Analytical performance estimation and optimization of cooperative multi-channel phase locked loops

Cooperative phase tracking enhances the mitigation of phase errors common for all channels, such as errors caused by phase noise of a local oscillator (LO) in multichannel receivers. Analysis and optimization of phase-locked loops (PLLs) in cooperative mode is significantly more complex than that of standalone PLLs, and to date their performance characteristics and optimal parameters are obtained numerically or by simulations. This complicates trade studies and implementation of cooperative phase tracking. In this paper, simple closed-form estimates for tracking errors and thresholds, as well as optimal noise bandwidths and filter coefficients of PLLs in cooperative mode have been derived for the case of mitigation of 1/f3 LO phase noise. The obtained equations can also be used to evaluate the applicability of cooperative phase tracking concept to a given scenario. An example of signal tracking with strong LO phase noise is analyzed, and good agreement between analytical results and simulations is demonstrated.