Aerospace and Electronic Systems Magazine August 2016 - 32

Pioneer Award gral parameters of the array. The optimization problem consists in finding the regular APD and placement of radiators such that, when being subjected to random variations with given probability characteristics, the criterion extreme value is provided. From there one can find, not only jointly the APD and placement of radiators, but also separately, the amplitude or phase distribution, placement of radiators, or some kind of their combination, depending on what parameters can be changed in the array antenna under consideration. Methods for solving the problem were developed in a general statement as well as in the particular one [21]. In a number of particular cases, it is possible to obtain the solution in the explicit form. In other cases, numerical rapid convergence methods of mathematical programming are pointed out. The problem of maximizing the mean directivity was considered in detail. The investigations were carried out for ordinary and dense array antennas. For the ordinary array antenna, when its spacing is equal to or more than half a wavelength, the optimal APD at the presence and at the absence of errors practically coincide and approach the normal distribution (the amplitude distribution is uniform, the phase one provides the beam orientation in a given direction). These array antennas are weakly sensitive to instabilities; random errors in the APD realization lead to the insignificant decrease in the directivity. The described properties reveal themselves both for broadside and end-fire array antennas. Let us proceed now to the consideration of array antennas with spacing smaller than half a wavelength (dense array antennas). Properties of broadside and end-fire array antennas here are essentially different. For perfect (the absence of errors) broadside array antennas, the maximum directivity monotonically decreases as the radiators approach each other. The allowance for random errors with the following maximization of directivity leads to its small additional decrease. The values herewith obtained for maximum mean directivities insignificantly differ from those at the normal excitation of array antennas. Thus, the directivity optimization, even in the case of small errors, does not yield noticeable gain in the mean directivity. Correspondingly, we can say that in the broadside array antennas, superdirectivity is practically unrealizable. Another picture is for dense end-fire array antennas. This is illustrated by Figure 8. It shows the results of calculations for a 10-element end-fire array antenna consisting of isotropic radiators. It is assumed that only those phase errors take place in the array antenna that have the variance of 0.04 rad2 and correlation radius equal to three interelement spacings. Figure 8 shows plots of the array antenna spacing d-dependences of maximum directivity D00 at the absence of errors (curve 1), maximum mean directivity Dcm (curve 2), mean directivity Ds (curve 3) at the normal array antenna excitation, and radiation efficiency μ (curve 4, in percents) for the optimal APD of the array antenna with the maximum mean directivity. The μ value is defined by a ratio between the radiation intensities at coherent and incoherent summations of fields (multiplied by N) in the main maximum direction. At the normal excitation, μ=100%. Array antenna spacing d in Figure 8 is expressed in shares of wavelength λ. In a perfect case, as the radiators approach each other, the maximum directivity rapidly grows and tends to N2 (curve 1). In this case, the features of superdirectivity (the APD oscillations, the decrease in the radiation efficiency, etc.) strengthen. When taking er32 Figure 8. Maximum directivity D00 (curve 1), maximum mean directivity Dcm (curve 2), mean. directivity Ds (curve 3), and radiation efficiency μ versus array antenna spacing d. rors into account, the plot for the maximum mean directivity (curve 2) takes a resonant character. The optimal spacing and the largest maximum mean directivity are subject to errors' statistics. For the array antenna under consideration, the optimal spacing constitutes 0.38λ (in this case, the array antenna dimension is L =3.8λ), whereas the largest value of the maximum mean directivity noticeably exceeds the mean directivity at the normal excitation (curve 3). For the aforementioned array antenna, it increases by a factor of 2.5. Herewith, the radiation efficiency (curve 4) decreases almost 7 times. Taking into account that in the one-beam mode, the directivity of an end-fire array antenna can be estimated as 4L/λ, the value of directivity corresponding to the optimal spacing can be obtained in the normally excited array antenna having dimension 9λ. Thus, the directivity optimization of end-fire array antennas under statistical approach obtains noticeable gains in mean directivity and in array antenna dimensions. The "payment" for this is the decrease in the radiation efficiency (and, correspondingly, the increase in the quality factor (or the passband narrowing), and the increase in loss [21]). Nevertheless, in a number of practical applications, both the decrease in the dimensions and the passband narrowing are rather desirable whereas the loss can be decreased at the expense of applying superconducting materials. In addition to the problem of statistical optimization of the array antenna integral parameters, we also considered problems of the statistical synthesis of the RP of a given shape. The regular APD was defined so that it minimized the mean value of the statistical average criterion that characterizes a degree of the synthesized RP spread with respect to the given RP in the presence of errors in the APD and placement of radiators. The solution is obtained in the explicit form for arbitrary array antennas and error statistics and requires that the matrix inversion operation be performed. The solution results (the degree in which the synthesized RP approaches the given one) are subject not only to the given RP shape and a value of errors, but also to the array antenna spacing. At the "bad" shape of given RP (either the increased directivity or the abrupt decays). The solution obtained for dense array antennas will contain noticeable features of superdirectivity with all the shortcomings inherent in it. In order to reduce these shortcomings, it is necessary IEEE A&E SYSTEMS MAGAZINE AUGUST 2016

Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine August 2016