Chapter 21: Array-Fed RIS and Reflective Architectures

Learning Objectives

• State the passive RIS signal model with programmable phase shifts $\Phi_n = e^{j\phi_n}$ and identify the double-fading problem that limits the Tx $\to$ RIS $\to$ Rx link
• Construct the array-fed RIS architecture in which a small active array of $N_a$ elements illuminates a passive RIS of $N_{\text{RIS}} \gg N_a$ elements, and explain how it avoids double fading by transmitting all power through a short Tx-to-RIS link
• Derive the effective cascaded channel $\mathbf{H}_{\text{eff}} = \mathbf{H}_{\text{RIS-Rx}} \,\text{diag}(\boldsymbol{\phi})\, \mathbf{H}_{\text{Tx-RIS}}$ and analyse its rank / eigenmode structure as a function of $N_a$ and $N_{\text{RIS}}$
• Jointly optimize the RIS phase profile and the active-array precoder for multiuser multibeam operation and quantify the achievable sum rate versus $N_{\text{RIS}}$ and $K$
• Compare the array-fed RIS with a fully digital array of equal aperture on three axes: achievable rate, transmit-power budget, and RF-chain count, and identify the operating points where array-fed RIS dominates
• Recognize how the CommIT array-fed RIS architecture of Caire and collaborators operationalizes these ideas at mmWave and sub-THz