On the Resilience of Direction-Shift Keying Against Phase Noise and Short Channel Coherence Time at mmWave Frequencies

Short channel coherence time and oscillator phase noise are two major impairments in millimeter-wave (mmWave) communication systems. Several studies indicate that a substantial fraction of the available bandwidth may be required as overhead to compensate for these impairments, potentially exceeding one third of the total capacity. In this paper, we study Direction-Shift Keying (DSK), a variant of Spatial Modulation (SM), which encodes information in the Direction-of-Arrival (DoA) rather than in the signal amplitude or phase. DSK is implemented over a Distributed Antenna System (DAS), enabling angular resolvability of the transmitted signals. We first derive the structure of the optimal detector for a mobile device equipped withMantennas. We then introduce and characterize the Direction Coherence Time (DCT), defined as the temporal interval over which the DoA remains approximately invariant. Our analysis shows that DCT scales withd/v(transmitter-receiver distance over velocity), whereas the conventional Channel Coherence Time (CCT) scales with λ/v, revealing a coherence-time gain proportional tod/λ, which can exceed several orders of magnitude in mmWave systems. Furthermore, we show that the proposed detector inherently cancels receiver phase noise, eliminating the need for explicit phase-noise tracking. Simulation results validate the analytical findings and demonstrate the robustness of DSK in mobile mmWave environments in the presence of phase noise.