MIMO雷达稳健的自适应波束形成方法研究
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摘要
近年来，MIMO雷达作为一种新技术受到了越来越多的关注，而稳健的波束形成算法是研究的热点与难点。本文主要从稳健的波束形成和稳健的方向图综合两方面，对单基和双基MIMO雷达进行了研究，主要工作包括以下几个方面：
1.针对单基MIMO雷达稳健的波束形成问题进行研究。首先给出了MIMO雷达的信号模型和两种信号处理结构，然后总结了已有的MIMO雷达稳健波束形成算法，指出先采用稳健的接收波束形成，再对发射导向矢量存在的误差进行稳健处理运算量更小，更能满足实际需求。最后针对发射阵存在的未知误差，提出了MIMO雷达稳健的发射波束形成算法和稳健的失配滤波器设计算法。
2.针对MIMO雷达方向图综合问题，提出了双边自适应矩阵(Two SidedAdaptive Matrix Approach, TS-AMA)算法。通过对雷达回波进行双边矩阵加权，将AMA算法的优化问题转化为关于两个低维权矩阵的双二次优化问题，从而可以利用双迭代算法求解。相比AMA算法，TS-AMA算法的运算量大大降低。
3.针对双基MIMO雷达在导向矢量存在误差情况下的波离角和波达角估计问题，提出了稳健的Capon波束形成算法。该算法利用发射-接收联合导向矢量的Kronecker结构，将稳健的Capon波束形成算法的代价函数转化为一个关于发射导向矢量和接收导向矢量的双二次代价函数。新的优化问题可以通过迭代算法和拉格朗日乘子法有效求解。由于在每一步迭代中，所提算法的参数更小，因此所提算法的稳健性更好，功率估计更准确。当阵列准确校正后，所提算法还能从得到的导向矢量中分别估计出感兴趣目标的波离角和波达角。
4.针对自适应阵列在存在未知误差情况下的密集干扰抑制问题，提出了一种稳健的赋形方向图综合算法。根据一定的先验信息，该算法约束密集干扰所在的特定角域增益较低，在保证稳健角域的响应不衰减的同时，最小化阵列在最差情况下的输出功率。所提算法可表述为一个半正定规划问题，因此可以利用凸优化工具包有效求解。相比已有算法，所提算法的稳健性更好、输出信干噪比更高、功率估计更准确。
Multiple-input multiple-output (MIMO) radar is an emerging technology that hasdrawn considerable attention recently. Robust adaptive beamforming is a key issue inMIMO radar. In this thesis, robust adaptive beamforming and robust beampatternsynthesis are studied for monotatic and bistatic MIMO radar. The main contributions ofthis thesis are summarized as follows:
1. Robust adaptive beamforming for monostatic MIMO radar is studied. Firstly,the signal model of MIMO radar and two signal processing constructions are given.Then almost all the available methods of robust adaptive beamforming for MIMO radarare shown. We point out the process that robust beamforming for transmitting arraydistortions is cascaded with robust receiving adaptive beamformer, is more fulfiled therequirement of practical systems due to the smaller computational complexity. Toprovide enough robustness to transmitting array distortions, a robust transmittingadaptive beamformer and a robust mismatched filter are proposed.
2. A two-side adaptive matrix approach (AMA) is proposed for beampatternsynthesis for MIMO radar. By two-side matrix weighting, the optimization problem ofAMA is converted to a double quadratic problem with two smaller dimension matrixweight. Comparing with AMA, TS-AMA has smaller computational complexity.
3. To estimate the DOD and DOA of bistatic MIMO radar when the transmittingand receiving arrays are not perfectly calibrated, a robust Capon beamformer (RCB) isproposed. Using the Kronecker structure of the transmitting-receiving steering vector,the proposed algorithm converts the cost function of RCB to a double quadratic onewith respect to the transmitting and receiving steering vectors. The new optimizationproblem can be efficiently solved by combining bi-iterative algorithm with Lagrangemultiplier methodology. Due to a smaller coefficient can be found in each step of theiterative procedure, the proposed algorithm is more robust and can estimate the powerof the desired target more accurately. When the arrays are perfectly calibrated, the DODand DOA can be estimated from the obtained transmitting and receiving steering vectors,respectively.
4. To suppress the concentrated jammers in the presence of unknown mismatchesof the adaptive arrays, a robust beampattern synthesis algorithm with low response in aspecified region is proposed. The proposed algorithm minimizes the worst-case output power while maintaining the response of the robust region distortionless and lowresponse in a specified region, where the concentrated jammers may impinge into thearrays according to some prior information. The proposed algorithm has the form of asemi-definite programming and hence can be efficiently solved by convex optimizationtoolbox. Compared with the available beampattern synthesis algorithms, the proposedalgorithm has better robustness, higher output signal to interference plus noise ratio andmore accurate power estimation.
1.针对单基MIMO雷达稳健的波束形成问题进行研究。首先给出了MIMO雷达的信号模型和两种信号处理结构，然后总结了已有的MIMO雷达稳健波束形成算法，指出先采用稳健的接收波束形成，再对发射导向矢量存在的误差进行稳健处理运算量更小，更能满足实际需求。最后针对发射阵存在的未知误差，提出了MIMO雷达稳健的发射波束形成算法和稳健的失配滤波器设计算法。
2.针对MIMO雷达方向图综合问题，提出了双边自适应矩阵(Two SidedAdaptive Matrix Approach, TS-AMA)算法。通过对雷达回波进行双边矩阵加权，将AMA算法的优化问题转化为关于两个低维权矩阵的双二次优化问题，从而可以利用双迭代算法求解。相比AMA算法，TS-AMA算法的运算量大大降低。
3.针对双基MIMO雷达在导向矢量存在误差情况下的波离角和波达角估计问题，提出了稳健的Capon波束形成算法。该算法利用发射-接收联合导向矢量的Kronecker结构，将稳健的Capon波束形成算法的代价函数转化为一个关于发射导向矢量和接收导向矢量的双二次代价函数。新的优化问题可以通过迭代算法和拉格朗日乘子法有效求解。由于在每一步迭代中，所提算法的参数更小，因此所提算法的稳健性更好，功率估计更准确。当阵列准确校正后，所提算法还能从得到的导向矢量中分别估计出感兴趣目标的波离角和波达角。
4.针对自适应阵列在存在未知误差情况下的密集干扰抑制问题，提出了一种稳健的赋形方向图综合算法。根据一定的先验信息，该算法约束密集干扰所在的特定角域增益较低，在保证稳健角域的响应不衰减的同时，最小化阵列在最差情况下的输出功率。所提算法可表述为一个半正定规划问题，因此可以利用凸优化工具包有效求解。相比已有算法，所提算法的稳健性更好、输出信干噪比更高、功率估计更准确。
Multiple-input multiple-output (MIMO) radar is an emerging technology that hasdrawn considerable attention recently. Robust adaptive beamforming is a key issue inMIMO radar. In this thesis, robust adaptive beamforming and robust beampatternsynthesis are studied for monotatic and bistatic MIMO radar. The main contributions ofthis thesis are summarized as follows:
1. Robust adaptive beamforming for monostatic MIMO radar is studied. Firstly,the signal model of MIMO radar and two signal processing constructions are given.Then almost all the available methods of robust adaptive beamforming for MIMO radarare shown. We point out the process that robust beamforming for transmitting arraydistortions is cascaded with robust receiving adaptive beamformer, is more fulfiled therequirement of practical systems due to the smaller computational complexity. Toprovide enough robustness to transmitting array distortions, a robust transmittingadaptive beamformer and a robust mismatched filter are proposed.
2. A two-side adaptive matrix approach (AMA) is proposed for beampatternsynthesis for MIMO radar. By two-side matrix weighting, the optimization problem ofAMA is converted to a double quadratic problem with two smaller dimension matrixweight. Comparing with AMA, TS-AMA has smaller computational complexity.
3. To estimate the DOD and DOA of bistatic MIMO radar when the transmittingand receiving arrays are not perfectly calibrated, a robust Capon beamformer (RCB) isproposed. Using the Kronecker structure of the transmitting-receiving steering vector,the proposed algorithm converts the cost function of RCB to a double quadratic onewith respect to the transmitting and receiving steering vectors. The new optimizationproblem can be efficiently solved by combining bi-iterative algorithm with Lagrangemultiplier methodology. Due to a smaller coefficient can be found in each step of theiterative procedure, the proposed algorithm is more robust and can estimate the powerof the desired target more accurately. When the arrays are perfectly calibrated, the DODand DOA can be estimated from the obtained transmitting and receiving steering vectors,respectively.
4. To suppress the concentrated jammers in the presence of unknown mismatchesof the adaptive arrays, a robust beampattern synthesis algorithm with low response in aspecified region is proposed. The proposed algorithm minimizes the worst-case output power while maintaining the response of the robust region distortionless and lowresponse in a specified region, where the concentrated jammers may impinge into thearrays according to some prior information. The proposed algorithm has the form of asemi-definite programming and hence can be efficiently solved by convex optimizationtoolbox. Compared with the available beampattern synthesis algorithms, the proposedalgorithm has better robustness, higher output signal to interference plus noise ratio andmore accurate power estimation.
引文
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