Prerequisites & Notation

Before You Begin

This chapter extends the MIMO broadcast channel theory of Chapter 16 and the interference channel results of Chapter 17 to advanced settings: user scheduling with many users, the ISAC tradeoff (a CommIT group contribution), and topological interference management. The reader should be comfortable with MIMO capacity, DPC, MAC-BC duality, and the degrees-of-freedom framework.

MIMO BC capacity region and DPC(Review ch16)
Self-check: Can you state the DPC rate region for the $K$ -user MIMO BC and explain the channel enhancement converse?
MAC-BC duality(Review ch16)
Self-check: Can you describe the duality transformation from MAC covariances to BC covariances?
Degrees of freedom and interference alignment(Review ch17)
Self-check: Can you state the $K$ -user IC DoF result and explain why IA requires global CSI?
MIMO channel capacity with CSIR and CSIT(Review ch13)
Self-check: Can you write the ergodic MIMO capacity formula and the water-filling solution?
Cramér-Rao bound and Fisher information
Self-check: Can you state the CRB for a vector parameter and relate it to the Fisher information matrix?

Notation for This Chapter

Key symbols for this chapter. We use notation consistent with earlier chapters and introduce new symbols for the ISAC framework.

Symbol	Meaning	Introduced
$K$	Number of users in the MIMO BC	s01
$n_t$	Number of transmit antennas at the base station	s01
$\mathbf{H}_{k}$	Channel matrix to user $k$	s01
$\mathcal{S} \subseteq [K]$	Scheduled user subset (size $\|\mathcal{S}\| \leq n_t$ )	s01
$R_{c}$	Communication rate	s02
$I_{s}$	Sensing mutual information	s02
$\mathbf{K}_c, \mathbf{K}_s$	Covariance matrices for communication and sensing signal components	s02
$\mathbf{J}(\boldsymbol{\theta})$	Fisher information matrix for target parameters	s02
$\mathcal{G} = (V, E)$	Interference topology graph	s03

← Ch 17 The

K

-User MIMO Broadcast Channel