Analysis of worst-case phase quantization sidelobes in focused beamforming

The effect of phase quantization errors on the sidelobe level in a phased-array beamformer is considered. The theory of random and periodic phase errors is reviewed. Periodic phase errors occur for an unfocused array with uniform element distance and give rise to discrete sidelobes. The main result of the paper is an analysis of the periodic phase error in the case that the beamformer is focused. An estimate for the worst-case discrete sidelobe level as a function of focal depth is derived. The theory is illustrated and verified by simulations.