The Effect of Normally Distributed Random Phase Errors on Synthetic Array Gain Patterns

In the practical formation of synthetic array patterns the individual signals which are integrated to form the array will sustain uncompensated phase shifts. If these uncompensated phase shifts are deterministic, the evaluation of their effect on the synthetic array radiation pattern is straightforward. On the other hand, if the uncompensated phase shifts are random, such as would be produced by propagation anomalies, a statistical study must be made to determine statistical measures of the effects on the radiation pattern. Part I describes an analytical study of the effects of normally distributed random phase errors on synthetic array performance. The statistical measures of performance derived include expected beam broadening, rms beam canting, and expected loss in peak gain. The analysis is limited to the case of small rms difference in phase error across the array. Part II describes a Monte Carlo simulation study which removed the restriction of small rms phase error difference. In addition, the simulated radiation pattems generated in the simulation study allowed the computation of the statistics of the ratio of main lobe to integrated sidelobe power. This performance parameter is, in general, the most sensitive of all the performance measures to residual uncompensated phase errors.