Chapter Summary

Chapter 24 Summary: Massive MIMO for ISAC

Key Points

• 1.

  Massive MIMO is the natural ISAC platform. The $N_t^{2}$ coherent array gain of a colocated array (one $N_t$ from transmit beamforming, one from receive combining) turns a communication-grade transmit power of 30 dBm into a 48 dB sensing gain that easily detects vehicle-sized targets at 100+ m. The spatial DoF surplus $N_t - K$ gives the sensing beam a wide null space in which to live without stealing DoF from communication.

• 2.

  Capacity–distortion is the unifying framework. On Gaussian MIMO channels, the Pareto boundary of communication rate versus sensing MSE is the image of a convex program in the transmit covariance $\mathbf{R}_x$, traced parametrically by a single Lagrange multiplier $\mu$ that trades mutual information against Fisher information. The CommIT result of Liu/Caire (IEEE TIT 2023) is the first fully information-theoretic synthesis of the tradeoff — and it shows that time-sharing is strictly suboptimal.

• 3.

  Beampattern synthesis is an SDP. Joint ISAC precoder design for specified per-user SINRs and a desired sensing beampattern reduces to a semidefinite program in per-user covariances $\mathbf{R}_k \succeq 0$ plus a sensing-only covariance $\mathbf{R}_s$. The problem is convex, polynomial-time, and typically yields rank-one $\mathbf{R}_k^\star$ at the optimum — making SDR tight and the per-user beamformers extractable by eigendecomposition.

• 4.

  Cell-free ISAC buys diversity. Distributed APs realize a multistatic sensing network whose target detection probability satisfies $1 - P_d \sim \mathcal{O}(\rho^{-L})$: each added AP increases the diversity order by one. The Liu–Wan–Caire cell-free ISAC architecture sidesteps the monostatic self-interference problem by separating Tx and Rx across APs, and reuses the same fronthaul the comm network already depends on.

• 5.

  OTFS is the ISAC-native waveform. The delay-Doppler domain where OTFS data lives is the same domain where targets manifest: the comm equalizer and the sensing detector merge into a single delay-Doppler channel estimator. OTFS-ISAC (Yuan–Schober–Caire 2021, Gaudio–Kobayashi–Caire 2020) matches CRB on range and velocity, retains full communication rates, and is robust at vehicular Doppler where OFDM suffers ICI loss.

• 6.

  Deterministic–random duality shapes the waveform. Communication prefers random waveforms (high entropy for Shannon capacity); sensing prefers deterministic waveforms (low variance for CRB). Liu et al. (TIT 2023) show that the optimal ISAC input is a convex dither between these extremes, with the mixing weight set by the same Lagrange multiplier $\mu$ from the capacity-distortion function. Every practical ISAC waveform — from 5G NR OFDM with probing beams to 6G OTFS — is an instance of this recipe.