Phase synchronization among distributed transmission reception points (TRPs) is a prerequisite for enabling coherent joint transmission and high-precision sensing in millimeter wave (mmWave) cell-free massive multiple-input and multiple-output (MIMO) systems. This paper proposes a bidirectional calibration scheme and a calibration coefficient estimation method for phase synchronization, and presents a calibration coefficient phase tracking method using unilateral uplink/downlink channel state information (CSI). Furthermore, this paper introduces the use of reciprocity calibration to eliminate non-ideal factors in sensing and leverages sensing results to achieve calibration coefficient phase tracking in dynamic scenarios, thus enabling bidirectional empowerment of both communication and sensing. Simulation results demonstrate that the proposed method can effectively implement reciprocal calibration with lower overhead, enabling coherent collaborative transmission, and resolving non-ideal factors to acquire lower sensing error in sensing applications. Experimental results show that, in the mmWave band, over-the-air (OTA) bidirectional calibration enables coherent collaborative transmission for both collaborative TRPs and collaborative user equipments (UEs), achieving beamforming gain and long-time coherent sensing capabilities.

Counting butterflies in bipartite graphs is a fundamental task that has gained increasing attention. Estimating butterfly counts with edge local differential privacy for privacy protection is meaningful. Existing methods struggle to balance estimation accuracy, running efficiency, user synchronization and communication cost. We propose 2-path-based butterfly counting (PBC), which accurately and efficiently counts the number of butterflies in bipartite graphs in a non-interactive manner. PBC enhances running efficiency by transforming the butterfly count into a function of the 2-path count, and improves estimation accuracy with an unbiased estimation of the butterfly count. Additionally, PBC includes privacy budget allocation that minimizes the variance of the 2-path count. We evaluate PBC on four real-world datasets, demonstrating it's superior estimation accuracy and running efficiency compared to existing methods.