Prerequisites & Notation

Before You Begin

This chapter introduces the cell-free massive MIMO paradigm. We assume fluency with the following topics. If any item feels unfamiliar, revisit the linked material before proceeding.

Channel hardening and favorable propagation in massive MIMO(Review ch01)
Self-check: Can you state the channel hardening law and explain why $\frac{1}{N_t} \mathbf{H}_{k}^{H} \mathbf{H}_{k} \to 1$ as $N_t \to \infty$ ?
Linear precoding: MRT, ZF, MMSE(Review ch06)
Self-check: Can you write the ZF precoder $\mathbf{W} = \mathbf{H}(\mathbf{H}^{H} \mathbf{H})^{-1}$ and explain when it is near-optimal?
Achievable rate analysis with the UatF bound(Review ch04)
Self-check: Can you derive a closed-form rate expression using the use-and-then-forget technique?
Pilot contamination and its impact on channel estimation(Review ch03)
Self-check: Can you explain why non-orthogonal pilots across cells cause an estimation floor that does not vanish with $N_t$ ?
Multi-cell cooperation and CoMP basics
Self-check: Can you describe Joint Transmission and Coordinated Scheduling as CoMP strategies? (See Telecom Ch. 24.6.)

Notation for This Chapter

Symbols introduced or specialized in this chapter. See the NGlobal Notation Table master table for general conventions.

Symbol	Meaning	Introduced
$L$	Number of access points (APs) in the cell-free network	s03
$K$	Number of users served simultaneously	s01
$N$	Number of antennas per AP (often $N = 1$ in the canonical cell-free model)	s03
$\mathbf{H}_{lk}$	Channel vector from AP $l$ to user $k$ , $\mathbf{H}_{lk} \in \mathbb{C}^N$	s03
$\beta_{lk}$	Large-scale fading coefficient between AP $l$ and user $k$	s03
$\hat{\mathbf{H}}_{lk}$	MMSE estimate of $\mathbf{H}_{lk}$ at AP $l$	s03
$\gamma_{lk}$	Mean-square channel estimation quality: $\gamma_{lk} = \mathbb{E}[\\|\hat{\mathbf{H}}_{lk}\\|^2] / N$	s04
$\eta_k$	Power control coefficient for user $k$ (downlink)	s04
$\text{SINR}_k^{\text{cell}}$	Downlink SINR of user $k$ in a conventional cellular network	s01
$\text{SINR}_k^{\text{cf}}$	Downlink SINR of user $k$ in the cell-free architecture	s04
$R_k$	Achievable downlink rate for user $k$ (bits/s/Hz)	s01

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