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Doppler Effect: Analyses and Applications in Wireless Sensing and Communications

Lie-Liang Yang

TL;DR

This work delivers a unified, rigorous treatment of Doppler effects for electromagnetic and acoustic waves across uniform and general motion, including relativistic and medium-dependent regimes relevant to wireless sensing, communications, and ISAC. It develops generalized Doppler expressions that decompose contributions from relative motion, time dilation, propagation media, and gravity, and extends them to remote and close zones, accelerated motion, and atmospheric layers. Practical insights include ionospheric/tropospheric Doppler modeling via TEC and refractivity, Sagnac corrections in satellite navigation, and land/satellite sensing formulas that enable velocity estimation from Doppler measurements. The results advance accurate velocity estimation, robust sensing, and ISAC system design in mmWave, terahertz, optical, and acoustic domains, while highlighting atmospheric and relativistic effects that must be mitigated for high-precision applications.

Abstract

This chapter is motivated by the need for a rigorous and comprehensive analysis of the Doppler effects encountered by electromagnetic and acoustic signals across a diverse spectrum of modern applications. These include land mobile communications, various Internet of Things (IoT) networks, machine-type communications (MTC), and various radar and satellite-based systems for navigation and sensing, as well as the emerging regime of integrated sensing and communications (ISAC). A wide array of kinematic profiles is investigated, ranging from uniform motion and constant acceleration to more complex general motion. Consequently, the multi-faceted factors influencing the Doppler shift are addressed in detail, encompassing classical kinematics, special and general relativity, atmospheric dynamics, and the properties of the propagation medium. This work is intended to establish a definitive theoretical foundation for both the general enthusiast and the specialized researcher seeking to master the complexities of signal frequency shifts in modern wireless sensing and communications systems.

Doppler Effect: Analyses and Applications in Wireless Sensing and Communications

TL;DR

This work delivers a unified, rigorous treatment of Doppler effects for electromagnetic and acoustic waves across uniform and general motion, including relativistic and medium-dependent regimes relevant to wireless sensing, communications, and ISAC. It develops generalized Doppler expressions that decompose contributions from relative motion, time dilation, propagation media, and gravity, and extends them to remote and close zones, accelerated motion, and atmospheric layers. Practical insights include ionospheric/tropospheric Doppler modeling via TEC and refractivity, Sagnac corrections in satellite navigation, and land/satellite sensing formulas that enable velocity estimation from Doppler measurements. The results advance accurate velocity estimation, robust sensing, and ISAC system design in mmWave, terahertz, optical, and acoustic domains, while highlighting atmospheric and relativistic effects that must be mitigated for high-precision applications.

Abstract

This chapter is motivated by the need for a rigorous and comprehensive analysis of the Doppler effects encountered by electromagnetic and acoustic signals across a diverse spectrum of modern applications. These include land mobile communications, various Internet of Things (IoT) networks, machine-type communications (MTC), and various radar and satellite-based systems for navigation and sensing, as well as the emerging regime of integrated sensing and communications (ISAC). A wide array of kinematic profiles is investigated, ranging from uniform motion and constant acceleration to more complex general motion. Consequently, the multi-faceted factors influencing the Doppler shift are addressed in detail, encompassing classical kinematics, special and general relativity, atmospheric dynamics, and the properties of the propagation medium. This work is intended to establish a definitive theoretical foundation for both the general enthusiast and the specialized researcher seeking to master the complexities of signal frequency shifts in modern wireless sensing and communications systems.
Paper Structure (37 sections, 282 equations, 23 figures, 1 table)

This paper contains 37 sections, 282 equations, 23 figures, 1 table.

Table of Contents

  1. Introduction
  2. Theoretical Basis of the Doppler Effect
  3. Doppler Effect in Uniform Motion
  4. Non-Relativistic Doppler Effect in Remote Zones
  5. Stationary Source and Moving Receiver
  6. Moving Source and Stationary Receiver
  7. Geometric Analysis of Doppler Effect
  8. Moving Source and Moving Receiver
  9. Non-Relativistic Doppler Effect in Close Zones
  10. Relativistic Doppler Effect
  11. Longitudinal Relativistic Doppler Effect
  12. Relativistic Doppler Effect in Uniform Medium
  13. Doppler Effect in General Motion
  14. Non-relativistic Doppler Effect in General Motion
  15. General Motiving Source and Stationary Observer
  16. ...and 22 more sections

Figures (23)

  • Figure 1: A plane wave generated by a remote-zone static (or moving) source is received by a moving (or static) receiver.
  • Figure 2: Graphic explanation of the Doppler effect occurred in remote zones. S=Source, R=Receiver.
  • Figure 3: A source sends radio signals to a receiver in its close-zone: (a) stationary source and moving receiver, (b) moving source and stationary receiver.
  • Figure 4: Graphic representation of the Doppler effect in general motion.
  • Figure 5: Graphic representation of the Doppler effect in general motion.
  • ...and 18 more figures

Theorems & Definitions (21)

  • Example 1
  • Example 2
  • Remark 1
  • Remark 2
  • Remark 3
  • Example 3
  • Example 4
  • Example 5
  • Remark 4
  • Example 6
  • ...and 11 more