Analysis of Over-the-air Frequency and Time Synchronization Requirements for Cooperative ISAC Radio Units with an RF Crystal Oscillator

Abstract - Cell-free densified networks of radio units (RUs) leveraging cooperative distributed multiple-input multiple-output (D-MIMO) can offer high data capacity per area, low latency, and uniform coverage. As fiber-access cannot be taken for granted in dense employments, some wireless RUs are required to use over-the-air synchronization (OAS). Distributed networks of cooperative RUs can also support multi-static integrated sensing and communication (ISAC) provided RUs are accurately synchronized.

Frequency synthesizer circuits in RUs are typically first optimized for short-term stability (jitter and phase noise), but long-term stability is also critical to limit timing drift between synchronization updates. At higher radio frequency (RF) carrier frequencies, equal jitter results in tighter phase-noise requirements for frequency references. This motivates the use of RF crystal oscillators (RFXOs) to achieve the required sub-100 fs jitter performance for 6G complex modulation schemes at centimeter-wave frequencies, but such crystals have a worse long-term stability, which we aim to evaluate. Long-term stability can be evaluated using two-sample variances such as modified Allan deviation (MDEV) and time deviation (TDEV). Combining these metrics enables the translation of system-level targets, such as 3.3 ppb frequency stability and 4 ps time error into synchronization-interval requirements.

Using simulation results of a representative frequency synthesizer, we compute the resulting TDEV and design a synchronization loop that improves long-term stability. Our results show that for RFXO-based RUs, our Allan deviation (ADEV) and TDEV requirements can still be met at millisecond-scale synchronization intervals assuming an Additive White Gaussian Noise (AWGN) channel.