Prerequisites & Notation

Before You Begin

This chapter builds directly on the achievable rate expressions derived in Chapter 4. We assume the reader is comfortable with the UatF bound and the closed-form SINR expressions for MRC, ZF, and MMSE combining. Basic convex optimization (KKT conditions, duality, geometric programming) is used throughout.

Achievable rate expressions with MRC, ZF, and MMSE combining(Review mimo-ch04)
Self-check: Can you write down the closed-form SINR expression for user $k$ under ZF combining in a massive MIMO system?
Channel estimation and pilot contamination(Review mimo-ch03)
Self-check: Can you express the MMSE channel estimate $\hat{\mathbf{h}}_k$ and its error covariance?
Channel hardening and favorable propagation(Review mimo-ch01)
Self-check: Do you understand why $\frac{1}{N_t} \mathbf{H}_{k}^{H} \mathbf{H}_{k} \to \beta_{k}$ as $N_t \to \infty$ ?
Convex optimization basics (KKT conditions, duality)
Self-check: Can you state the KKT conditions for a constrained convex problem and explain complementary slackness?

Notation for This Chapter

Symbols introduced or heavily used in this chapter. See also the global notation table in the front matter.

Symbol	Meaning	Introduced
$p_k$	Transmit power allocated to user $k$	s01
$R_k$	Achievable rate (spectral efficiency) of user $k$	s01
$\text{SINR}_k$	Signal-to-interference-plus-noise ratio for user $k$	s01
$\beta_{k}$	Large-scale fading coefficient (path loss) of user $k$	s01
$K$	Number of users	s01
$N_t$	Number of base station antennas	s01
$\sigma^2$	Noise variance	s01
$P_t$	Total transmit power budget	s01
$\alpha$	Fractional power control exponent	s04
$\gamma_{kl}$	Interference coupling coefficient from user $l$ to user $k$	s01
$t$	Target minimum rate in max-min fairness (bisection variable)	s01

← Ch 4 Max-Min Fairness