Prerequisites & Notation

Before You Begin

This chapter extends massive MIMO from narrowband to wideband (frequency-selective) channels using OFDM. The reader should be comfortable with the following topics before proceeding.

OFDM system model: cyclic prefix, DFT decomposition, parallel flat-fading subchannels(Review ch24)
Self-check: Can you explain why the cyclic prefix converts a linear convolution into a circular one?
Massive MIMO channel estimation: LS/MMSE estimation, pilot contamination(Review ch03)
Self-check: Can you write the MMSE channel estimate given pilot observations and channel covariance?
Linear precoding in massive MIMO: MRT, ZF, regularized ZF(Review ch06)
Self-check: Can you write the ZF precoding matrix and its per-user SINR expression?
Frequency-selective fading and coherence bandwidth(Review ch10)
Self-check: Can you relate the RMS delay spread $\sigma_\tau$ to the coherence bandwidth $B_c$ ?

Notation for This Chapter

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

Symbol	Meaning	Introduced
$\mathbf{H}[k]$	Channel matrix at subcarrier $k$ , dimension $N_t \times N_r$	s01
$L$	Number of resolvable delay taps in the frequency-selective channel	s01
$\mathbf{H}_\ell$	$\ell$ -th delay-domain channel tap matrix	s01
$N$	Number of OFDM subcarriers (DFT size)	s01
$\Delta f$	OFDM subcarrier spacing (Hz)	s01
$T_{\text{cp}}$	Cyclic prefix duration	s01
$\mathbf{W}[k]$	Precoding matrix at subcarrier $k$	s02
$\mathcal{P}$	Set of pilot subcarrier indices	s03
$N_p$	Number of pilot subcarriers per coherence block	s03
$\hat{\mathbf{H}}[k]$	Estimated channel matrix at subcarrier $k$	s03
$f_k$	$k$ -th OFDM subcarrier frequency	s01

← Ch 9 The Wideband Massive MIMO Channel