基于SDP的发射方向图设计方法与稳健波束形成研究

发布时间：2018-05-31 02:06

本文选题：半正定规划 + 发射方向图设计　；参考：《西安电子科技大学》2014年博士论文

【摘要】：本文研究了基于半正定规划(SDP)的发射方向图设计方法和稳健波束形成，SDP优化模型具有凸优化特性，具有SDP特性的波束形成方法优化模型可以求得全局最优解。传统的向量加权发射方向图设计方法和稳健波束形成方法并不能很好控制主瓣形状，，而MIMO雷达发射方向图设计方法的优化变量是发射信号协方差矩阵，有效提高了方向图设计方法中可利用的自由度，自由度的提高为设计具有期望主瓣形状和低旁瓣特性的方向图提供了一个很好的先决条件。可以将发射信号协方差矩阵看作是加权向量的协方差矩阵，将加权向量的协方差矩阵作为阵列信号处理中波束形成方法的优化变量，设计具有期望特性的波束方向图。本文具体的研究内容：低旁瓣MIMO雷达发射方向图设计方法，基于阵列结构划分的MIMO雷达发射方向图设计方法，基于SDP的优化布阵方法，基于矩阵加权和半正定秩松弛(SDR)方法的稳健波束形成，基于时变向量加权的稳健波束形成。 1.低旁瓣MIMO雷达发射方向图可以在保证主瓣发射能量的前提下，抑制旁瓣杂波和虚假目标能量，从而达到提升回波信噪比的目的。本文提出了两种低旁瓣MIMO雷达发射方向图设计方法。(1)通过对已有发射信号协方差矩阵的非对角线元素进行修正来实现低旁瓣方向图的优化设计。首先，利用方向图匹配设计方法得到具有期望主瓣形状的发射方向图，并以其作为初始值；其次，以最小化峰值旁瓣或积分旁瓣为目标函数，在约束修正后的信号协方差矩阵为半正定矩阵的前提下，利用修正矩阵的Frobenius范数为量度约束主瓣形状失真程度。(2)以最小化峰值旁瓣或积分旁瓣为目标函数，约束主瓣幅度波动范围、零点深度以及主波束间的互相关性（多波束方向图）建立优化模型；或者以最小化幅度波动范围为目标函数，约束峰值旁瓣电平、零点深度以及主波束间的互相关性（多波束方向图）建立优化模型。这两个方法都可以得到具有期望主瓣形状和低旁瓣特性的方向图，第二种方法得到的方向图还可有效设置零点深度和主波束间的互相关性。上述优化问题都是SDP凸优化问题，可以求得全局最优解。 2.针对现有MIMO雷达发射方向图设计方法无法直接推广到大规模阵列MIMO雷达的问题，本文提出了基于阵列结构划分方法的MIMO雷达发射方向图设计方法。(1)将阵列划分为阵列结构相同的子阵，各个子阵的发射信号不同，子阵内阵元发射信号相同，以每个子阵的第一个阵元组成新的稀疏阵列MIMO雷达，子阵划分以后的发射方向图为稀疏阵列MIMO雷达的方向图与子阵方向图的乘积。该方法可以降低发射信号矩阵的维度以及方向图设计中的角度范围，这就有效降低了发射方向图设计方法的运算量。(2)基于平面阵方向图可以由水平和垂直方向的线阵方向图合成的思想，本文提出了应用基波束和概率选择方法设计平面阵MIMO雷达发射方向图的方法。该方法首先将期望方向图沿方位角累加，形成一维俯仰角方向图，建立垂直方向线阵的俯仰角基波束集合和该集合元素的概率选择优化模型；其次针对每个俯仰角对应的一维方位角期望方向图，建立水平方向线阵的方位角基波束集合和该集合元素的概率选择优化模型；最后合成两维基波束集合和集合中元素的选择概率，并求得平面阵MIMO雷达的发射方向图和发射信号。以上方法中的优化模型都是SDP优化模型，可以求得全局最优解。 3.现有优化布阵方法的优化模型是以阵元位置为优化变量，通常以指数函数出现，该优化问题非凸。针对该问题，本文中提出了基于SDP的优化布阵方法，该方法的实现步骤：首先，将需要稀疏布阵的区域划分为很小的栅格，每个栅格点上有一个待选阵元；其次，以每个待选阵元的选择概率为优化变量，设计具有强指向性的发射方向图；最后，在最小阵元间距的约束下，以选择概率的大小以及重心准则将待选阵元进行聚合，得到满足最小阵元间距要求的稀疏布阵。该方法可以看作是基于概率选择加权向量的发射方向图设计方法，优化模型是一个SDP优化模型，可以求得全局最优解。相比传统的智能优化算法的优化布阵方法，本文方法只需进行单次求解，并且可以从单次求解结果中选择不同阵元数的稀疏布阵。 4.本文提出了基于矩阵加权和半正定秩松弛(SDR)方法的稳健波束形成。(1)约束主瓣幅度波动范围的矩阵加权稳健波束形成方法，与已有方法相比该方法可以有效控制方向图的主瓣形状、旁瓣电平以及零点深度。存在噪声和系统误差时，该方法对于信号功率的估计具有更好的稳健性。通过约束主瓣幅度波动范围波束形成方法求得加权矩阵的协方差矩阵，对该协方差矩阵做特征值分解求得加权矩阵，通过划分特征值大小来确定最小维度的加权矩阵，该加权矩阵可以在不损失方向图形状和信号功率估计性能的条件下有效降低系统实现复杂度。(2)与向量加权稳健波束形成方法相比，矩阵加权稳健波束形成方法系统实现复杂度较大。针对该问题，本文中给出了基于SDR方法的稳健波束形成，该方法优化模型与矩阵加权方法优化模型的不同只是多了协方差矩阵的秩为1的约束。应用SDR方法求得加权向量的协方差矩阵，将该矩阵中的每一行(列)转化为加权向量，然后选择加权向量使方向图主瓣与0dB之间失真最大值最小。该方法的系统实现复杂度与传统向量加权方法一致，对信号功率的估计性能与矩阵加权方法相当。 5.尽管矩阵加权稳健波束形成方法对于目标信号功率估计较为准确，对于误差也更稳健，但是该方法的系统实现复杂度较大。针对这个问题，我们提出了基于时变向量加权的稳健波束形成方法。已有的波束形成方法是对每次快拍信号加相同的权向量或权矩阵，这里我们借鉴MIMO雷达的思想，对不同时刻的快拍信号加不同的权向量，这些加权向量组成一个加权向量组，以加权向量组的协方差矩阵为优化变量，建立与矩阵加权稳健波束形成方法相同的优化模型。该方法的信号功率估计性能与矩阵加权方法一致，但是系统的匹配滤波输出会有信干噪比(SINR)损失。通过约束每次快拍的阵列向量加权幅度响应，可以有效降低SINR损失，并且可以显式求解加权向量组。
[Abstract]:In this paper, the design method of emission pattern based on semi positive definite programming (SDP) and robust beamforming are studied. The SDP optimization model has convex optimization characteristics. The optimization model of beamforming method with SDP characteristics can obtain the global optimal solution. The traditional vector weighted emission pattern setting method and the robust beamforming method can not be well controlled. The shape of the main lobe is made, and the optimization variable of the MIMO radar emission pattern design method is the emission covariance matrix, which effectively improves the degree of freedom that can be used in the pattern design method. The improvement of the degree of freedom provides a good precondition for the direction drawing with the desired main lobe shape and low sidelobe characteristics. The covariance matrix of the number is regarded as the covariance matrix of the weighted vector, and the covariance matrix of the weighted vector is used as the optimization variable of the beam forming method in the array signal processing, and the beampattern with the desired characteristic is designed.
The specific research content of this paper is: the design method of the emission pattern of the low sidelobe MIMO radar, the design method of the MIMO radar emission pattern based on the array structure division, the optimized array method based on the SDP, the robust beamforming based on the matrix weighting and the semi positive definite rank relaxation (SDR) method, and the robust beamforming based on the time variable vector weighting.
The 1. low sidelobe MIMO radar emission pattern can suppress the sidelobe clutter and false target energy on the premise of guaranteeing the energy of the main lobe, thus achieving the purpose of improving the signal to noise ratio of the echo. In this paper, two kinds of low sidelobe radar emission pattern design methods are proposed. (1) through the non diagonal elements of the covariance matrix of the existing transmitted signals The optimization design of the low sidelobe pattern is carried out. First, the direction map matching design method is used to get the desired main lobe shape of the emission pattern, and take it as the initial value. Secondly, to minimize the peak sidelobe or integral sidelobe as the objective function, the signal covariance matrix after the constraint correction is the front of the semi positive definite matrix. The degree of the main lobe shape distortion is constrained by the Frobenius norm of the modified matrix. (2) to minimize the peak sidelobe or integral sidelobe as the objective function, the optimization model is established to constrain the range of the main lobe amplitude, the depth of the zero point and the cross correlation between the main beam (multi beam direction), or to minimize the range fluctuation range. The objective function, the constraint peak sidelobe level, the zero point depth and the cross correlation between the main beam (multi beam pattern) are used to establish the optimization model. These two methods can all get the pattern with the desired main lobe shape and low sidelobe characteristics. The second methods can also effectively set the zero point depth and the cross correlation between the main beam. The above optimization problems are all SDP convex optimization problems, and the global optimal solution can be obtained.
2. in view of the problem that the existing MIMO radar transmitting pattern design method can not be directly extended to the large-scale array MIMO radar, this paper proposes a design method of the MIMO radar transmitting direction map based on the array structure division method. (1) the array is divided into the same array structure, the transmitting signals of each subarray are different and the array elements in the subarray are transmitted. The signal is the same, a new sparse array MIMO radar is composed of the first array element of each subarray. The emission direction after subarray division is the product of the direction map of the sparse array MIMO radar and the subarray pattern. This method can reduce the dimension of the transmitting signal matrix and the angle range in the design of the directional map, which effectively reduces the emission. The calculation of the pattern design method. (2) based on the idea that the planar array direction map can be synthesized by the horizontal and vertical direction map, this paper presents a method for the design of the plane array MIMO radar emission pattern by using the fundamental wave beam and the probability selection method. In the direction map, the pitch base beam set of vertical directional linear array and the probability selection optimization model of the set element are established. Secondly, the azimuth base beam set of the horizontal linear array and the probability selection optimization model of the set element are established according to the expected direction of the azimuth angle corresponding to each pitching angle. Finally, the two wiki wave is synthesized. The selection probability of the elements in the set and set is obtained, and the emission pattern and the transmitting signal of the plane array MIMO radar are obtained. The optimization model in the above method is all SDP optimization model, and the global optimal solution can be obtained.
3. the optimization model of the existing optimized array method is based on the array element position as the optimization variable, which usually appears with the exponential function, and the optimization problem is not convex. In this paper, an optimized array method based on SDP is proposed. The implementation steps of this method are as follows: first, the areas needing sparse array are divided into small grids and each grid point is on the grid point. There is an array element to be selected; secondly, with the selection probability of each selected element as the optimization variable, a strong directional emission pattern is designed. Finally, under the constraints of the minimum element spacing, the selected array element is aggregated with the size of the selection probability and the center of gravity criterion, and the sparse array is obtained to meet the minimum element spacing requirements. The method can be considered as a design method based on the weighted vector of probability selection. The optimization model is a SDP optimization model, and the global optimal solution can be obtained. Compared with the traditional optimization algorithm of intelligent optimization algorithm, this method only needs a single solution and can select the sparse number of elements from the single solution. Sparse array.
4. this paper presents a robust beamforming based on matrix weighting and semi positive definite rank relaxation (SDR). (1) a matrix weighted robust beamforming method that constrains the range of the amplitude fluctuation of the main lobe. Compared with the existing methods, the method can effectively control the main lobe shape, sidelobe level and zero point depth of the pattern, when there is noise and system error, This method has a better robustness for the estimation of the signal power. The covariance matrix of the weighted matrix is obtained by restricting the range beam forming method of the main lobe amplitude. The weighted matrix is obtained by eigenvalue decomposition of the covariance matrix, and the weighting matrix of the smallest dimension is determined by dividing the eigenvalues to determine the weighted matrix. The weighted matrix can be used. The complexity of the system is effectively reduced without losing the shape of the direction map and the performance of the signal power estimation. (2) the matrix weighted robust beamforming method is more complex than the vector weighted robust beamforming method. In this paper, the robust beamforming based on the SDR method is given in this paper, and the method is optimized. The difference between the model and the matrix weighted method is only the constraint of the rank of 1 of the covariance matrix. The covariance matrix of the weighted vector is obtained by using the SDR method, and every row (column) of the matrix is transformed into a weighted vector, and then the weighted vector is selected to minimize the distortion maximum between the principal lobe and the 0dB. The complexity is consistent with the traditional vector weighting method, and the estimated signal power is comparable to the matrix weighting method.
5. although the matrix weighted robust beamforming method is more accurate for the target signal power estimation and is more robust to the error, the system is more complex. We propose a robust beamforming method based on time variable vector weighting. Some beamforming methods have been added to each fast beat signal. The same weight vector or weight matrix, here we use the idea of MIMO radar to add different weight vectors to the snapshot signals at different times. These weighted vectors constitute a weighted vector group, and the covariance matrix of the weighted vector group is the optimal variable, and the same optimization model is established with the matrix weighted robust beamforming method. The performance of the signal power estimation is the same as that of the matrix weighted method, but the output of the matched filter of the system will have the loss of the signal to noise ratio (SINR). By restricting the array vector weighted amplitude response of each snapshot, the SINR loss can be effectively reduced and the weighted vector group can be solved explicitly.
【学位授予单位】：西安电子科技大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN957.51

【参考文献】