外文翻译-比幅单脉冲雷达二阶判别函数

外文资料原文SECOND ORDER DISCRIMINANT FUNCTION FOR AMPLITUDE COMPARISON MONOPULSEElsayed E. Agrama, Onsy A. Abdel-Alim,and Mohamed A. Ezz-El-ArabFaculty of Engineering,Alexandria University,Alexandria,EgyptA new three receiving elements amplitude comparison monopulse Direction Finding (DF) technique is introduced. An appropriate second order discriminant function is chosen for this technique. Then, simulation is used to compare its accuracy to that of the two receiving elements direction finding technique. Different sources of error were taken into consideration, such as, for example, receiver noise, pattern errors, amplitude imbalance, mechanical and quantization errors.Introduction and theoryThe term amplitude comparison monopulse direction finding technique is used to calculate the angle of arrival of a radio frequency signa1, usually a radar signa1, at a receiving antenna array using the output signal amplitudes from TWO adjacent antenna elements. In this technique, the angle of arrival is related to a discriminant function which is a first order function in the output signal amplitude and is given by:where A and A, are the output signal amplitudes from the two receiving adjacent antenna elements i and i+l respectively, is the field patterns of the above two antenna elements which are assumed to be identical with pattern beam width but squinted from each other by an angle :Here we introduce the principle of the second order amplitude comparison monopulse direction finding technique in which the output signals from THREE adjacent antenna elements are used to calculate the angle of arrival of the incident signal. For this technique, a second order discriminant function is introduced such that:Where is a second order function in the output signal amplitude ;and A are as defined before.Figure (1) illustrates (a) antenna arrays geometry (b) antenna elements field patterns;(c) the function and (d) the function for equals45 and = 80.2-elements system 3-elements systemfigure I-a antenna elements geometryfigure 1-b antenna elements field patterns figure 1-c Discriminant function figure 1-d Discriminant function Figure 1 ，and for =80，=45SIMULATIONA program is designed following the block diagram of figure (2) to generate the theoritical correct output signal amplitude from each of the antenna array receiving elements and then to corrupt these output amplitudes by different sources of errors. The corrupted amplitudes are then used to calculate the incidence angle using and .The calculation is repeated 2001 times for each incidence angle under the following conditions:1. Pattern beam width = 702. Squint angle equals 35；40and 453. The signal to noise ratio varies between 20 dB to 35 dB in steps of 5dB.4. The amplitude imbalance varies between 20% and 40% in steps of 10%5. Mechanical and quantization errors are assumed less than 0.5and 0.25respectively.The angle of arrival is varried between from antenna boresight axis.Figure 2 The simulation block diagram.RESUTS OF SIMULATIONFigure (3) shows the RMS error as a function of the incidence angle-for (a) 40% amplitude imbalance and 25 dB signal to noise ratio; (b) 30% imbalance and 30 dB (S/N) ratio , (c)20% imbalance and 35 dB(S/N) ratio- with pattern error of 7.5% introduced to the first antenna element output. Figures (4) and (5) shows the same but for pattern error introduced to the second and third antenna element output respectively.Tables (1),(2)and(3) presents the resultant RMS errors for different simulation conditions.NOTE: In figures 3,4 and 5;the RMS angle error obtainedusing F() is plotted in (+ ) and that obtained using is plotted in (*)Figure 3-a Imbalance error=40%;(S/N)=25 dBFigure 3-b Imbalance error=30%;(S/N)=30 dBFigure 3-c Imbalance error=20%;(S/N)=35 dBFigure 3 RMS angle measurement error as function of the incident angle for =35；=70with additional 7.5%pattern error introduced to antenna1Figure 4-a Imbalance error=40%; (S/N)= 25 dBFigure 4-b Imbalance error=30%; (S/N)= 30 dBFigure 4-c Imbalance error=20%; (S/N)= 35 dBFigure 4 RMS angle measurement error as a function of the incident angle for =35；=70with additional 7.5%pattern error introduced to antenna 2Figure 5-a Imbalance error=40%;(S/N)=25dBFigure 5-b Imbalance error=30%;(S/N)=30dBFigure 5-b Imbalance error=20%;(S/N)=35dBFigure 5 RMS angle measurement error as a function of incident angle for =35；=70with additional 7.5% pattern error introduced to antenna3Table 1Resultant RMS bearing error for =70with additional 7.5% pattern error introduced to antenna 1.Table 2Resultant RMS bearing error for =70 with additional 7.5% pattern error introduced to antenna 2Table 3Resultant RMS bearing error for=70with additional 7.5% pattern error introduced to antenna 3The effect of the pattern error is noticed clearly in figures 3,4 and 5 in the RMS error obtained using 。as a change in the average RMS error before and after ;except in figure 4 where this change does not exists .That is because the function is varied from that of the first pair of antennas to that of the second pair.ConclusionThe obtained results presented in figures 3,4 and 5show that the RMS error of angle measurement using is always better than that using F().The average improvement over the incident angle range to around the three elements system axis is deducted from the tables of results ,and is found better than 10% to 15%.The significant improvement is that obtained when comparing the accuracy of both systems near to the array axis. the improvement in this case is better than 25% for all the simulated conditions.The final conclusion is that the three receiving elements amplitude comparison monopulse system is always more accurate than the two elements system specially around the receiving array axis.外文资料译文比幅单脉冲雷达二阶判别函数Elsayed E. Agrama, Onsy A. Abdel-Alim,and Mohamed A. Ezz-El-ArabFaculty of Engineering,Alexandria University,Alexandria,Egypt本文介绍了一种新型的三通道接收单元幅度比较单脉冲方位测定技术，该技术通过首先选取一个合适的二阶判别函数。为了与两通道接收单元的测向精度进行比较，本文随后在不同的误差源下进行了对比。这些误差源包括：接收机噪声，天线误差，幅度不平衡，各种机械以及统计误差。理论及其介绍比幅单脉冲测向技术是用来计算来波信号的角度，信号通常是指雷达信号。在接收天线处对相邻两天线接收信号的幅度进行比较。这项技术中，来波角度与一个一阶判别函数有关，它是输出信号幅度的函数，形式如下：式中Ai和分别为相邻两天线单元（i，i+1）输出信号的幅度值，为上述两天线的场强形式，假设它与天线波速宽度一致，但相互偏离这里我们介绍一种二阶比幅测向方法，这种方法中，用相邻三个天线单元的输出对来波信号的角度进行计算。其二阶函数表达式如下：是一输出信号幅度的二阶函数。其他定义如前。图一（a）为天线阵列几何图。（b）为天线单元场强形式；（c）为函数，（d）为函数，当为45度，为80度的情况。图1-b 天线阵列场强模式G()图1-c 判别函数图 1-d 判别函数仿真按照流程图2设计仿真程序，由每个天线阵列接收单元产生理论上正确的输出信号幅度，然后在这些输出幅度中加入不同来源的噪声信号。此混合信号被用来利用计算入射角。此计算在不同的入射角下重复2001次，各次仿真条件如下：1. 天线波束宽度2. 偏角=35，40以及453. 信噪比以5dB步长在20dB到35dB之间变换4. 幅度不平衡以10%步长在20%到40%之间变换5. 机械和量化误差分别设为小于0.5度，0.25度。来波信号在偏离等信号轴之间变化。图2 仿真流程图仿真结果图（3）显示了以入射角为函数的均方根误差。其中（a）代表40%幅度失衡以及25dB的信噪比；（b）为30%的幅度失衡和30的信噪比；（c）为20%的失衡和35dB的信噪比，引入天线输出的模式误差为7.5%，图（4）和图（5）仅在引入到第二，第三个天线单元输出的模式误差方面有差别。表格（1）（2）（3）代表不同仿真条件下的均方根误差值。从图（3）（4）（5）看出用函数来代表在前后平均均方根误差的该变量对模式误差有非常明显的影响；但在图（4）这种改变不存在。这是因为函数是从第一对天线变到第二对。结论由图（3）（4）（5）输出结果可以看出，利用来测量测角均方根误差比用要好。在三轴线的系统中到的入射角之间的平均改善量可由表中结果得到，而且结果要比10%到50%的时候好。最显著的改善是在两个系统靠近阵列轴线附近处的精度，对于所有的仿真结果此处改善量要比25%明显。因此，最终得出的结论是，在接收阵列轴线附近，三个接收单元的幅度比较单脉冲雷达始终都比只有两个接收单元的单脉冲雷达精度更高。