Prerequisites & Notation

Before You Begin

This chapter builds directly on the cell-free massive MIMO concept introduced in Chapter 11. We address the scalability bottleneck of the original formulation and develop user-centric architectures that make cell-free practical at scale. Familiarity with the following topics is essential.

Cell-free massive MIMO: architecture, no-cell principle, initial rate analysis(Review ch11)
Self-check: Can you write the cell-free downlink signal model $y_k = \sum_{m=1}^{M} \sqrt{\eta_{mk}} \hat{g}_{mk}^* s_k + \text{interference} + \text{noise}$ ?
Pilot contamination: shared pilots, estimation error scaling(Review ch03)
Self-check: Can you explain why pilot contamination does not vanish with increasing AP count in cell-free?
Achievable rate analysis: use-and-then-forget (UatF) bound(Review ch04)
Self-check: Can you derive the UatF SINR expression for MRC processing?
Power control: max-min fairness, bisection algorithm(Review ch05)
Self-check: Can you formulate the max-min power control problem as a convex feasibility problem?
Large-scale fading: path loss models, shadow fading
Self-check: Can you compute the large-scale fading coefficient $\beta_{mk} = \text{PL}(d_{mk}) \cdot 10^{\sigma_{\text{sh}} z / 10}$ ?

Notation for This Chapter

Symbols introduced in this chapter. See also the NGlobal Notation Table master table in the front matter.

Symbol	Meaning	Introduced
$M$	Total number of access points (APs) in the network	s01
$K$	Total number of users in the network	s01
$\mathcal{M}_k$	Serving cluster of APs for user $k$ (user-centric set)	s02
$\mathcal{K}_m$	Set of users served by AP $m$ (dual perspective)	s02
$D_{mk}$	Binary cluster indicator: $D_{mk} = 1$ if AP $m$ serves user $k$	s02
$\|\mathcal{M}_k\|$	Cluster size (number of serving APs) for user $k$	s02
$\beta_{mk}$	Large-scale fading coefficient between AP $m$ and user $k$	s01
$g_{mk}$	Channel coefficient between AP $m$ and user $k$	s01
$\hat{g}_{mk}$	MMSE channel estimate of $g_{mk}$	s01
$\gamma_{mk}$	Estimation quality: $\gamma_{mk} = \mathbb{E}[\|\hat{g}_{mk}\|^2]$	s01
$m^*(k)$	Master AP index for user $k$	s03
${\mathbf{S}_{i,k}}_{k}$	Pilot index assigned to user $k$	s04
$\tau_p$	Number of orthogonal pilot sequences	s04
$\mathcal{P}_t$	Set of users sharing pilot $t$ : $\mathcal{P}_t = \{k : {\mathbf{S}_{i,k}}_{k} = t\}$	s04

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