Effects of phase shift errors on the antenna directivity of phased arrays in indoor terahertz communications

Phased arrays provide a high antenna gain and improve the signal quality in the presence of high propagation path loss. However, an imprecise phase shift could reduce the antenna performance. This problem is especially serious when the carrier frequency is very high because the short wave length results in a high sensitivity against phase impairments. Any phase shift error effectively affects the radiation pattern and thereby reduces the antenna directivity. This paper derives the expectation of the antenna directivity in the presence of random phase shift errors. The theoretical estimate is validated with the simulation result and offers a simple way to determine the precision requirement of the phase shifter for a given necessary directivity.