摘要:

针对大规模多用户多输入多输出(MU-MIMO)系统,研究了一种低复杂度的高斯消息传递迭代检测(GMPID)算法,其中基站采用$M$天线同时服务于$K$高斯信源。$K$和$M$都是非常大的数,我们考虑的情况下,$K<M$。GMPID是一种基于全连通循环图的低复杂度消息传递算法,众所周知,该算法在某些情况下是不收敛的。由于GMPID难以直接分析,因此利用大规模MU-MIMO的大规模特性来简化分析。首先,我们证明了GMPID的方差绝对收敛于最小均方误差(MMSE)检测的均方误差。其次,我们提出了两个充分条件的GMPID的平均值收敛到MMSE检测。然而,当$ K/M\geq (\sqrt{2}-1)^2$。因此,提出了一种新的收敛型GMPID(SA-GMPID),它对任意$K<M$均收敛于MMSE检测,且收敛速度快于GMPID,但复杂度不高于GMPID。最后通过数值计算验证了理论结果的正确性和有效性。

英文摘要:

This paper considers a low-complexity Gaussian Message Passing Iterative Detection (GMPID) algorithm for massive Multiuser Multiple-Input Multiple-Output (MU-MIMO) system, in which a base station with $M$ antennas serves $K$ Gaussian sources simultaneously. Both $K$ and $M$ are very large numbers, and we consider the cases that $K<M$. The GMPID is a low-complexity message passing algorithm based on a fully connected loopy graph, which is well understood to be not convergent in some cases. As it is hard to analyse the GMPID directly, the large-scale property of the massive MU-MIMO is used to simplify the analysis. Firstly, we prove that the variances of the GMPID definitely converge to the mean square error of Minimum Mean Square Error (MMSE) detection. Secondly, we propose two sufficient conditions that the means of the GMPID converge to those of the MMSE detection. However, the means of GMPID may not converge when $ K/M\geq (\sqrt{2}-1)^2$. Therefore, a new convergent GMPID called SA-GMPID (scale-and-add GMPID) , which converges to the MMSE detection in mean and variance for any $K<M$ and has a faster convergence speed than the GMPID, but has no higher complexity than the GMPID, is proposed. Finally, numerical results are provided to verify the validity and accuracy of the theoretical results.

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