# Mainlobe jamming can pose problems

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3 X: Y: Convex programming is employed to construct a difference beam with the constraints that the difference-to-sum beam ratio must be close to in the mainlobe region while the difference beam will approximate the sum beam in the sidelobe region. Finally, the resulting sum beam,, and the difference beam, Δ, derived from the weight vectors, W S and W D, respectively, can be used to estimate the angle of the illuminated target. In brief, this proposed monopulse radar system method uses convex programming to maintain desirable target response characteristics while minimizing the effects of jamming in the sidelobe and/or mainlobe regions. A key to achieving success with this approach is synthesis of the difference beam and how well it approximates a desired pattern. This can be measured in several ways, but least-squares analysis is used here. To obtain an unbiased angle estimation for the target, the monopulse response curve should pass through the coordinate (θ s, ). So, additional constraint must be provided at the desired target direction. The difference pattern synthesis problem is stated in Equation 1: Estimation angle (RSME) deg X: Y: (d) Interference angle deg.. The RMSE is maintained under control as a function of the mainlobe jamming angle. where: Θ m = the mainlobe region Θ s = the mainlobe region ε = a nonnegative real value. In general, the ratio P D /P S is a complex value including both magnitude and phase responses. Once a target is not in the direction of monopulse radar beam illumination, an error voltage can be obtained from monopulse ratio analysis. That is, the error value depends on the magnitude of, and it is unrelated to the phase of. When there is no phase requirement for the monopulse response within the mainlobe region, the problem of the difference pattern then can be stated by Equation : min max P D (θ)/p S (θ),θ Θ m subject to P D (θ) P S (θ) <ε,θ Θ m min max P D (θ)/p S (θ),θ Θ m subject to P D (θ) P S (θ) <ε,θ Θ m P D (θ)/p S (θ) θ=θs = Go To mwrf.com

4 Monopole System Jamming X: 1 Y: PD()/PS() θ=θs, = As a consequence, much better performance levels are expected when only magnitude is involved. 1 It should be noted that Equation 1 can be rewritten as Equation. The resulting optimization problem is nonconvex. Therefore, the difference pattern cannot be synthesized directly by classic convex optimization approaches. The optimality is guaranteed only to a locally optimal solution, while global optimality cannot be guaranteed. In this section, an iterative algorithm is introduced to solve it by iteratively solving a convex optimization problem. At each iterative solution, the convex optimization problem can be formulated in the form of a second-order cone program (SOCP) for the solution. For the desired response difference pattern synthesis problem, the specific phase of the desired response is unknown. The phase of the can be modified to create the desired. The difference pattern synthesis problem described in Equation can be solved by iteratively refining a suitable phase and then solving for Equation 1. This iterative X: 1 Y: (d) Interference angle deg. 5. The target angle RMSE remains manageable even with larger interference angles. Estimation angle RMSE deg algorithm can be described as a fourstep process. In the first step, an artificial desired phase (e.g., zero phase) is constructed for, since there is no phase requirement for the monopulse response within the mainlobe region. Find an initialization of optimal weight vector W D1 and the resulting monopulse ratio curve 1 = P D1 / P S by solving Equation 1, where P D1 = W D1 T V and P S is obtained by the adaptive sum beamforming network. In the second step, the phase of 1 (such as 1 ) is used to define a new desired as: ' = exp[j 1 ] The new optimal weight vector W D can be found by solving Equation 1. The resulting difference beam and are P D1 = W D T V and = P D /P S, respectively. In the third step, with the new desired monopulse ratio curve response, ', a new optimal weight vector, W D, can be calculated using Equation 1. The results can be obtained for: P D = W D T V = P D /P S. Compared with 1, is more approximate to the desired response ' due to the optimal solution. The final step of the iterative algorithm involves returning to step until the best attainable monopulse ratio curve response has been found. The convergence of the iterations follows from the following sequence of inequalities shown in Equation 3: = ' ' 1 ' = 1 ' X:.5 Y:. X: 17 Y: X:.5 Y: 3.53 X: 17 Y: The new monopulse method, yielded this sum pattern, difference pattern, and desired and adaptive monopulse ratio cures. 5 month year microwaves & RF

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