Chapter Summary

Chapter Summary

Key Points

• 1.

  MIMO-OTFS is the DD-angle channel tensor. A MIMO-OTFS channel with $P$ paths, $M \times N$ DD grid, and $N_r \times N_t$ antennas has $7P$ real parameters — roughly 10,000 times smaller than the dense time-varying MIMO channel matrix. This sparsity drives all the favourable properties of MIMO-OTFS-ISAC.

• 2.

  Sensing depends only on $\mathbf{R}_x$; comms depends on $\mathbf{F}$. The structural asymmetry is the lever for joint ISAC beamforming. Two precoders with the same $\mathbf{F}\mathbf{F}^H$ produce identical sensing; pick among them the one that maximizes comms rate. The resulting problem reduces to an SDP on the covariance cone, solvable globally in tens of ms.

• 3.

  The rate-CRB Pareto frontier has a knee. The frontier is concave (achievable region is convex), so a linear-scalarized SDP parameterized by $\alpha \in [0, 1]$ traces out all Pareto-optimal points. For angularly separated comms and sensing, the knee retains $\geq 85\%$ of both single-objective optima — the quantitative case for joint ISAC vs separate designs.

• 4.

  Multi-target tracking on DD-angle is cm-level. Extended Kalman filtering with DD-angle observations and constant-velocity state model achieves steady-state position MSE $\sim 1$ cm at 100 Hz frame rate with modern mmWave arrays. Predictive beamforming provides a multiplicative factor $N_t/T_{\text{tgt}}$ of additional gain over blind illumination.

• 5.

  CommIT contribution: Liu-Caire 2022 covariance formulation; Cui-Yuan-Caire 2023 predictive MIMO-OTFS tracking. These two results together define the quantitative foundation for joint ISAC beamforming in the OTFS literature — the former establishes the convex structure and the latter establishes the tracking dynamics.

• 6.

  Silicon-feasibility is realistic. $10^{10}$ ops/sec for a representative automotive BS; $\sim 10^8$ ops/sec for urban cellular. 2024-era automotive SoCs already accommodate this. 77 GHz automotive ISAC is commercially deployable 2025+; 28 GHz cellular ISAC expected in 6G (2028+).

• 7.

  Scale reasoning. DD-based processing scales as $\mathcal{O}(MN \cdot P \cdot N_r)$, whereas TF-based processing scales as $\mathcal{O}(MN \cdot N_t \cdot N_r)$ — the former exploits channel sparsity, the latter does not. For $P \ll N_t$ (typical), DD-based is 10-100$\times$ cheaper.