基于凸优化理论的自适应波束形成技术
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摘要
阵列信号处理作为信号处理领域的一个重要分支,其应用涉及雷达、声纳、通信以及医疗诊断多个领域。通过对信号在时间和空间上的采样和处理,能够更加充分地发掘信号中蕴含的信息,有效地抑制干扰,提高系统的效率。虽然自适应阵列信号处理在理想的情况下可以达到良好的性能,但是实际系统存在的误差会严重影响阵列信号处理最后的输出性能。所以,寻求稳健的自适应信号处理算法一直是广大研究者追求的目标。本文通过对阵列信号处理中现有算法的研究,提出和改进了一些现有的算法,使之更具有稳健性,适应更加复杂和恶劣的环境。本文所做的主要工作概述如下:
1.针对传统波束形成算法对指向误差敏感的缺点,提出了一种基于概率约束的有效设计方法,它在假定随机的方向矢量符合高斯分布的前提下,保证其指向约束以一定的概率大于单位响应,并将概率约束的优化问题通过凸近似的方法转变成一个迭代的二阶锥优化问题,从而可以利用内点法求解。此外,迭代过程的收敛性也在文中进行了分析和证明。与现有的算法相比,文中提出的算法具有较低的复杂度,更易于实现,且算法的性能较好,因而具有较高的实用价值。
2.通信中的大部分信号具有循环平稳特性,利用信号的循环平稳特性已经在阵列信号处理中形成了很多算法。它们无需事先已知信号的指向,因此属于盲波束形成算法。本文分析了当系统存在循环频率误差时基于梯度下降的循环平稳算法,由于存在sinc的零点效应,算法的性能随着快拍数的增加而出现周期性的恶化。基于上述现象,文中提出了一种利用共轭梯度求解的稳健算法,它利用共轭梯度算法快速收敛的特点,首先寻求一个粗略的解,并求出大致的方向矢量作为信号的指向,进而利用传统的波束形成算法求解,避免了循环频率误差对其的影响,仿真实验证明了算法具有较好的性能。
3.近期,基于多输入多输出系统的线性接收技术也得到了较多的关注,其核心思想与波束形成算法类似,在提取感兴趣用户信号的同时抑制其他用户对它的干扰。然而,其算法的性能同样依赖于信道状态信息的精确程度。因此,文中提出了一种基于随机规划理论的稳健线性接收算法。在已知信道误差统计信息的情况下,利用切比雪夫不等式求解最差分布情况下的概率约束表达式,并将其转化成迭代的凸优化问题求解,同时,本文还证明了算法的收敛性。与现有的稳健接收算法相比,文中提出的算法通过允许小的溢出概率和更具一般性的不确定模型来提高算法的性能,并在文末给出了一些有意义的结论。
The array signal processing as an important branch of the signal processing domain is applied for many areas such as radar, sonar, communication and biomedical testing. It can exploit sufficiently the information of the signal by sampling the signal in time-spatial domain to suppress the interference and increase the signal to interference and noise ratio of the system. The adaptive array signal processing can obtain good performance in the ideal cases. But the errors in the system always severely affect the performance of the array signal processing. So many researchers are trying to research robust array signal processing algorithms. This paper introduces several algorithms to improve the robustness, which makes the system more robust for the complicated scenario. The main work in this paper is listed as follows:
1. A powerful adaptive beamforming algorithm in the presence of the pointing error is proposed by probabilistic constraints, aiming at the shortcoming of the sensitivity to the pointing error. It is under the assumption that the random steering vector mismatch has Gaussian distribution, we guarantee that the pointing constraint is greater than unit response with some selected probability. Then by convex approximation, the original problem is converted to an iterative second-order cone programming problem, which can be solved efficiently via well-established interior-point method. Furthermore, a mathematical convergence analysis of the iterative solution is also provided. Compared to existing approaches, our proposed method enjoys the advantages of easier implementation and lower computational complexity, and has better performance. So it is more appropriate in practice.
2. The most signals in the communication system have the cyclostationary property. Many algorithms based on the cyclostationary of the signal in the array signal processing have been exploited. They can well worked without knowing the steering vector of interested signal, thus they all belong to the blind algorithms. In the presence of cycle frequency error, a mathematical analysis of gradient decent-based algorithm is provided. It points out that due to the effect of the sinc function, the above approach have periodic zeros point as the number of snapshot increasing. Hence, a novel robust cyclostationary beamformer based on conjugate gradient algorithm, which can be used to extract signals with cy-clostationarity in the presence of cycle frequency error, is proposed. Because of its fast convergence, periodic nulls can be circumvented, and the steering vector of interested signal is estimated. Then we use traditional beamformer to avoid the influence of cycle frequency error. Simulations show that our new algorithm performs well under cycle frequency mismatches.
3. On the other hand, many researchers are also trying to research the linear receiver based on multiple-input multiple-output system. The key idea of it is similar to adaptive beamforming algorithms. Both of them are trying to extract the information of interested user, while rejecting the interference and noise component. However, the performance of linear receiver highly depends on the channel state information. Hence, based on probability-constrained optimization, a robust linear receiver with worst-case probability guarantee is proposed in this paper. Using the multivariate Chebyshev inequality, the deterministic expressions of the worst-case probabilistic constraints are derived in the presence of statistical property of channel state information. Then an iterative convex programming algorithm is developed to obtain the robust solutions, and the mathematical convergence analysis is also provided. Compared to the existing receivers, our proposed receiver improves the performance by allowing small outage probability and more general uncertainty model, and some significant conclusions are also obtained.
1.针对传统波束形成算法对指向误差敏感的缺点,提出了一种基于概率约束的有效设计方法,它在假定随机的方向矢量符合高斯分布的前提下,保证其指向约束以一定的概率大于单位响应,并将概率约束的优化问题通过凸近似的方法转变成一个迭代的二阶锥优化问题,从而可以利用内点法求解。此外,迭代过程的收敛性也在文中进行了分析和证明。与现有的算法相比,文中提出的算法具有较低的复杂度,更易于实现,且算法的性能较好,因而具有较高的实用价值。
2.通信中的大部分信号具有循环平稳特性,利用信号的循环平稳特性已经在阵列信号处理中形成了很多算法。它们无需事先已知信号的指向,因此属于盲波束形成算法。本文分析了当系统存在循环频率误差时基于梯度下降的循环平稳算法,由于存在sinc的零点效应,算法的性能随着快拍数的增加而出现周期性的恶化。基于上述现象,文中提出了一种利用共轭梯度求解的稳健算法,它利用共轭梯度算法快速收敛的特点,首先寻求一个粗略的解,并求出大致的方向矢量作为信号的指向,进而利用传统的波束形成算法求解,避免了循环频率误差对其的影响,仿真实验证明了算法具有较好的性能。
3.近期,基于多输入多输出系统的线性接收技术也得到了较多的关注,其核心思想与波束形成算法类似,在提取感兴趣用户信号的同时抑制其他用户对它的干扰。然而,其算法的性能同样依赖于信道状态信息的精确程度。因此,文中提出了一种基于随机规划理论的稳健线性接收算法。在已知信道误差统计信息的情况下,利用切比雪夫不等式求解最差分布情况下的概率约束表达式,并将其转化成迭代的凸优化问题求解,同时,本文还证明了算法的收敛性。与现有的稳健接收算法相比,文中提出的算法通过允许小的溢出概率和更具一般性的不确定模型来提高算法的性能,并在文末给出了一些有意义的结论。
The array signal processing as an important branch of the signal processing domain is applied for many areas such as radar, sonar, communication and biomedical testing. It can exploit sufficiently the information of the signal by sampling the signal in time-spatial domain to suppress the interference and increase the signal to interference and noise ratio of the system. The adaptive array signal processing can obtain good performance in the ideal cases. But the errors in the system always severely affect the performance of the array signal processing. So many researchers are trying to research robust array signal processing algorithms. This paper introduces several algorithms to improve the robustness, which makes the system more robust for the complicated scenario. The main work in this paper is listed as follows:
1. A powerful adaptive beamforming algorithm in the presence of the pointing error is proposed by probabilistic constraints, aiming at the shortcoming of the sensitivity to the pointing error. It is under the assumption that the random steering vector mismatch has Gaussian distribution, we guarantee that the pointing constraint is greater than unit response with some selected probability. Then by convex approximation, the original problem is converted to an iterative second-order cone programming problem, which can be solved efficiently via well-established interior-point method. Furthermore, a mathematical convergence analysis of the iterative solution is also provided. Compared to existing approaches, our proposed method enjoys the advantages of easier implementation and lower computational complexity, and has better performance. So it is more appropriate in practice.
2. The most signals in the communication system have the cyclostationary property. Many algorithms based on the cyclostationary of the signal in the array signal processing have been exploited. They can well worked without knowing the steering vector of interested signal, thus they all belong to the blind algorithms. In the presence of cycle frequency error, a mathematical analysis of gradient decent-based algorithm is provided. It points out that due to the effect of the sinc function, the above approach have periodic zeros point as the number of snapshot increasing. Hence, a novel robust cyclostationary beamformer based on conjugate gradient algorithm, which can be used to extract signals with cy-clostationarity in the presence of cycle frequency error, is proposed. Because of its fast convergence, periodic nulls can be circumvented, and the steering vector of interested signal is estimated. Then we use traditional beamformer to avoid the influence of cycle frequency error. Simulations show that our new algorithm performs well under cycle frequency mismatches.
3. On the other hand, many researchers are also trying to research the linear receiver based on multiple-input multiple-output system. The key idea of it is similar to adaptive beamforming algorithms. Both of them are trying to extract the information of interested user, while rejecting the interference and noise component. However, the performance of linear receiver highly depends on the channel state information. Hence, based on probability-constrained optimization, a robust linear receiver with worst-case probability guarantee is proposed in this paper. Using the multivariate Chebyshev inequality, the deterministic expressions of the worst-case probabilistic constraints are derived in the presence of statistical property of channel state information. Then an iterative convex programming algorithm is developed to obtain the robust solutions, and the mathematical convergence analysis is also provided. Compared to the existing receivers, our proposed receiver improves the performance by allowing small outage probability and more general uncertainty model, and some significant conclusions are also obtained.
引文
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