Chapter 4: The Delay-Doppler Channel Model

Learning Objectives

• Derive the continuous-time DD input-output relation $y(\tau, \nu) = h \star\star x$ from the time-domain channel
• State and prove the discrete-time DD input-output relation with $P$ sparse taps
• Build the $MN \times MN$ DD channel matrix and characterize its sparsity
• Establish the time-invariance of the DD channel: one kernel $h(\tau, \nu)$ suffices for the entire frame
• Quantify the sparsity advantage: $P$ parameters vs $MN$ parameters, with concrete consequences for estimation and detection