A Research On Tolerance Analysis And Optimal Design Algorithm For Non-ideal Antenna Arrays

In many practical applications, errors are usually existed in the control points of antenna arrays because of the non-ideal manufacturing process and working environment. These uncertain errors will cause the uncertainties of the excitation amplitude and phase coefficients of antenna arrays, which may lead to the fluctuations of the performance metrics in a definitive range. Consequently, it is necessary to estimate the effect of these uncertainties on the antenna performance during the analysis and design process for actual antenna array systems, thus reducing the extra time and cost for the calibration process while ensuring the desired radiation performance when manufacturing tolerances are exist. In this paper, a research on tolerance analysis and optimal design algorithm for non-ideal antenna arrays is presented, specific tasks are given as follows:1. The non-probabilistic Interval Analysis(IA) algorithm is used for tolerance analysis of the non-ideal uniform linear array in this work. Toward this purpose, corresponding interval models of the power pattern functions are established respectively with the consideration of the amplitude errors, phase errors, or both simultaneously, in antenna arrays. Besides, the tolerance for the amplitude-phase error of the main function parameters including the beamwidth, side lobe level, and the directivity are simulated by computer according to the indicators and the actual requirements. Accordingly, the worst admissible performance of an array can be evaluated, which may provide theoretical reference for optimal design of antenna arrays.2. To deal with the problem of the interval extension caused by IA when errors are large or different errors coexist simultaneously, the second order perturbation method is proposed to translate the problem to find out the interval solution of the short interval with uncertain parameters into computing the low-order Taylor expansion perturbation of system response, thus approaching the practical power sliding interval. Simulation results show that IA can be substituted by the second order perturbation method to calculate the interval value of the power pattern function within a specific tolerance range, which will improve computing precision effectively.3. As for the problem of the array optimization design in the presence of various tolerances, Interval Analysis-Convex Programming(IA-CP) is presented to establish an IA-based convex optimization model for the excitation amplitudes so that the power pattern which meets the performance request can be synthesized. Compared with Interval Analysis-Particle Swarm Optimization(IA-PSO), the proposed algorithm obtains more optimal excitation parameters in the presence of the same array errors. Moreover, the impact of the manufacturing tolerances of the excitation amplitudes, phases and amplitude-phase as well as the number of elements on the optimization results is also considered in this paper. Experiment results show that the IA-CP-based synthesis technique is not only robust for the amplitude and phase errors, but also suitable for large arrays.