Prerequisites & Notation

Before You Begin

Chapter 17 closes the technical development of the book by composing AirComp (Chapter 16), federated learning fundamentals (Chapter 9), and secure aggregation (Chapter 10) into a single wireless-FL pipeline. The golden thread — privacy, robustness, communication efficiency — is here recast as a three-way design trade-off over a physical wireless channel. The CommIT contribution on information-theoretically secure federated representation learning appears in §17.4.

FedAvg and FL convergence (§9.2)(Review ch09)
Self-check: State the convergence rate of FedAvg under smoothness and bounded gradient assumptions.
Secure aggregation threat model (Chapter 10)(Review ch10)
Self-check: Recall the honest-but-curious server model and its privacy objective.
AirComp MSE bound (Theorem 16.2.1)(Review ch16)
Self-check: State $\mathsf{MSE}^{\star}$ as a function of $\min_k \gamma_k$ .
Wireless resource allocation basics(Review ch06)
Self-check: What does water-filling power allocation optimize?
Stochastic gradient descent convergence(Review ch28)
Self-check: How does noisy gradient descent with variance $\sigma^2$ behave asymptotically for strongly-convex losses?

Notation for This Chapter

Chapter 17 combines FL notation (rounds, learning rate, gradients) with wireless notation (channel, power, MSE).

Symbol	Meaning	Introduced
$t$	FL round index, $t = 0, 1, \ldots, T - 1$	s01
$T$	Total FL rounds (budget)	s01
$\boldsymbol{\theta}_t$	Global model parameters at round $t$	s01
$\mathbf{g}_k^{(t)}$	Local gradient of user $k$ at round $t$	s01
$\eta_{\text{lr}}$	Learning rate (distinguished from receive amplitude)	s01
$\hat{\mathbf{G}}_t$	Estimated aggregate gradient at round $t$	s01
$\ntn{mseagg}$	Per-round aggregation MSE $= \mathbb{E}[\\|\hat{\mathbf{G}}_t - \sum_k \mathbf{g}_k^{(t)}\\|^2]$	s02
$\mathcal{S}_t \subseteq [n]$	Scheduled users at round $t$	s03
$L$	Smoothness constant of the FL loss	s02
$\mu$	Strong-convexity constant of the FL loss	s02
$\mathbf{z}_k$	Learned representation of user $k$ (§17.4)	s04

← Ch 16 The Wireless FL Pipeline