A comparison of methods for randomizing phase quantization errors in phased arrays

Beamsteering for phased arrays normally employs electronically switchable digital phase shifters. These can only approximate to the desired phase distribution across the array, and if a straightforward rounding off is used, a periodic phase error arises which causes a pointing deviation of the main beam and introduces a parasitic sidelobe. Various methods have been given in the literature for randomizing the phase errors to reduce these problems. Here a general formula is derived to evaluate the parasitic sidelobe level for different methods. The various methods are compared with reference to 1) the parasitic sidelobe level, 2) the variances of the field pattern and the pointing direction, 3) gain reduction, and 4) any extra array hardware requirements and beamsteering unit resources.