矩阵大规模运算硬件结构及其在移动通信测向和MIMO接收中的应用

发布时间：2018-03-14 13:39

本文选题：矩阵　切入点：并行运算　出处：《电子科技大学》2014年硕士论文　论文类型：学位论文

【摘要】：矩阵运算是科学和工程中的基本数值计算,在通信系统中很多场合都需要这样的计算,如MIMO接收机,阵列信号处理等。工程应用中大都有实时性的要求,然而矩阵运算具有计算量大,实现起来复杂的特点,单一的处理器难以满足这样的要求。针对这一情况,有必要采取并行计算来加快矩阵运算速度。并行运算最重要的地方就在于并行结构的设计,任务的分配,数据与处理单元的映射,各处理单元的互联,使各处理单元能够并行、高效、协调地运作,从而高速地完成整个运算。本文将结合通信系统的实际需要,介绍常用的矩阵运算的并行结构,本文将介绍以下几个方面的内容:1.矩阵基本运算的并行结构,包括矩阵加、减法、Hardmard乘积以及矩阵向量乘法,然后重点介绍矩阵乘法的几种阵列结构2.矩阵求逆的问题,该运算是MIMO接收算法中重要组成部份。首先介绍了常用的矩阵求逆的方法,然后结合并行结构重点介绍采用三角分解的方法,主要介绍LU分解和QR分解的方法与实现结构,最后阐述了上三角矩阵的求逆及其实现结构。该部份采用硬件描述语言实现了采用阵列结构QR分解与上三角矩阵的求逆并给出了实际的仿真结果。3.矩阵的奇异值分解,该计算可以用来对MIMO信道作并行分解。该部份首先绍了单边Jacobi算法和它的一维阵列结构。然后详细介绍双边Jacobi算法,包括它的算法原理、阵列结构的设计、数据在各处理单元间的流动、各处理单元的具体流程。最后给出4阶方阵的具体实现结果和基本性能分析。4.矩阵的并行运算及结构在空间测向MUSIC算法中的具体应用。该部份内容从基本的天线阵元开始,逐一介绍阵列信号的数学模型及统计特性。接着介绍测向算法中最重要的算法之一,即MUSIC算法,并给出了相关的性能分析与仿真。由于该算法是在复数域内进行,将会增加硬件的复杂度,接着便介绍了如何通过变换在实数域内实现MUSIC算法。最后介绍如何运用矩阵的并行运算结构进行MUSIC算法各部份的计算,同时又给出了又一重要的矩阵分解运算的算法原理和实现结构,即特征值分解。此外,还提出了改进的谱函数的计算方法,该方法只需一个乘法周期即可完成一个搜索点的计算。
[Abstract]:Matrix operation is the basic numerical calculation in science and engineering, which is needed in many communication systems, such as MIMO receiver, array signal processing and so on. However, the matrix operation has the characteristics of large amount of computation and complex implementation, so it is difficult for a single processor to meet such a requirement. It is necessary to adopt parallel computing to speed up matrix operation. The most important aspects of parallel computing are the design of parallel structure, the assignment of tasks, the mapping of data and processing units, the interconnection of processing units, so that each processing unit can be parallelized. This paper will introduce the parallel structure of common matrix operation in combination with the actual needs of the communication system. This paper will introduce the following aspects: 1. Parallel structure of basic matrix operations, including matrix addition, subtraction, Hardmard product and matrix vector multiplication. This operation is an important part of the MIMO receiving algorithm. Firstly, the common methods of matrix inversion are introduced, then the triangular decomposition method is introduced in combination with the parallel structure, and the LU decomposition and QR decomposition method and the implementation structure are mainly introduced. Finally, the inverse of the upper triangular matrix and its implementation structure are described. In this part, the QR decomposition of the array structure and the inverse of the upper triangular matrix are realized by using the hardware description language, and the simulation results .3. the singular value decomposition of the matrix are given. This algorithm can be used to decompose the MIMO channel in parallel. In this part, the one-sided Jacobi algorithm and its one-dimensional array structure are introduced. Then, the two-sided Jacobi algorithm is introduced in detail, including its algorithm principle, array structure design. The flow of data between processing units, The concrete flow of each processing unit. Finally, the concrete implementation results and basic performance analysis of the fourth order square matrix are given. Finally, the parallel operation of the matrix and the concrete application of the structure in the spatial direction finding MUSIC algorithm are given. The content of this part begins with the basic antenna array element. The mathematical model and statistical characteristics of array signal are introduced one by one. Then one of the most important algorithms in direction-finding algorithm, the MUSIC algorithm, is introduced, and the related performance analysis and simulation are given. It will increase the complexity of hardware, then it introduces how to realize MUSIC algorithm in real number domain by transformation. Finally, it introduces how to use the parallel computing structure of matrix to calculate the parts of MUSIC algorithm. At the same time, the principle and implementation structure of another important matrix decomposition algorithm, namely eigenvalue decomposition, are given. In addition, an improved method for calculating spectral functions is also presented. The method only needs a multiplication period to complete the calculation of a search point.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN929.5;TN919.3

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