[Paper Review] Doppler Effect: Analyses and Applications in Wireless Sensing and Communications

Lie-Liang Yang|arXiv (Cornell University)|Feb 10, 2026

Radio Wave Propagation Studies0 citations

TL;DR

This chapter provides a comprehensive theoretical analysis of the Doppler effect across uniform, general, and accelerated motions in EM and acoustic signals, with applications to wireless sensing, ISAC, and navigation, including atmospheric and relativistic considerations.

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.

Motivation & Objective

• Establish a rigorous theoretical foundation for Doppler shifts in modern wireless sensing and communications.
• Bridge traditional Doppler analyses with mmWave, terahertz, and optical bands where ray-level Doppler effects matter.
• Characterize Doppler effects due to atmosphere, gravity, and propagation media in ISAC and ISAGN contexts.
• Provide practical guidance for velocity estimation and sensing by distinguishing Doppler contributions from different factors.

Proposed method

• Derive Doppler shift formulas from phase, time, and path-length variations using classical kinematics and relativity.
• Differentiate remote vs. close zone analyses and provide plane-wave versus spherical-wave treatments.
• Incorporate propagation medium and refractive index variations via the phase path P(n,t) and its time derivative.
• Present non-relativistic and relativistic Doppler effects for uniform and general motion, including multiple moving transmitter/receiver scenarios.
• Illustrate with examples and geometric interpretations to highlight asymmetries between moving source and moving receiver.

Figure 1: A plane wave generated by a remote-zone static (or moving) source is received by a moving (or static) receiver.

Experimental results

Research questions

• RQ1 How does Doppler shift depend on relative motion in various zones (remote vs close) and motion configurations (source/receiver moving, both moving, with acceleration).
• RQ2 What additional Doppler contributions arise from propagation medium, atmospheric conditions, and gravitational effects in ISAC and satellite navigation contexts.
• RQ3 How can ray-level Doppler effects be estimated and separated in sparse, mmWave/terahertz channels for sensing and communications.
• RQ4 What are the limits of non-relativistic approximations and when are relativistic corrections necessary.

Key findings

• Doppler frequency shifts can be expressed via fD = - (f/c) dP(n,t)/dt, where P(n,t) accounts for path length and refractive index along the propagation path.
• In remote zones, moving receiver or source yields f' ≈ f (1 ± v cosθ / c), with exact forms depending on which end moves and the geometry.
• In close zones, spherical-wave effects require solving for T' with a quadratic relation, yielding corrections to T and f' that depend on r1 and v, θ′.
• When both source and receiver move, the Doppler effect generalizes to f' = f[(1 - (v′ cosθ′)/c) / (1 - (v cosθ)/c)], highlighting asymmetries at finite speeds.
• Relativistic and gravitational-field effects introduce additional Doppler-like shifts, including time-dilation contributions and gravity-induced frequency changes, relevant for satellite navigation and ISAGN.
• Atmospheric propagation (ionosphere, troposphere) introduces path-dependent Doppler variations that must be accounted for to achieve accurate sensing and navigation.

Figure 2: Graphic explanation of the Doppler effect occurred in remote zones. S=Source, R=Receiver.