Chapter 24: Information-Theoretic Bounds for Estimation

Learning Objectives

• State and prove the Van Trees inequality as the Bayesian counterpart of the CRLB
• Derive the Ziv-Zakai bound via binary hypothesis testing between neighboring parameters
• Explain why Ziv-Zakai is tighter than the CRLB in the threshold region of non-linear estimation
• State and apply the Guo-Shamai-Verdu I-MMSE identity connecting mutual information to MMSE
• Formulate the joint delay-angle-Doppler CRB for an ISAC system
• Describe the rate-CRB tradeoff and set up the beampattern design problem for ISAC