阵列自适应波束形成及空时自适应处理方法研究
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摘要
近年来，伴随阵列天线在现代雷达、通信、声纳等应用领域的发展，阵列规模越来越大、信号维数也越来越高，然而受工作环境、硬件设备和制造工艺等诸多因素的限制，阵列信号处理中自适应算法的计算复杂度高、训练样本需求较多及性能受非理想因素的影响等问题表现地愈加凸显。本文主要从降维和稳健处理两方面，对多输入多输出（Multiple-Input Multiple-Output, MIMO）雷达、机载预警雷达及机载MIMO雷达信号处理中的自适应波束形成(Adaptive Beamforming)和空时自适应处理（Space-TimeAdaptive Processing, STAP）方法进行了研究，主要工作包括以下几个方面：
1.针对相干MIMO雷达自适应波束形成问题，讨论并分析了相干MIMO雷达发射阵和接收阵的双边导向矢量失配模型，提出了一种双边稳健降维自适应波束形成算法。该方法结合双迭代算法（Bi-IterativeAlgorithm, BIA）和二阶凸优化（Second-Order Cone Programming, SOCP）算法，通过松弛和收发分离处理，将原本基于高维协方差矩阵的SOCP问题转化为两个基于低维协方差矩阵的SOCP问题，然后循环优化两个低维的发射权矢量和接收权矢量。与全维稳健算法相比，所提算法能有效克服收发误差耦合问题，具有较好的稳健性，并能大幅降低计算复杂度和对训练样本数的需求。
2.建立了机载雷达杂波空时二维数据的矩阵模型，在充分利用载机速度和雷达工作参数等先验信息的基础上，提出了一种机载雷达杂波非自适应空时块对消器(Space-Time Block Canceller, STBC)，并给出了关于STBC权系数的最小二乘代价函数，从而优化得到STBC的权系数。由于STBC权系数仅利用载机速度和雷达工作参数等先验信息计算得到，属于非自适应处理器，因而具有运算量小、无收敛过程等优点，并且可作为机载雷达的杂波预滤波器，从而进一步改善常规动目标显示（Moving Target Indication, MTI）处理和降维STAP算法的性能。此外，在杂波模型中考虑了偏航角的存在，因此，STBC既适用于正侧视雷达，也适用于非正侧视阵雷达。
3.利用最优STAP权矩阵的低秩特性，提出了一种基于非正交基迭代（Non-Orthogonal Basis Iterative, NOBI）的空时降维自适应算法。该方法将空时联合滤波器分离为多对空域滤波器组和时域滤波器组，采用截断和堆栈处理，建立了关于空域滤波器权向量组和时域滤波权向量组的双二次代价函数，然后基于非正交基迭代求解滤波器权矢量组，实现了对杂波的空时可分离滤波。与最优STAP相比，NOBI算法避免了高维数据协方差矩阵的估计和求逆运算，有效降低了计算量和对训练样本的需求。
4.将空时二维自适应处理（2D-STAP）扩展到空域俯仰、方位和时域三维空间，针对空时三维自适应处理（3D-STAP）提出了两种降维自适应杂波抑制算法。第一种方法是基于先时后空的处理结构，首先采用具有超低旁瓣的时域多普勒预滤波处理实现一级降维，然后将空域俯仰-方位二维波束形成转化为两个一维波束形成问题，从而进一步降低了处理器的维数，实现对杂波空时三维数据的两级降维处理；第二种算法是直接将3D-STAP转化为俯仰、方位和时域三维可分离处理，即将三维权向量近似表示为三个低维权向量的Kronecker积形式，然后基于三迭代算法，依次固定两个权矢量，并构造相应的降维矩阵在低维空间上循环优化另一个权矢量。由于上述两种算法所求权矢量的维数均大幅降低，在小样本情况下具有较好的性能，因而其随样本的收敛性能较好，并具有计算量低、样本需求小等优点。
5.构建了机载MIMO雷达杂波模型，并从功率谱和自由度分布对杂波特性进行了分析。探讨了几种经典降维STAP算法在机载MIMO雷达中的应用问题，然后，针对机载MIMO雷达回波数据所具有的发射-接收-脉冲三维结构与3D-STAP中的俯仰、方位和时域三维结构类似，我们将3D-STAP中的降维自适应算法应用到机载MIMO雷达空时自适应处理(MIMO-STAP)中，并通过仿真实验验证了它们的性能。
In recent years, with the development of array antenna in the area of radar, communication,sonar and so on, the scale of the antenna arrays and the dimension of signals become larger andlarger. However, due to the limitations of work environment, hardware, manufacturing processesand other factors, the problems including computational complexity, samples demand andperformance under the influence of non-ideal factors of adaptive array signal processing algorithmsare particularly highlighted. In this thesis, on the basis of Multiple-Input Multiple-Output（MIMO）radar, airborne radar and airborne MIMO radar, adaptive beamforming and space-time adaptiveprocessing（STAP）methods are studied from two aspects of reducing dimension and robustness.The main contributions of this thesis are summarized as follows:
1. Aiming at collocated MIMO radar, a robust adaptive beamforming method is developed forMIMO radar in the presence of unknown mismatches. Explicit models of uncertainties in bothtransmitted and received signal steering vectors are considered. Combined the bi-iterative algorithmand the second convex optimization algorithm, a robust adaptive beamforming method for MIMOradar is proposed. It is shown that the robust adaptive beamforming problem can be solved byminimizing a convex quadratic cost function based on the optimization of worst-case performancewhen full DOFs of MIMO radar are used. Whereas, we reformulate the quadratic cost function intoa bi-quadratic cost function by adopting a separable form for the weight vector and the minimumpoint of the new cost function can be efficiently found by combining bi-iterative algorithm (BIA)with second-order cone programming (SOCP). Compared with the robust adaptive beamformingalgorithms using full DoFs, the proposed beamformer has lower computational complexity andfaster convergence rate, while, at the same time, it provides better robustness in the non-ideal casesand reduces the training samples required.
2. A model with matrix form of ground clutter data is established. Then taking full advantage ofthe prior information, such as platform velocity, radar parameters and so on, we propose a space-timeblock cancelle（rSTBC）to suppress the ground clutter for airborne radar. A least-squares cost functionassociated with the filter coefficient matrix of the STBC is established. Since the coefficient matrix isonly determined by the prior information, the proposed STBC belongs to a non-adaptive processorand owns small computation load and non-convergence process. It is shown that the proposed STBCcan also be used as an efficient pre-filtering tool before the conventional moving target indication（MTI）processing and the classical reduced-dimension adaptive processing. Moreover, since theclutter model has taken into account of the drift angle, the STBC is applicable not only to the sidelooking airborne radar but also to the non-sidelooking airborne radar.
3. By utilizing the low rank property of optimal STAP weight matrix, a reduced-dimensionSTAP algorithm is introduced. It is shown that the optimum weight matrix can be naturallyexpressed as the sum of several paired spatial and temporal weight vectors. After truncated andstack processing, the weight vectors can be obtained by optimizing a bi-quadratic cost functionbased on the non-orthogonal basis iterative（NOBI）algorithm. Compared with the optimal STAPmethod, high-dimensional covariance matrix inversion is avoided in our method, and therefore, thecomputational complexity and the demand of training samples is significantly reduced.
4. Extending the spatial-temporal adaptive processing (2D-STAP) to the azimuthal, elevationaland temporal three-dimensional adaptive processing (3D-STAP), two kinds of reduced-dimensionadaptive algorithms are proposed for airborne radar to suppress ground clutter. The first methodbased on the frame of the mDT-SAP applies a Doppler pre-filter to realize the first step ofreduced-dimension. Then followed by azimuthal and elevational adaptive beamforming instead oftwo-dimensional spatial beamforming, the dimensions of the processor are further reduced. Insecond method, the optimal weight vector is approximatively denoted by the Kronecker product ofthree low-dimensional weight vectors. Then we cyclically optimize a low-dimensional weightvector by applying a reduced-dimension matrix constructed by the other two fixed weight vectors.It is shown that the proposed above two methods seek weight vectors in lower dimensional spaceand perform better in small samples, thus both of them convergence fast and own low computationload and small training data demand.
5. An airborne MIMO radar clutter model is established, and its characteristics are analyzedfrom the distribution of space-time power spectrum and freedoms. The problems of several classicalreduced-dimension STAP algorithms used in airborne MIMO radar are explored. Due to the factthat the received clutter data of airborne MIMO radar own a three-dimensional (transmitting,receiving and temporal) structure, which is similar to3D-STAP, then the3D-STAP methods forairborne array radar are introduced into the airborne MIMO radar space-time adaptive processing(MIMO-STAP), and their performance are testified via simulations results.
1.针对相干MIMO雷达自适应波束形成问题，讨论并分析了相干MIMO雷达发射阵和接收阵的双边导向矢量失配模型，提出了一种双边稳健降维自适应波束形成算法。该方法结合双迭代算法（Bi-IterativeAlgorithm, BIA）和二阶凸优化（Second-Order Cone Programming, SOCP）算法，通过松弛和收发分离处理，将原本基于高维协方差矩阵的SOCP问题转化为两个基于低维协方差矩阵的SOCP问题，然后循环优化两个低维的发射权矢量和接收权矢量。与全维稳健算法相比，所提算法能有效克服收发误差耦合问题，具有较好的稳健性，并能大幅降低计算复杂度和对训练样本数的需求。
2.建立了机载雷达杂波空时二维数据的矩阵模型，在充分利用载机速度和雷达工作参数等先验信息的基础上，提出了一种机载雷达杂波非自适应空时块对消器(Space-Time Block Canceller, STBC)，并给出了关于STBC权系数的最小二乘代价函数，从而优化得到STBC的权系数。由于STBC权系数仅利用载机速度和雷达工作参数等先验信息计算得到，属于非自适应处理器，因而具有运算量小、无收敛过程等优点，并且可作为机载雷达的杂波预滤波器，从而进一步改善常规动目标显示（Moving Target Indication, MTI）处理和降维STAP算法的性能。此外，在杂波模型中考虑了偏航角的存在，因此，STBC既适用于正侧视雷达，也适用于非正侧视阵雷达。
3.利用最优STAP权矩阵的低秩特性，提出了一种基于非正交基迭代（Non-Orthogonal Basis Iterative, NOBI）的空时降维自适应算法。该方法将空时联合滤波器分离为多对空域滤波器组和时域滤波器组，采用截断和堆栈处理，建立了关于空域滤波器权向量组和时域滤波权向量组的双二次代价函数，然后基于非正交基迭代求解滤波器权矢量组，实现了对杂波的空时可分离滤波。与最优STAP相比，NOBI算法避免了高维数据协方差矩阵的估计和求逆运算，有效降低了计算量和对训练样本的需求。
4.将空时二维自适应处理（2D-STAP）扩展到空域俯仰、方位和时域三维空间，针对空时三维自适应处理（3D-STAP）提出了两种降维自适应杂波抑制算法。第一种方法是基于先时后空的处理结构，首先采用具有超低旁瓣的时域多普勒预滤波处理实现一级降维，然后将空域俯仰-方位二维波束形成转化为两个一维波束形成问题，从而进一步降低了处理器的维数，实现对杂波空时三维数据的两级降维处理；第二种算法是直接将3D-STAP转化为俯仰、方位和时域三维可分离处理，即将三维权向量近似表示为三个低维权向量的Kronecker积形式，然后基于三迭代算法，依次固定两个权矢量，并构造相应的降维矩阵在低维空间上循环优化另一个权矢量。由于上述两种算法所求权矢量的维数均大幅降低，在小样本情况下具有较好的性能，因而其随样本的收敛性能较好，并具有计算量低、样本需求小等优点。
5.构建了机载MIMO雷达杂波模型，并从功率谱和自由度分布对杂波特性进行了分析。探讨了几种经典降维STAP算法在机载MIMO雷达中的应用问题，然后，针对机载MIMO雷达回波数据所具有的发射-接收-脉冲三维结构与3D-STAP中的俯仰、方位和时域三维结构类似，我们将3D-STAP中的降维自适应算法应用到机载MIMO雷达空时自适应处理(MIMO-STAP)中，并通过仿真实验验证了它们的性能。
In recent years, with the development of array antenna in the area of radar, communication,sonar and so on, the scale of the antenna arrays and the dimension of signals become larger andlarger. However, due to the limitations of work environment, hardware, manufacturing processesand other factors, the problems including computational complexity, samples demand andperformance under the influence of non-ideal factors of adaptive array signal processing algorithmsare particularly highlighted. In this thesis, on the basis of Multiple-Input Multiple-Output（MIMO）radar, airborne radar and airborne MIMO radar, adaptive beamforming and space-time adaptiveprocessing（STAP）methods are studied from two aspects of reducing dimension and robustness.The main contributions of this thesis are summarized as follows:
1. Aiming at collocated MIMO radar, a robust adaptive beamforming method is developed forMIMO radar in the presence of unknown mismatches. Explicit models of uncertainties in bothtransmitted and received signal steering vectors are considered. Combined the bi-iterative algorithmand the second convex optimization algorithm, a robust adaptive beamforming method for MIMOradar is proposed. It is shown that the robust adaptive beamforming problem can be solved byminimizing a convex quadratic cost function based on the optimization of worst-case performancewhen full DOFs of MIMO radar are used. Whereas, we reformulate the quadratic cost function intoa bi-quadratic cost function by adopting a separable form for the weight vector and the minimumpoint of the new cost function can be efficiently found by combining bi-iterative algorithm (BIA)with second-order cone programming (SOCP). Compared with the robust adaptive beamformingalgorithms using full DoFs, the proposed beamformer has lower computational complexity andfaster convergence rate, while, at the same time, it provides better robustness in the non-ideal casesand reduces the training samples required.
2. A model with matrix form of ground clutter data is established. Then taking full advantage ofthe prior information, such as platform velocity, radar parameters and so on, we propose a space-timeblock cancelle（rSTBC）to suppress the ground clutter for airborne radar. A least-squares cost functionassociated with the filter coefficient matrix of the STBC is established. Since the coefficient matrix isonly determined by the prior information, the proposed STBC belongs to a non-adaptive processorand owns small computation load and non-convergence process. It is shown that the proposed STBCcan also be used as an efficient pre-filtering tool before the conventional moving target indication（MTI）processing and the classical reduced-dimension adaptive processing. Moreover, since theclutter model has taken into account of the drift angle, the STBC is applicable not only to the sidelooking airborne radar but also to the non-sidelooking airborne radar.
3. By utilizing the low rank property of optimal STAP weight matrix, a reduced-dimensionSTAP algorithm is introduced. It is shown that the optimum weight matrix can be naturallyexpressed as the sum of several paired spatial and temporal weight vectors. After truncated andstack processing, the weight vectors can be obtained by optimizing a bi-quadratic cost functionbased on the non-orthogonal basis iterative（NOBI）algorithm. Compared with the optimal STAPmethod, high-dimensional covariance matrix inversion is avoided in our method, and therefore, thecomputational complexity and the demand of training samples is significantly reduced.
4. Extending the spatial-temporal adaptive processing (2D-STAP) to the azimuthal, elevationaland temporal three-dimensional adaptive processing (3D-STAP), two kinds of reduced-dimensionadaptive algorithms are proposed for airborne radar to suppress ground clutter. The first methodbased on the frame of the mDT-SAP applies a Doppler pre-filter to realize the first step ofreduced-dimension. Then followed by azimuthal and elevational adaptive beamforming instead oftwo-dimensional spatial beamforming, the dimensions of the processor are further reduced. Insecond method, the optimal weight vector is approximatively denoted by the Kronecker product ofthree low-dimensional weight vectors. Then we cyclically optimize a low-dimensional weightvector by applying a reduced-dimension matrix constructed by the other two fixed weight vectors.It is shown that the proposed above two methods seek weight vectors in lower dimensional spaceand perform better in small samples, thus both of them convergence fast and own low computationload and small training data demand.
5. An airborne MIMO radar clutter model is established, and its characteristics are analyzedfrom the distribution of space-time power spectrum and freedoms. The problems of several classicalreduced-dimension STAP algorithms used in airborne MIMO radar are explored. Due to the factthat the received clutter data of airborne MIMO radar own a three-dimensional (transmitting,receiving and temporal) structure, which is similar to3D-STAP, then the3D-STAP methods forairborne array radar are introduced into the airborne MIMO radar space-time adaptive processing(MIMO-STAP), and their performance are testified via simulations results.
引文
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