The Robustness of Pencil Beam Synthesis Without Considering Sensor Uncertainties

Sensor uncertainties such as amplitude and phase errors may deteriorate the performance of array pattern synthesis. Therefore, several robust synthesis methods have been proposed. In this communication, we show that, for pencil beams, the direct synthesis method that does not take into account sensor errors also has robustness against sensor uncertainties. We first reformulate the robust synthesis method based on the worst-case performance criterion as a perturbation of the direct synthesis method. Then we prove that the direct and robust synthesis methods have the same solution up to a scaling factor. Thus, they produce the same array pattern (normalized). The condition for this result is that the error norms of steering vectors in different directions are equal to a small positive number, which is a reasonable assumption in practice. In addition, we derive a new optimization model for the robust synthesis method that can be solved much faster than the existing one.