空间谱快速算法的研究与实现
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摘要
随着电磁环境的日益恶化,以及低检测概率、低截获概率等通信技术的广泛应用,往往需要在较大的带宽内同时对多个信号进行处理,才能够在大量信号中找到有用信号,因此对空间谱估计算法的时效性也提出了更高的要求。本文研究了空间谱快速算法及实现问题,通过改进算法减少计算量,并合理利用硬件平台,将快速测向算法在FPGA+DSP平台上联合实现。本文的主要内容如下:
1、研究了基于直线阵的空间谱估计快速算法。针对MUSIC等测向算法大多需要特征分解和谱峰搜索,计算量较大的问题,给出了一种基于传播算子的Root-MUSIC算法,该算法避免了经典MUSIC算法中的特征分解和谱峰搜索,大大减小了计算复杂度;针对该算法存在低信噪比时性能下降严重的缺陷,给出了一种新的快速Root-MUSIC算法,新算法由协方差矩阵直接估计出信号子空间,无需特征分解和谱峰搜索,减小了计算量,同时在低信噪比条件下也能达到较好的测向性能。上述两种算法在损失一定性能的前提下大大减少了计算量,提高了测向时效性。
2、研究了基于均匀圆阵的空间谱估计快速算法。首先介绍了基于相位模式激励的实值波束空间的MUSIC算法,该算法在阵元数目较大时能够在很大程度上降低计算量,但仍需二维谱峰搜索;在此基础上介绍一种无需二维谱峰搜索的快速测向算法:UCA-ESPRIT算法,但该算法受到阵列孔径及阵元个数的限制,针对此缺陷,本文在傅里叶域的Root-MUSIC算法基础上给出了一种二维快速测向算法,它无需谱峰搜索,计算量相比于经典MUSIC算法大大减小,同时克服了UCA-ESPRIT算法性能受阵列孔径和阵元个数限制的缺点,为了进一步减小算法中多项式求根的计算量,用一种线性搜索的方法来代替多项式求根。
3、研究了线性搜索算法的快速实现。分析了在编程实现过程中需要考虑的数据量化误差、运算误差及算法的定点编程实现流程;利用MATLAB对算法的各个部分进行定点仿真,根据定点仿真的结果,分别设计了算法各部分进行定点运算FPGA实现结构,并给出了初步的资源和性能评估。
4、在FPGA+DSP硬件平台上编程实现了线性搜索算法。首先对快速测向处理平台的各个部分进行简要介绍;其次,对算法进行了任务分配,给出了算法在硬件中的详细实现流程;针对线性搜索算法的实现步骤,进行了FPGA及DSP编程仿真和实现,包括:协方差矩阵的计算、特征分解及信源个数判断、多项式系数求解和多项式求根的编程实现。仿真结果验证了本设计的正确性。最后给出了总体资源的需求和性能评估。
With the development of communication technology of low interception and detection probability, and the electromagnetic environment becoming much worse, it is often needed to process multiple signals in a wide bandwidth at one time, which brings about stricter demand for the real-time property and validity of DOA estimation algorithms. This paper focuses on fast DOA estimation algorithms and their realization in order to reduce the computational complexity by improving these algorithms and realize these algorithms on the FPGA plus DSP platform. The main contents can be summarized as follow:
1、Fast DOA estimation algorithms in ULA are studied. A fast algorithm without eigendecomposition and spectrum peak search is proposed based on propagator method. The algorithm can reduce the computational complexity largely. But this algorithm has bad performance in the condition of low SNR. So, a new fast Root-MUSIC algorithm is presented,which can obtain the signal subspace from the covariance matrix without eigendecompsition and spectrum peak search,and has better performance in the condition of the low SNR as well. These algorithms introduced in this paper do not only reduce the computational complexity, but they also improve the efficiency largely with their performance becoming worse to a certain extent.
2、Fast DOA estimation algorithms in UCA are studied. The real beamspace-MUSIC algorithm based on the phase mode excitation can reduce the computational complexity when the number of array element is large. But it needs 2-D spectrum peak search. With an eye to this, a UCA-ESPRIT algorithm without 2-D spectrum search is introduced. However, the performance of this algorithm is limited by the aperture of the array and the number of sensors. So, a fast algorithm for 2-D direction-of-arrival (DOA) estimation is given on the basis of FD Root-MUSIC algorithm. This algorithm utilizes the method of finding the roots of multinomial instead of spectrum peak search. As a result, it has a lower computational complexity in comparison with the MUSIC algorithm and it is free of the aperture of the array and the number of sensors limitation. Meanwhile, in order to reduce the computational complexity farther the algorithm applies the linear search method instead of finding the multinomial roots.
3、Fast realization of the linear search algorithm is studied. Firstly, the problem of quantification errors and calculation errors is analyzed before the algorithm is realized on hardware platform, and the flow of fixed-point simulation is introduced. Then, based on the result of fixed-point simulation in MATLAB, the realization structure of fixed-point data in FPGA is designed. Finally, a preliminary assessment of the amount of necessary hardware resources together with the performance of this algorithm is presented.
4、Program of the linear search algorithm in FPGA plus DSP platform is studied. Firstly, every part of the process platform is introduced. Secondly, assignment allocation on this platform is fixed according to characteristics of hardware and algorithm, and the detailed realization flow chart is given. Then, the algorithm is carried out by programming and simulation in FPGA plus DSP platform, including: calculation of covariance matrix, eigendecomposition, judging the number of signals, finding the coefficients of polynomial and roots of the polynomial. And simulation results verify the design. Finally, resources utilization and performance for the spatial spectrum direction-finding algorithm are evaluated on the present platform.
1、研究了基于直线阵的空间谱估计快速算法。针对MUSIC等测向算法大多需要特征分解和谱峰搜索,计算量较大的问题,给出了一种基于传播算子的Root-MUSIC算法,该算法避免了经典MUSIC算法中的特征分解和谱峰搜索,大大减小了计算复杂度;针对该算法存在低信噪比时性能下降严重的缺陷,给出了一种新的快速Root-MUSIC算法,新算法由协方差矩阵直接估计出信号子空间,无需特征分解和谱峰搜索,减小了计算量,同时在低信噪比条件下也能达到较好的测向性能。上述两种算法在损失一定性能的前提下大大减少了计算量,提高了测向时效性。
2、研究了基于均匀圆阵的空间谱估计快速算法。首先介绍了基于相位模式激励的实值波束空间的MUSIC算法,该算法在阵元数目较大时能够在很大程度上降低计算量,但仍需二维谱峰搜索;在此基础上介绍一种无需二维谱峰搜索的快速测向算法:UCA-ESPRIT算法,但该算法受到阵列孔径及阵元个数的限制,针对此缺陷,本文在傅里叶域的Root-MUSIC算法基础上给出了一种二维快速测向算法,它无需谱峰搜索,计算量相比于经典MUSIC算法大大减小,同时克服了UCA-ESPRIT算法性能受阵列孔径和阵元个数限制的缺点,为了进一步减小算法中多项式求根的计算量,用一种线性搜索的方法来代替多项式求根。
3、研究了线性搜索算法的快速实现。分析了在编程实现过程中需要考虑的数据量化误差、运算误差及算法的定点编程实现流程;利用MATLAB对算法的各个部分进行定点仿真,根据定点仿真的结果,分别设计了算法各部分进行定点运算FPGA实现结构,并给出了初步的资源和性能评估。
4、在FPGA+DSP硬件平台上编程实现了线性搜索算法。首先对快速测向处理平台的各个部分进行简要介绍;其次,对算法进行了任务分配,给出了算法在硬件中的详细实现流程;针对线性搜索算法的实现步骤,进行了FPGA及DSP编程仿真和实现,包括:协方差矩阵的计算、特征分解及信源个数判断、多项式系数求解和多项式求根的编程实现。仿真结果验证了本设计的正确性。最后给出了总体资源的需求和性能评估。
With the development of communication technology of low interception and detection probability, and the electromagnetic environment becoming much worse, it is often needed to process multiple signals in a wide bandwidth at one time, which brings about stricter demand for the real-time property and validity of DOA estimation algorithms. This paper focuses on fast DOA estimation algorithms and their realization in order to reduce the computational complexity by improving these algorithms and realize these algorithms on the FPGA plus DSP platform. The main contents can be summarized as follow:
1、Fast DOA estimation algorithms in ULA are studied. A fast algorithm without eigendecomposition and spectrum peak search is proposed based on propagator method. The algorithm can reduce the computational complexity largely. But this algorithm has bad performance in the condition of low SNR. So, a new fast Root-MUSIC algorithm is presented,which can obtain the signal subspace from the covariance matrix without eigendecompsition and spectrum peak search,and has better performance in the condition of the low SNR as well. These algorithms introduced in this paper do not only reduce the computational complexity, but they also improve the efficiency largely with their performance becoming worse to a certain extent.
2、Fast DOA estimation algorithms in UCA are studied. The real beamspace-MUSIC algorithm based on the phase mode excitation can reduce the computational complexity when the number of array element is large. But it needs 2-D spectrum peak search. With an eye to this, a UCA-ESPRIT algorithm without 2-D spectrum search is introduced. However, the performance of this algorithm is limited by the aperture of the array and the number of sensors. So, a fast algorithm for 2-D direction-of-arrival (DOA) estimation is given on the basis of FD Root-MUSIC algorithm. This algorithm utilizes the method of finding the roots of multinomial instead of spectrum peak search. As a result, it has a lower computational complexity in comparison with the MUSIC algorithm and it is free of the aperture of the array and the number of sensors limitation. Meanwhile, in order to reduce the computational complexity farther the algorithm applies the linear search method instead of finding the multinomial roots.
3、Fast realization of the linear search algorithm is studied. Firstly, the problem of quantification errors and calculation errors is analyzed before the algorithm is realized on hardware platform, and the flow of fixed-point simulation is introduced. Then, based on the result of fixed-point simulation in MATLAB, the realization structure of fixed-point data in FPGA is designed. Finally, a preliminary assessment of the amount of necessary hardware resources together with the performance of this algorithm is presented.
4、Program of the linear search algorithm in FPGA plus DSP platform is studied. Firstly, every part of the process platform is introduced. Secondly, assignment allocation on this platform is fixed according to characteristics of hardware and algorithm, and the detailed realization flow chart is given. Then, the algorithm is carried out by programming and simulation in FPGA plus DSP platform, including: calculation of covariance matrix, eigendecomposition, judging the number of signals, finding the coefficients of polynomial and roots of the polynomial. And simulation results verify the design. Finally, resources utilization and performance for the spatial spectrum direction-finding algorithm are evaluated on the present platform.
引文
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