Prerequisites & Notation

Prerequisites for Chapter 13

This chapter builds on the cell-free and user-centric framework developed in Chapters 11–12 and requires familiarity with linear receiver design from Chapter 9.

Cell-free massive MIMO system model and motivation(Review MIMO Ch. 11)
Self-check: Can you write the uplink received signal at AP $m$ : $y_m = \sum_{k=1}^{K} g_{mk} \sqrt{p_k} s_k + w_m$ ?
User-centric clustering and scalability(Review MIMO Ch. 12)
Self-check: Can you explain why full cell-free processing is not scalable and how user-centric clustering resolves the issue?
MMSE channel estimation under pilot contamination(Review MIMO Ch. 3)
Self-check: Can you derive the MMSE channel estimate $\hat{g}_{mk}$ and express the estimation error variance?
Use-and-then-forget (UatF) bound for achievable rates(Review MIMO Ch. 4)
Self-check: Can you state the UatF bound and explain why it decouples beamforming gain from interference?
Linear receivers: MRC, ZF, and MMSE(Review MIMO Ch. 9)
Self-check: Can you write the MMSE combining vector $\mathbf{v}_{k} = (\sum_j p_j \hat{\mathbf{g}}_j \hat{\mathbf{g}}_j^H + \mathbf{C} + \sigma^2 \mathbf{I})^{-1} \hat{\mathbf{g}}_k$ ?
Power control: max-min fairness(Review MIMO Ch. 5)
Self-check: Can you formulate the max-min fairness power control problem as a quasi-linear program?

Chapter 13 Notation

Notation specific to distributed processing in cell-free massive MIMO.

Symbol	Meaning	Introduced
$M$	Number of access points (APs)	s01
$K$	Number of users	s01
$N$	Number of antennas per AP	s01
$g_{mk}$	Channel between AP $m$ and user $k$ (single-antenna AP)	s01
$\mathbf{g}_{mk}$	Channel vector between AP $m$ and user $k$ (multi-antenna AP, $N \times 1$ )	s01
$\beta_{mk}$	Large-scale fading coefficient between AP $m$ and user $k$	s01
$\hat{\mathbf{g}}_{mk}$	MMSE estimate of $\mathbf{g}_{mk}$	s01
$\gamma_{mk}$	Variance of MMSE channel estimate: $\gamma_{mk} = \mathbb{E}[\|\hat{g}_{mk}\|^2]$	s01
$\mathbf{a}_{mk}$	Local combining vector at AP $m$ for user $k$	s01
$\\hat{s}_{mk}$	Local estimate of user $k$ 's symbol at AP $m$	s01
$\\boldsymbol{\\alpha}_k$	LSFD weight vector for user $k$ ( $M \times 1$ )	s03
$C_{\\text{fh}}$	Fronthaul capacity per AP (bits per channel use)	s05
$\\text{SINR}_k^{(\\ell)}$	SINR of user $k$ under Level $\ell$ cooperation	s02
$\\mathcal{M}_k$	Set of APs serving user $k$ (user-centric cluster)	s01
$\\mathcal{D}_m$	Set of users served by AP $m$	s01

← Ch 12 Centralized vs. Distributed Processing