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

2025-08-31

AI Summary

Millimeter-wave and sub-terahertz communications face dual challenges of short channel coherence time and severe oscillator phase noise. Existing Directional Symbol Keying (DSK) studies are confined to oversimplified scenarios and two-antenna terminals, lacking systematic analysis of robustness mechanisms under general multi-antenna configurations. This paper introduces the novel concept of Directional Coherence Time (DCT), theoretically characterizing its dependence on distance, velocity, and wavelength; it proves that DSK extends the effective coherence time by up to 10⁴-fold—scaling as *d/λ*. For the first time, we rigorously establish DSK’s intrinsic immunity to oscillator phase noise, eliminating its impact without auxiliary compensation. By integrating Direction-of-Arrival (DoA) coding, spatial modulation, optimal detection, and phase-noise modeling—supported by theoretical analysis and simulations—we demonstrate that DSK achieves high robustness, scalability, and engineering feasibility in distributed multi-antenna systems.

Technology Category

• Search and Optimization: Distributed Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

The rapid variation of the wireless channel (short channel coherence time) and the phase noise are two prominent concerns in Millimeter-wave (mmWave) and sub-Terahertz systems communication systems. Equalizing the channel effect and tracking the phase noise necessitate dense pilot insertion. Direction-Shift Keying (DSK), a recent variant of Spatial Modulation (SM), addresses these challenges by encoding information in the Direction-of-Arrival (DoA) using a distributed antenna system (DAS), rather than relying on amplitude or phase. DSK has been shown to extend coherence time by up to four orders of magnitude. Despite its promise, existing DSK studies are largely simulation-based and limited to simplified roadside unit scenarios and mobile device (MD) equipped with only two antennas. DSK's performance in general settings, along with the fundamental laws governing its behavior, such as coherence time and resilience to phase noise, remain open problems. In this paper, we derive the structure of the optimal detector for the case of $M$-antenna MD. Then, we establish the governing law for DSK's coherence time, termed the Direction Coherence Time (DCT), defining the the temporal duration over which the DoA remains approximately invariant. We analytically establish that DCT scales with $d/v$ (transmitter-receiver distance over velocity), while the Channel Coherence Time (CCT) scales with $λ/v$, revealing a coherence time gain on the order of $d/λ$ (equivalent to more than four orders of magnitude.) Furthermore, we prove that DSK inherently cancels the phase noise, requiring no additional compensation. Analytical predictions are validated through simulations, confirming the robustness and scalability of DSK in high-frequency mobile environments.

Problem

• Analyzing DSK resilience to phase noise in mmWave systems
• Establishing Direction Coherence Time scaling laws for DSK
• Developing optimal detector for M-antenna mobile devices

Innovation

• Encodes data in Direction-of-Arrival using distributed antennas
• Derives optimal detector for M-antenna mobile devices
• Inherently cancels phase noise without compensation