Prerequisites & Notation

This chapter requires linear algebra (Chapter 6), digital modulation (Chapter 20), and MIMO channel models (Chapter 21).

SVD, matrix inversion, pseudoinverse (Chapter 6)(Review ch06)
Self-check: Can you compute np.linalg.svd and np.linalg.pinv?
QAM constellations and BER simulation (Chapter 20)(Review ch20)
Self-check: Can you implement ML detection for M-QAM?
MIMO channel matrices (Chapter 21)(Review ch21)
Self-check: Can you generate a correlated MIMO channel with the Kronecker model?

MIMO detection and precoding notation.

Symbol	Meaning	Introduced
$N_t$	Number of transmit antennas	s01
$N_r$	Number of receive antennas	s01
$\\mathbf{H}$	MIMO channel matrix ( $N_r \times N_t$ )	s01
$\\mathbf{x}$	Transmitted signal vector ( $N_t \times 1$ )	s01
$\\mathbf{y}$	Received signal vector ( $N_r \times 1$ )	s01
$\\mathbf{W}$	Precoding matrix ( $N_t \times N_s$ )	s02
$\\mathbf{G}$	Detection/equalization matrix ( $N_s \times N_r$ )	s01
$N_s$	Number of spatial streams	s01