Prerequisites & Notation

Before You Begin

This chapter builds on relay channel fundamentals, multiple-access capacity, and Gaussian channel theory. Ensure you are comfortable with the following before proceeding.

Relay channel models: decode-and-forward and compress-and-forward(Review ch22)
Self-check: Can you state the DF and CF achievable rates for the relay channel?
Cut-set bound for relay networks(Review ch22)
Self-check: Can you write the cut-set bound for a two-relay diamond network?
Multiple-access channel capacity region(Review ch14)
Self-check: Can you sketch the MAC capacity region for two users and identify the corner points?
Gaussian channel capacity and water-filling(Review ch10)
Self-check: Can you derive the water-filling power allocation for parallel Gaussian channels?
Wyner-Ziv source coding with side information(Review ch07)
Self-check: Can you state the Wyner-Ziv rate-distortion function?
MIMO channel model and capacity
Self-check: Can you write the MIMO capacity $C = \log\det(\mathbf{I} + \text{SNR}\,\mathbf{H}\mathbf{H}^{H})$ and explain the role of each term?

Notation for This Chapter

Symbols introduced in this chapter. See also the global notation table in the front matter.

Symbol	Meaning	Introduced
$K$	Number of cooperating users or access points	s01
$X_k, Y_k$	Transmitted and received signals at user/AP $k$	s01
$d^*(r)$	Optimal diversity-multiplexing tradeoff function	s01
$C_{\text{fh}}$	Fronthaul capacity (bits per channel use)	s02
$\hat{Y}_k$	Quantized observation at relay/AP $k$	s02
$\mathbf{H}_{k}$	Channel vector from user to AP $k$	s02
$L$	Number of access points in cell-free architecture	s03
$\mathbf{g}_{kl}$	Channel coefficient from user $k$ to AP $l$	s03
$\beta_{kl}$	Large-scale fading coefficient from user $k$ to AP $l$	s03
$\eta_{kl}$	Power control coefficient at AP $l$ for user $k$	s03

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