Chapter 1: The Delay-Doppler Domain

Learning Objectives

• Understand why multipath and mobility naturally produce a discrete, sparse representation in the delay-Doppler plane
• State Bello's four equivalent system functions and map each into a physical picture
• Derive the spreading function and the scattering function from first principles
• Contrast the time-frequency representation (dense, time-varying) with the delay-Doppler representation (sparse, time-invariant)
• Translate system parameters — bandwidth, frame duration, mobility — into delay and Doppler resolutions