Prerequisites & Notation

Before You Begin

This chapter treats coded caching over time-varying (fading) channels. The reader needs familiarity with block-fading models, coherence time, outage capacity, and pilot-based CSI estimation. Chapters 5–6 established the static-channel DoF result; this chapter introduces the time variation and shows how coded caching partially substitutes for CSIT.

Cache-aided MIMO BC and $\mathrm{DoF} = t + L$ (Ch 5)(Review ch05)
Self-check: Can you state the Lampiris-Caire DoF formula and its CSIT assumption?
Degraded BC with heterogeneous users (Ch 6)(Review ch06)
Self-check: Can you state the JLEC separation theorem for mixed cacheable/uncacheable traffic?
Block-fading channel model: coherence time $T_c$ , coherence bandwidth $B_c$ (Review ch06)
Self-check: Given $v = 60$ km/h at $f_c = 2$ GHz, can you estimate $T_c$ ?
Outage probability and outage capacity under Rayleigh fading(Review ch13)
Self-check: Can you derive the $\epsilon$ -outage capacity for a single-user Rayleigh channel?
Pilot-based CSI acquisition: estimation overhead(Review ch03)
Self-check: Why does the number of pilots in an $L$ -antenna system scale as $L$ ?
Interference alignment basics(Review ch26)
Self-check: What are the required CSIT assumptions for interference alignment to achieve optimal DoF?

Notation for This Chapter

Symbols introduced for the fading setting.

Symbol	Meaning	Introduced
$T_c$	Coherence block length in channel uses; $T_c = B_c \cdot T_{\text{coh}}$	s01
$\tau$	Number of pilot channel uses per coherence block (typically $\tau = L$ )	s02
$\hat{\mathbf{h}}_k$	Estimated channel to user $k$	s02
$\sigma_e^2$	CSIT estimation error variance	s02
$C_\epsilon$	$\epsilon$ -outage capacity	s04
$t$	Caching gain $t = KM/N$	s01
$L$	Number of transmit antennas $L$	s01
$\text{SNR}$	Transmit SNR	s01
$\mathbf{w}$	AWGN vector at the receiver	s01

← Ch 6 The Cache-Aided Fading Broadcast Channel