无线通信  >> Vol. 3 No. 3 (June 2013)

单侧Jacobi矩阵求逆算法及其DSP实现
One-Side Jacobi Matrix Inversion Algorithm and DSP Realization

DOI: 10.12677/HJWC.2013.33011, PDF, HTML, 下载: 2,444  浏览: 9,598  国家科技经费支持

作者: 阳 析, 李 峥, 房 帅, 周 天, 江 彬, 郭 骎:东南大学信息科学与工程学院

关键词: 单侧Jacobi算法矩阵求逆TMS320C6474DSP/BIOS并行One-Side Jacobi Algorithm; Matrix Inversion; TMS320C6474; DSP/BIOS; Parallel Realization

摘要: 链路自适应与先进接收机是宽带无线通信系统的核心技术,其设计与实现均涉及大量的矩阵分解以及矩阵求逆运算,提高矩阵分解和矩阵求逆运算的效率是提高宽带无线通信系统传输效能的基本途径。针对此目的,本文提出一种在经典Jacobi算法上改进的单侧Jacobi算法。由于该算法具有并行的特性,相比于串行(单核)实现在指令执行周期数上可提高至少两倍的运行效率。本文首先重点介绍改进的单侧Jacobi算法和TMS320C6474 DSP的内部架构与特性,然后重点阐述结合TI的实时多任务操作系统内核(DSP/BIOS)并行实现此算法,最后在同样精度的计算结果下比较并行算法与串行算法指令执行周期数,由此验证改进的单侧Jacobi算法在并行实现上的高效性
Abstract: Link adaptive transmission and advanced receiver are two key technologies in broadband wireless communi- cation system. The design and realization of the system both involve a large number of matrix decomposition and inver- sion. The basic way to improve transmission efficiency of broadband wireless communication system is to enhance the efficiency of matrix decompose and inverse computations. For this purpose, this paper develops a kind of one-sided Jacobi algorithm based on classic Jacobi. Since this algorithm has the characteristic of parallelism, it can increase the efficiency at least twice in terms of the instruction execution cycle numbers. This article will first focus on the im- proved one-sided Jacobi algorithm as well as internal architecture and characteristics of DSP TMS320C6474. It then elaborates on how to implement this algorithm in parallel using TI’s real-time multi-tasking operating system kernel (DSP/BIOS). Finally, this paper will compare instruction execution cycle numbers between parallel and serial algorithm under the same accuracy, proving the high efficiency of the improved one-sided Jacobi algorithm.

文章引用: 阳析, 李峥, 房帅, 周天, 江彬, 郭骎. 单侧Jacobi矩阵求逆算法及其DSP实现[J]. 无线通信, 2013, 3(3): 71-76. http://dx.doi.org/10.12677/HJWC.2013.33011

参考文献

[1] J. Demmel, K. Veselic. Jacobi’s method is more accurate than QR. SIAM Journal on Matrix Analysis and Applications, 1992, 11: 1204-1246.
[2] A. H. Sameh. On Jacobi and Jacobi-like algorithms for a parallel computer. Mathematics of Computation, 1971, 25(115): 579- 590.
[3] R. P. Brent, F. T. Luk. The solution of singular-value and symmetric eigenvale problems on multiprocessor arrays. SIAM Journal on Scientific and Statistical Computing, 1985, 6(1): 69- 84.
[4] M. Gentleman. Least squares computations by Givens transformations without square roots. Journal of the Institute of Mathematics and its Applications, 1973, 12(3): 329-336.
[5] A. A. Anda, H. Park. Fast plane rotations with dynamic scaling. SIAM Journal on Matrix Analysis and Applications, 1994, 15(1): 162-174.
[6] J. Yan, S. Osher. A local discontinuous Galerkin method for directly solving Hamilton-Jacobi equations, Journal of Computational Physics, 2011, 230(1): 232-244.
[7] M. Baggio, J. de Boer and K. Holsheimer. Hamilton-Jacobi renormalization for Lifshitz spacetime. Journal of High Energy Physics, 2012. http://arxiv.org/abs/1107.5562