实对称矩阵特征值分解高速并行算法的FPGA实现

The Implementation of High-speed parallel Algorithm of Real-valued Symmetric Matrix Eigenvalue Decomposition through FPGA

针对MUSIC(Multiple Signal Classification,多重信号分类)算法中的信号子空间和噪声子空间分离的硬件实现实时性需要,对矩阵特征值分解的Jacobi算法进行了并行改进,采用脉动阵列结构在FPGA(Field Programmable Gate Array)上高速并行实现了对数据协方差矩阵的特征值分解。采用矢量模式CORDIC算法和旋转模式CORDIC算法实现脉动阵列结构的细胞单元。系统字长选用16 bit定点数,采用硬件描述语言VHDL进行描述,在Altera公司的EP2S60中实现。整个特征值分解模块消耗24 372个FPGA中基本逻辑单元(LE),系统最高工作频率145 MHz,完成一次特征值分解的最低耗时为14.82μs。通过理论分析和实验验证,该实现方法精度高、速度快,大大提高了MUSIC算法的实时性,扩大了MUSIC算法的应用范围。

To meet the application need of the separation of signal subspace and noise subspace in the MUSIC algorithm, this paper presents an improved Jacobi algorithm - - parallel Jacobi algorithm, and gives a method of achieving the modification of data covariance matrix eigenvalue decomposition based on the Systolic Array structure. The vectoring mode CORDIC algorithm and rotation mode CORDIC algorithm are adopted to realize the Systolic Array structure. Fixed - point operation of 16 bit is selected by system finite bit - length. The whole matrix eigenvalue decomposition consumes 24 372 basic logic elements in FPGA, the maximum system frequency is 145 MHz, and the lowest time consumption in achieving once matrix eigenvalue decomposition is 14.82. The theory analysis and experiment validation show that this method is of high precision, and fast in speed, which greatly improves the real time property and enlarges the application scope of MUSIC algorithm.