Performance analysis of derivative constraint adaptive arrays with pointing errors

The performance of adaptive arrays with arbitrary order derivative constraints to avoid the signal nulling caused by the error in the steering angle is investigated. The generalized sidelobe canceller (GSC) is used to evaluate the bearing responses of adaptive arrays with pointing errors. Under the assumption of equispaced linear arrays, the Legendre polynomial is used to derive a closed-form formula for the sidelobe leakage factor, the ratio in which the signal leaks into the GSC sidelobe cancelling branch. Moreover, the effective beamwidth, the maximum range of pointing inaccuracy allowable to keep the signal loss in array output less than a given value, is derived for the GSC with a delay-and-sum quiescent beamformer. Such adaptive arrays can achieve the maximum output signal-to-noise ratio when the presteering is perfect, and the performance is independent of the location of the phase origin. Numerical results are presented to confirm the analysis