本文選題：半正定規(guī)劃 + 發(fā)射方向圖設(shè)計(jì)�。� 參考：《西安電子科技大學(xué)》2014年博士論文

【摘要】：本文研究了基于半正定規(guī)劃(SDP)的發(fā)射方向圖設(shè)計(jì)方法和穩(wěn)健波束形成，SDP優(yōu)化模型具有凸優(yōu)化特性，具有SDP特性的波束形成方法優(yōu)化模型可以求得全局最優(yōu)解。傳統(tǒng)的向量加權(quán)發(fā)射方向圖設(shè)計(jì)方法和穩(wěn)健波束形成方法并不能很好控制主瓣形狀，，而MIMO雷達(dá)發(fā)射方向圖設(shè)計(jì)方法的優(yōu)化變量是發(fā)射信號協(xié)方差矩陣，有效提高了方向圖設(shè)計(jì)方法中可利用的自由度，自由度的提高為設(shè)計(jì)具有期望主瓣形狀和低旁瓣特性的方向圖提供了一個很好的先決條件。可以將發(fā)射信號協(xié)方差矩陣看作是加權(quán)向量的協(xié)方差矩陣，將加權(quán)向量的協(xié)方差矩陣作為陣列信號處理中波束形成方法的優(yōu)化變量，設(shè)計(jì)具有期望特性的波束方向圖。 本文具體的研究內(nèi)容：低旁瓣MIMO雷達(dá)發(fā)射方向圖設(shè)計(jì)方法，基于陣列結(jié)構(gòu)劃分的MIMO雷達(dá)發(fā)射方向圖設(shè)計(jì)方法，基于SDP的優(yōu)化布陣方法，基于矩陣加權(quán)和半正定秩松弛(SDR)方法的穩(wěn)健波束形成，基于時變向量加權(quán)的穩(wěn)健波束形成。 1.低旁瓣MIMO雷達(dá)發(fā)射方向圖可以在保證主瓣發(fā)射能量的前提下，抑制旁瓣雜波和虛假目標(biāo)能量，從而達(dá)到提升回波信噪比的目的。本文提出了兩種低旁瓣MIMO雷達(dá)發(fā)射方向圖設(shè)計(jì)方法。(1)通過對已有發(fā)射信號協(xié)方差矩陣的非對角線元素進(jìn)行修正來實(shí)現(xiàn)低旁瓣方向圖的優(yōu)化設(shè)計(jì)。首先，利用方向圖匹配設(shè)計(jì)方法得到具有期望主瓣形狀的發(fā)射方向圖，并以其作為初始值；其次，以最小化峰值旁瓣或積分旁瓣為目標(biāo)函數(shù)，在約束修正后的信號協(xié)方差矩陣為半正定矩陣的前提下，利用修正矩陣的Frobenius范數(shù)為量度約束主瓣形狀失真程度。(2)以最小化峰值旁瓣或積分旁瓣為目標(biāo)函數(shù)，約束主瓣幅度波動范圍、零點(diǎn)深度以及主波束間的互相關(guān)性（多波束方向圖）建立優(yōu)化模型；或者以最小化幅度波動范圍為目標(biāo)函數(shù)，約束峰值旁瓣電平、零點(diǎn)深度以及主波束間的互相關(guān)性（多波束方向圖）建立優(yōu)化模型。這兩個方法都可以得到具有期望主瓣形狀和低旁瓣特性的方向圖，第二種方法得到的方向圖還可有效設(shè)置零點(diǎn)深度和主波束間的互相關(guān)性。上述優(yōu)化問題都是SDP凸優(yōu)化問題，可以求得全局最優(yōu)解。 2.針對現(xiàn)有MIMO雷達(dá)發(fā)射方向圖設(shè)計(jì)方法無法直接推廣到大規(guī)模陣列MIMO雷達(dá)的問題，本文提出了基于陣列結(jié)構(gòu)劃分方法的MIMO雷達(dá)發(fā)射方向圖設(shè)計(jì)方法。(1)將陣列劃分為陣列結(jié)構(gòu)相同的子陣，各個子陣的發(fā)射信號不同，子陣內(nèi)陣元發(fā)射信號相同，以每個子陣的第一個陣元組成新的稀疏陣列MIMO雷達(dá)，子陣劃分以后的發(fā)射方向圖為稀疏陣列MIMO雷達(dá)的方向圖與子陣方向圖的乘積。該方法可以降低發(fā)射信號矩陣的維度以及方向圖設(shè)計(jì)中的角度范圍，這就有效降低了發(fā)射方向圖設(shè)計(jì)方法的運(yùn)算量。(2)基于平面陣方向圖可以由水平和垂直方向的線陣方向圖合成的思想，本文提出了應(yīng)用基波束和概率選擇方法設(shè)計(jì)平面陣MIMO雷達(dá)發(fā)射方向圖的方法。該方法首先將期望方向圖沿方位角累加，形成一維俯仰角方向圖，建立垂直方向線陣的俯仰角基波束集合和該集合元素的概率選擇優(yōu)化模型；其次針對每個俯仰角對應(yīng)的一維方位角期望方向圖，建立水平方向線陣的方位角基波束集合和該集合元素的概率選擇優(yōu)化模型；最后合成兩維基波束集合和集合中元素的選擇概率，并求得平面陣MIMO雷達(dá)的發(fā)射方向圖和發(fā)射信號。以上方法中的優(yōu)化模型都是SDP優(yōu)化模型，可以求得全局最優(yōu)解。 3.現(xiàn)有優(yōu)化布陣方法的優(yōu)化模型是以陣元位置為優(yōu)化變量，通常以指數(shù)函數(shù)出現(xiàn)，該優(yōu)化問題非凸。針對該問題，本文中提出了基于SDP的優(yōu)化布陣方法，該方法的實(shí)現(xiàn)步驟：首先，將需要稀疏布陣的區(qū)域劃分為很小的柵格，每個柵格點(diǎn)上有一個待選陣元；其次，以每個待選陣元的選擇概率為優(yōu)化變量，設(shè)計(jì)具有強(qiáng)指向性的發(fā)射方向圖；最后，在最小陣元間距的約束下，以選擇概率的大小以及重心準(zhǔn)則將待選陣元進(jìn)行聚合，得到滿足最小陣元間距要求的稀疏布陣。該方法可以看作是基于概率選擇加權(quán)向量的發(fā)射方向圖設(shè)計(jì)方法，優(yōu)化模型是一個SDP優(yōu)化模型，可以求得全局最優(yōu)解。相比傳統(tǒng)的智能優(yōu)化算法的優(yōu)化布陣方法，本文方法只需進(jìn)行單次求解，并且可以從單次求解結(jié)果中選擇不同陣元數(shù)的稀疏布陣。 4.本文提出了基于矩陣加權(quán)和半正定秩松弛(SDR)方法的穩(wěn)健波束形成。(1)約束主瓣幅度波動范圍的矩陣加權(quán)穩(wěn)健波束形成方法，與已有方法相比該方法可以有效控制方向圖的主瓣形狀、旁瓣電平以及零點(diǎn)深度。存在噪聲和系統(tǒng)誤差時，該方法對于信號功率的估計(jì)具有更好的穩(wěn)健性。通過約束主瓣幅度波動范圍波束形成方法求得加權(quán)矩陣的協(xié)方差矩陣，對該協(xié)方差矩陣做特征值分解求得加權(quán)矩陣，通過劃分特征值大小來確定最小維度的加權(quán)矩陣，該加權(quán)矩陣可以在不損失方向圖形狀和信號功率估計(jì)性能的條件下有效降低系統(tǒng)實(shí)現(xiàn)復(fù)雜度。(2)與向量加權(quán)穩(wěn)健波束形成方法相比，矩陣加權(quán)穩(wěn)健波束形成方法系統(tǒng)實(shí)現(xiàn)復(fù)雜度較大。針對該問題，本文中給出了基于SDR方法的穩(wěn)健波束形成，該方法優(yōu)化模型與矩陣加權(quán)方法優(yōu)化模型的不同只是多了協(xié)方差矩陣的秩為1的約束。應(yīng)用SDR方法求得加權(quán)向量的協(xié)方差矩陣，將該矩陣中的每一行(列)轉(zhuǎn)化為加權(quán)向量，然后選擇加權(quán)向量使方向圖主瓣與0dB之間失真最大值最小。該方法的系統(tǒng)實(shí)現(xiàn)復(fù)雜度與傳統(tǒng)向量加權(quán)方法一致，對信號功率的估計(jì)性能與矩陣加權(quán)方法相當(dāng)。 5.盡管矩陣加權(quán)穩(wěn)健波束形成方法對于目標(biāo)信號功率估計(jì)較為準(zhǔn)確，對于誤差也更穩(wěn)健，但是該方法的系統(tǒng)實(shí)現(xiàn)復(fù)雜度較大。針對這個問題，我們提出了基于時變向量加權(quán)的穩(wěn)健波束形成方法。已有的波束形成方法是對每次快拍信號加相同的權(quán)向量或權(quán)矩陣，這里我們借鑒MIMO雷達(dá)的思想，對不同時刻的快拍信號加不同的權(quán)向量，這些加權(quán)向量組成一個加權(quán)向量組，以加權(quán)向量組的協(xié)方差矩陣為優(yōu)化變量，建立與矩陣加權(quán)穩(wěn)健波束形成方法相同的優(yōu)化模型。該方法的信號功率估計(jì)性能與矩陣加權(quán)方法一致，但是系統(tǒng)的匹配濾波輸出會有信干噪比(SINR)損失。通過約束每次快拍的陣列向量加權(quán)幅度響應(yīng)，可以有效降低SINR損失，并且可以顯式求解加權(quán)向量組。
[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.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TN957.51

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