Massive MIMO中矩阵SVD分解算法研究

发布时间：2018-04-02 21:47

  本文选题：Massive　切入点：MIMO　出处：《电子科技大学》2016年硕士论文

【摘要】：随着无线通信技术的不断发展,传统的MIMO技术已经无法满足日益增加的数据需求。Massive MIMO作为5G标准的备选方案之一,通过增加发射和接收天线数目,可以极大的提高信道容量,并且可以相对方便的从现有的MIMO系统下进行平滑过渡。同时,大规模的天线阵列增加了信道的维度,对于信道矩阵相关的算法,比如预编码、信道检测和信道估计等,实现复杂度上也会迅速上升。SVD作为矩阵分解的重要手段,在这些算法上均有着广泛的应用,如何在大规模矩阵下实现低复杂度的SVD算法,成为亟待解决的问题。本文首先介绍了Massive MIMO的特点和存在的一些技术挑战,以及SVD在MIMO下的应用。接着对常见的SVD分解算法做了介绍,对于Golub-Kahan算法,主要研究了块对角化和QR迭代过程。对于Jacobi旋转算法,分析了实数域双边Jacobi变换和对应的脉动执行过程。对于Hestenes-Jacobi算法,主要介绍了两种重要的数据计算顺序。这些算法都求解了矩阵的完整SVD,在大规模矩阵中拥有较高复杂度。在MIMO预编码系统中只需要较大奇异值对应的奇异向量。本文提出了一种基于Hestenes-Jacobi的局部SVD分解方法。该算法收敛后只得到矩阵的部分奇异值和对应的奇异向量,不需要求解整个SVD,在一定程度上减少了运算量,但是同时会影响收敛性能。通过结合局部SVD和完整SVD的各自优点,本文对该算法作了进一步改进,使得收敛性能得到了极大的改善。另外,本文研究了一种基于格拉斯曼流形的梯度跟踪算法,并且对其性能做了仿真验证。该算法将最优化问题引入到流形中,同时利用了常见场景中时变信道缓慢连续变化的特点,实现了奇异向量实时跟踪信道变化,降低了SVD复杂度。最后对于提出的局部SVD分解方法,本文设计了VLSI硬件架构和FPGA实现,同时通过比特量化分析,提高了资源利用率。本文设计的架构主要包括控制器、数据缓冲区、数据总线、存储器、处理器和连接器,利用CORDIC核进行角度计算和向量旋转。该架构可以满足任意m×n(max(m,n)≤32)矩阵、所需奇异值个数为2的的局部SVD分解,并且具有优秀的扩展性,可以很容易地增加矩阵维度以及奇异值个数。
[Abstract]:With the continuous development of wireless communication technology, the traditional MIMO technology can no longer meet the increasing data demand. Massive MIMO as one of the 5G standard options, by increasing the number of transmitting and receiving antennas, can greatly improve the channel capacity.And it is relatively convenient to smooth the transition from the existing MIMO system.At the same time, the large-scale antenna array increases the channel dimension. For the algorithms related to channel matrix, such as precoding, channel detection and channel estimation, the implementation complexity of SVD will rise rapidly as an important means of matrix decomposition.It is widely used in these algorithms. How to implement the low complexity SVD algorithm under the large-scale matrix has become an urgent problem to be solved.This paper first introduces the characteristics and some technical challenges of Massive MIMO, and the application of SVD in MIMO.Then the common SVD decomposition algorithm is introduced. For the Golub-Kahan algorithm, block diagonalization and QR iteration are mainly studied.For the Jacobi rotation algorithm, the two-sided Jacobi transform in real number domain and the corresponding pulsation execution process are analyzed.For Hestenes-Jacobi algorithm, two kinds of important data order are introduced.These algorithms solve the complete SVD of the matrix, and have high complexity in the large-scale matrix.In MIMO precoding systems, only singular vectors corresponding to large singular values are required.In this paper, a local SVD decomposition method based on Hestenes-Jacobi is proposed.After the algorithm converges, only the partial singular values of the matrix and the corresponding singular vectors are obtained. It does not need to solve the entire SVD, which reduces the computational complexity to a certain extent, but it will affect the convergence performance at the same time.By combining the respective advantages of local SVD and complete SVD, the algorithm is further improved in this paper, and the convergence performance is greatly improved.In addition, a gradient tracking algorithm based on Glassmann manifold is studied, and its performance is verified by simulation.The algorithm introduces the optimization problem into the manifold, and makes use of the slow and continuous variation of time-varying channels in common scenarios. It realizes the real-time tracking of channel changes by singular vectors and reduces the complexity of SVD.Finally, for the proposed local SVD decomposition method, this paper designs the VLSI hardware architecture and FPGA implementation, and improves the resource utilization rate by bit quantization analysis.The architecture of this paper mainly includes controller, data buffer, data bus, memory, processor and connector. Angle calculation and vector rotation are carried out by using CORDIC core.This scheme can satisfy the local SVD decomposition of arbitrary m 脳 nn maxm n) 鈮，

本文编号：1702238