Closed-Form Performance of Receiver Beamformer Driven by Imperfect Clock Distribution Circuit

The quality of clock signal sources is essential to modern electronic systems, but it is subject to physical limitations, such as phase noise and timing jitter. In some applications a clock distribution circuit or network is required to drive multiple elements, at the cost of an increased level of total phase noise (TPN) (contributed by the phase noise and timing jitter). A windband receiver beamforming is used to study the impact of TPN. An analytical framework along with error vector magnitude (EVM) in closed-form is presented. In particular, this paper demonstrates how the phase noise correlations affect the beam pattern. Verified by the actual beamforming design, an important conclusion is drawn: the EVM decreases as the TPN correlation between channels increases; hence, increasing the clock phase correlation between channels is even more effective than purifying the clock source (suppressing the phase noise and jitter).