Chapter 22: Relay, Cooperative, and Multi-Hop Communications

Learning Objectives

• Describe the three canonical relay protocols — decode-and-forward (DF), amplify-and-forward (AF), and compress-and-forward (CF) — and derive their achievable rates relative to the cut-set bound
• Analyse cooperative diversity protocols (repetition-coded, space-time-coded, and selection relaying) and prove that full spatial diversity order is achievable with single-antenna cooperating nodes
• Optimise the relay position between source and destination and derive the optimal placement as a function of path-loss exponent and protocol type
• Explain two-way relay communication with physical-layer network coding and quantify the spectral efficiency gain over conventional four-phase exchange
• State the Gupta--Kumar scaling law $\Theta(1/\sqrt{n \log n})$ for the per-node throughput in a random wireless network and explain the role of the transport capacity
• Compare hierarchical cooperation (Ozgur--Leveque--Tse) with multi-hop and quantify the linear throughput scaling $\Theta(1)$ achievable with MIMO cooperation
• Evaluate relay-assisted rates as a function of SNR and relay position, understanding when relaying outperforms direct transmission