Doppler Effect: Analyses and Applications in Wireless Sensing and Communications

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.

💡 Research Summary

This chapter provides a comprehensive treatment of the Doppler effect as it applies to modern wireless sensing and communication systems, spanning electromagnetic (EM) and acoustic waves. It begins by highlighting the limitations of traditional textbook treatments, which typically address only a few simple scenarios such as non‑relativistic uniform motion of a source or receiver, or the classic relativistic longitudinal Doppler shift. Recognizing that contemporary systems operate at millimeter‑wave, terahertz, and even optical frequencies, and often integrate sensing and communication functions (ISA‑C), the authors argue that a more rigorous, physics‑based analysis is required.

The theoretical foundation is built on the representation of a wave as a space‑time dependent cosine function, from which frequency and phase relationships are derived. The Doppler phenomenon is reframed in terms of a time‑varying phase path (P(t)), which incorporates both the geometric distance (r(t)) between transmitter and receiver and the refractive index (n(t)) of the propagation medium. This leads to a generalized Doppler formula:
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