Wind farm controllers such as the Helix approach have shown potential in increasing plant power production through wake mixing. The concept suggests that actuating the upstream turbines' blade pitching with a specific periodic signal can induce a helix-shaped wake, thereby alleviating wind velocity deficit on downstream turbines. Wake mixing initiation by downstream turbines may also be shown advantageous for power production; however, little to no attention has been given to such an approach. Similar wake mixing is expected to be achievable at lower control costs if the downstream turbine can benefit from the periodic component already present in the wake of the upstream turbine. Such a hypothesis is studied in this work by designing a minimal control scheme where the wake acting on the downstream turbine is simulated by a periodic input disturbance. A Kalman filter is proposed for incoming input disturbance phase estimation using SCADA data. The reconstructed phase information allows synchronization of the downstream control action with the periodic input disturbance by means of a phase synchronization wake mixing controller. The periodic component was estimated with a minimal root-mean-square error and the resulting control action was in phase with the input disturbance and demonstrated satisfactory performance even with a small phase perturbation. Future work will include applications in a high-fidelity wind turbine model and wind tunnel studies.