The Influence of Random Phase Errors on the Angular Resolution of Synthetic Aperture Radar Systems

Abstract

The influence of random phase errors on the angular resolution of a focused synthetic aperture radar system is treated. The principal measure of performance has been taken as the mean envelope power at the system output. This system output power is evaluated exactly, although not in closed form, based on the following reasonable assumptions: (1) the real beam pattern is Gaussian; (Z) the random phase error is essentially a geometry independent ergodic process with a Gaussian amplitude distribution and zero mean; and (3) the random phase error has a Gaussian co.rrelation function.The curves presented in this report can be used to estimate expected system power response, expected system resolution, and effective aperture length beyond which, inthe presence of phase error, little gain in resolution is expected.It was found that multiple sources of error with different correlation intervals make explicit solution of the integral equation for system power response practicallyimpossible. Inthis situation, a reasonable approach is to evaluate the system power response separately for 'ach error. If one of the errors is clearly dominant, it maybe regarded as bounding achievable performance.

Statistical patterns of a general array

“…At any rate, all that is required for estimation of the accuracy of the calculated results is a comparison of u:+ua2 with 1.0. As demonstrated by applications here and elsewhere [6], [7], values of u,2 and ua2, which render the analyses useless, are of little interest in practical antenna design, since they result in high sidelobes (> -10 dB) or low gain in all cases, except when correlation among phase errors of neighboring elements in the array is high [7].…”

“…However, it was pointed out previously that a binary autocorrelation coeffi-1 cient greatly reduces the size of the lengthy summations in the analytical results. Nevertheless some special choices for ,,fi (no-error amplitude distribution and antenna element pattern) still provide tractable results with other realistic autocorrelation coefficients [7]. However, if the summations are still too lengthy to be cheaply computed, an integral approximation, or lower order sum, may be used with some success [ 6 ] .…”

“…Then Greene and Moller [ 6 ] applied the main beam analyses to synthetic arrays with external Gaussian phase errors. Develet [7] derived stochastic average results for a focused synthetic array with Gaussian phase-error spatial correlation. And Cheng [ 151 treated the effects of phase errors on the antenna gain and beamwidth.…”

K-Band Tracking System for Domestic Satellite Communication System

“…The signal-tothermal-noise ratio (S/N) increases in proportion as the PLL noise bandwidth becomes narrower. Develet [5] found that the PLL unlocks if loop S/N falls below 1.34 dB. At this threshold level the rms phase error is calculated to be 1.0 rad.…”