Prerequisites & Notation

Before You Begin

Chapter 13 treated MIMO-OTFS for ISAC — the channel was a tool for joint sensing and communication. This chapter zooms in on the modulation-and-detection side: MIMO-OTFS as a pure wireless waveform, serving multiple data streams over the delay-Doppler- angle tensor without the ISAC overlay. Most of the tools reappear — beamforming, spatial multiplexing, ZF/MMSE detection — but the DD-domain framing gives them a different flavor from MIMO-OFDM.

DD channel model(Review OTFS Ch. 4)
Self-check: Can you write the discrete DD input-output relation $\mathbf{y} = \mathbf{H}_{DD}\mathbf{x} + \mathbf{w}$ ?
OTFS modulation and detection(Review OTFS Ch. 6, Ch. 8)
Self-check: Do you remember the ISFFT/SFFT chain and how MP detection works on the factor graph?
MIMO fundamentals (SVD, beamforming, ZF/MMSE)(Review Telecom Ch. 18, 19)
Self-check: Can you write the ZF and MMSE detectors for a flat MIMO channel?
MIMO-OTFS-ISAC tensor channel(Review OTFS Ch. 13)
Self-check: Can you state the MIMO DD spreading function and its parameter count $7P$ ?

Notation for This Chapter

MIMO-OTFS symbols introduced or specialized here.

Symbol	Meaning	Introduced
$N_t, N_r$	Number of transmit/receive antennas	s01
$N_s$	Number of spatial data streams	s03
$\mathbf{a}(\theta) \in \mathbb{C}^{N_r}$	Array response vector at angle $\theta$	s01
$\mathcal{H}_{\mathrm{DD}} \in \mathbb{C}^{N_r \times N_t \times MN}$	MIMO-OTFS channel tensor (Rx × Tx × DD grid)	s01
$\mathbf{F}_{BS}, \mathbf{W}_{BS}$	Beamspace transmit and receive matrices (DFT-like)	s02
$\mathbf{V} \in \mathbb{C}^{N_t \times N_s}$	Precoding matrix (spatial)	s03
$\mathbf{U} \in \mathbb{C}^{N_r \times N_s}$	Combining/equalization matrix (spatial)	s03
$d(r)$	Diversity-multiplexing tradeoff function	s04

← Ch 15 The 3D MIMO-OTFS Channel Tensor