Differential Space-Time Block Coding for Phase-Unsynchronized Cell-Free MIMO Downlink

In the downlink of a cell-free massive multiple-input multiple-output (CF-mMIMO) system, spectral efficiency gains critically rely on joint coherent transmission, as all access points (APs) must align their transmitted signals in phase at the user equipment (UE). Achieving such phase alignment is technically challenging, as it requires tight synchronization among geographically distributed APs. In this paper, we address this issue by introducing a differential space-time block coding (DSTBC) approach that bypasses the need for AP phase synchronization. We first provide analytic bounds to the achievable spectral efficiency of CF-mMIMO with phase-unsynchronized APs. Then, we propose a DSTBC-based transmission scheme specifically tailored to CF-mMIMO, which operates without channel state information and does not require any form of phase synchronization among the APs. We derive a closed-form expression for the resulting signal-to-interference-plus-noise ratio (SINR), enabling quantitative comparisons among different DSTBC schemes. Numerical simulations confirm that phase misalignments can significantly impair system performance. In contrast, the proposed DSTBC scheme successfully mitigates these effects, achieving performance comparable to that of fully synchronized systems.