Prerequisites & Notation

Before You Begin

This chapter builds on MU-MIMO precoding (Chapter 6) and channel estimation with spatial correlation (Chapters 2–3). A solid grasp of eigenvalue decomposition and subspace projections (Book Telecom, Chapter 1) is essential.

Spatially correlated channel models: one-ring, Kronecker, angular domain(Review mimo-ch02)
Self-check: Can you write the channel covariance $\mathbf{R}_k = \mathbb{E}[\mathbf{h}_k \mathbf{h}_k^H]$ for a ULA with a given angular spread?
MMSE channel estimation under spatial correlation(Review mimo-ch03)
Self-check: Can you state how the MMSE channel estimate exploits the covariance eigenspace?
Linear precoding: MRT, ZF, regularized ZF(Review mimo-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?
Eigenvalue decomposition of Hermitian matrices(Review telecom-ch01)
Self-check: Can you compute the eigenvalues and eigenvectors of a $3 \times 3$ Hermitian matrix?

Notation for This Chapter

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

Symbol	Meaning	Introduced
$\mathbf{R}_k$	Spatial covariance matrix of user $k$ : $\mathbf{R}_k = \mathbb{E}[\mathbf{h}_k \mathbf{h}_k^H]$	s01
$\mathbf{U}_g$	Eigenvector matrix spanning the dominant eigenspace of group $g$	s01
$r_g$	Effective rank (dimension) of group $g$ 's channel subspace	s01
$\mathcal{G}$	Set of user groups: $\mathcal{G} = \{1, \ldots, G\}$	s01
$\mathbf{B}_g$	Pre-beamforming matrix for group $g$ ( $N_t \times r_g$ )	s02
$\mathbf{P}_g$	Inner MU-MIMO precoding matrix for group $g$ ( $r_g \times \|\mathcal{S}_g\|$ )	s02
$\tilde{\mathbf{H}}_k$	Effective reduced-dimension channel: $\tilde{\mathbf{H}}_k = \mathbf{H}_{k}^{H} \mathbf{B}_g$	s02
$\mathcal{S}_g$	Set of users assigned to group $g$	s01
$G$	Total number of user groups	s01
$N_t$	Number of transmit antennas at the base station	s01
$K$	Total number of users	s01
$R_k$	Achievable rate for user $k$ (bits/s/Hz)	s04

← Ch 6 Spatial Correlation Structure