Chapter 5: Joint Active-Passive Beamforming

Learning Objectives

• State the joint active-passive beamforming problem as rate maximization over $\mathbf{W}$ and $\boldsymbol{\Phi}$ with the unit-modulus constraint
• Explain why the problem is non-convex and identify the unit-modulus constraint as the source
• Derive the alternating-optimization framework: fix $\mathbf{W}$, optimize $\boldsymbol{\Phi}$; fix $\boldsymbol{\Phi}$, optimize $\mathbf{W}$
• Prove the convergence of AO to a stationary point and discuss the local-minimum risk
• Use the AO framework to compute the rate under realistic CSI conditions