Integrated Sensing and Communications (ISAC)

• Integrated Sensing and Communications (ISAC) is a unified paradigm that jointly performs localization, environmental perception, and data exchange using shared spectral, hardware, and signal resources.
• ISAC leverages high-dimensional antenna arrays, CRB-based sensing uncertainty, and mutual information frameworks to optimize resource allocation and improve motion planning.
• Its practical impact is demonstrated in enhancing autonomous vehicle safety and efficiency through real-time, convex optimization-driven trajectory planning.

Integrated Sensing and Communications (ISAC) is a unified paradigm in wireless system engineering that enables joint localization, situational environment perception, and data exchange using shared spectral, hardware, and signal resources. ISAC has moved beyond treating sensing and communications as independent operations, bridging physical-layer resource allocation with motion-level planning and application-layer intelligence. Recent research demonstrates that purposefully linking sensing uncertainty with motion planning, for instance in autonomous vehicle contexts, significantly improves operational safety and efficiency by focusing resources on bottleneck obstacles and dynamically expanding navigable paths (Jin et al., 27 Oct 2025). The technical landscape includes mutual information frameworks, estimation bounds linking transmit power to localization accuracy, advanced optimization architectures, and real-time distributed algorithms.

1. Physical Layer System Model and Joint Signal Structure

ISAC systems utilize high-dimensional antenna configurations—such as massive MIMO arrays in roadside units (RSUs)—to simultaneously transmit beamformed signals for both sensing and communication tasks. The transmitter generates a matrix $\mathbf{F}=[\,\mathbf{f}_1,\dots,\mathbf{f}_K\,]$ where $\mathbf{f}_k = \mathbf{a}(\theta_k)$ points toward each obstacle vehicle (OV) at angle $\theta_k$. The received radar echo and downlink communication signals are modeled as:

$$\mathbf{y}_k^R(t) = \kappa_R\,\beta_k\,\sqrt{p_k}\,\mathbf{b}(\theta_k)\,\mathbf{a}^H(\theta_k)\mathbf{f}_k\,\tilde s_k(t-\tau_k) + \mathbf{z}_k^R(t)$$

$$y_k^C(t) = \kappa_C\,\alpha_k\,\sqrt{p_k}\,\mathbf{a}^H(\theta_k)\mathbf{f}_k\,\tilde s_k(t-\tfrac{\tau_k}{2}) + z_k^C(t)$$

Here $p_k$ is the per-beam transmit power, and $\kappa_R, \kappa_C$ are array gains dependent on the number of transmit/receive antennas. By reusing these beams for sensing (measuring $(\theta_k,d_k)$) and communication, ISAC systems leverage hardware and spectral efficiencies while introducing a direct coupling between the physical-layer resource distribution and environmental awareness.

2. Sensing Uncertainty Quantification and Safety Bounds

Central to planning-aware ISAC is the explicit calculation of sensing uncertainty using the Cramér–Rao Bound (CRB). For the $k$th OV, the CRB matrix for position estimation is:

$$\mathrm{CRB}_k = [\mathbf{J}_k^{\mathbf s}]^{-1} = p_k^{-1}\,\mathbf C_k$$

The per-coordinate lower bounds are: $$E[(\hat x_k - x_k)^2] \ge p_k^{-1} c^k_{11}, \quad E[(\hat y_k - y_k)^2] \ge p_k^{-1} c^k_{22}$$ yielding a position covariance

$$\Sigma_{\mathbf s_k} = \mathrm{diag}(p_k^{-1} c^k_{11},\, p_k^{-1} c^k_{22})$$

Safety for motion planning is enforced by inflating the occupancy grid of each obstacle proportionally to its CRB, wrapping the associated confidence ellipsoid by a rectangle whose half-widths explicitly decrease with increasing $p_k$. The deterministic collision-avoidance constraint (Property 2) guarantees:

$$\mathrm{dis}(\mathbb G_t(\mathbf s^E_t),\,\mathbb O^p_k(p_k)) \ge d_{\rm safe} \implies \Pr\{\text{collision}\} \le p_\epsilon$$

This directly operationalizes the link between ISAC transmit power, sensing accuracy, and planning safety margins.

3. Bilevel Optimization: Power Allocation and Trajectory Planning

ISAC resource allocation and trajectory planning are formulated as a tightly coupled bilevel optimization, termed "planning-oriented ISAC" (PISAC):

• Inner Layer (Physical Layer): Optimizes $\{p_k\}$ to minimize combined safety-space shrinkage $\Xi(\{p_k\})$ (from inflated obstacles) and a sensing regularization term $\varphi(\{p_k\})$. The constraints enforce communication sum-rate thresholds and a total power budget.
• Outer Layer (Motion Planning): Given the inflated-occupancy grids from the physical layer, plans ego-vehicle trajectories $\{\mathbf{s}^E_t, \mathbf{u}^E_t\}$ to minimize deviation from waypoints under safety and dynamic constraints.

Mathematically: $$\min_{\{p_k\}}\, \Xi(\{p_k\}) + \varphi(\{p_k\}), \quad \text{s.t. } \sum_k \log_2 \left(1+ \frac{p_k \kappa_C^2 |\alpha_k|^2 |\delta_k|^2}{\sigma_C^2}\right) \ge R_0,\, \sum_k p_k \le P_{\rm sum}$$ and

$$\min_{\{\mathbf{s}^E_t,\mathbf{u}^E_t\}}\, \sum_{t=0}^H \|\mathbf{s}^E_t - \mathbf{s}^\diamond_t\|_2^2, \quad \text{s.t. safety, dynamics, control limits}$$

The recursive feedback between $p_k$ selection and path planning maximizes safe free-space and collision-free trajectory options.

4. Convex Algorithms and Efficient Solution Methods

The structure of the problem enables convex relaxations and efficient solutions:

• Inner Layer: The occupancy rectangle is approximated by two circles (Double Circle Approximation), allowing the shrinkage cost to be written as convex functions of $\{p_k\}$, solvable with polynomial-time convex optimization tools (e.g., CVXPY, complexity $\mathcal O(K^{3.5})$).
• Outer Layer: ADMM (Alternating Direction Method of Multipliers) is employed after dualizing the distance constraints. The bi-convex program alternates trajectory and dual variable updates with guaranteed stationary convergence and tractable per-iteration complexity.

This enables real-time deployment in high-fidelity simulators and real-world vehicular contexts.

5. Simulation Results and Empirical Performance

Extensive tests in urban driving environments (CARLA Town04, $K=7$ obstacles, Tesla Model 3, $N_t=N_r=64$ antennas, SNR levels 36dB/38dB) demonstrate:

SNR	Baseline	Success Rate (%)	Traversal Time (s)	Path Length (m)
36 dB	ISAC [7]	60	17.22	90.39
	SRM [11]	50	16.51	88.80
	MMF [10]	55	16.85	88.00
	PISAC	100	15.79	84.56

PISAC achieves up to 40% higher success rates and over 5% shorter traversal times compared to previous ISAC resource allocation and comm-oriented benchmarks. Its balanced design yields 4-12% higher sum-rate (comm) and 22-60% lower CRB (sensing) than alternatives, and robustly prevents unsafe motion.

6. Impact, Generalization, and Research Directions

The closed-form link between ISAC transmit power, CRB-based occupancy inflation, and collision-avoidance constraints establishes a rigorous and practical approach to coupling environment perception with motion planning. By moving beyond uniform resource allocation to planning bottleneck-aware sensing, PISAC enables performance-driven safety enhancements for autonomous agents.

A plausible implication is that such frameworks will generalize to dynamic obstacle scenarios, multi-agent coordination, and can integrate with learning-based trajectory planners and event-triggered communication protocols. Future work should address extensions to distributed multi-RSU deployments, time-varying obstacle fields, and quantification under imperfect channel state information.

In summary, planning-oriented ISAC bridges the gap between low-level (resource) and high-level (motion) decision-making, deriving efficiency directly from physical-layer design via closed-form CRB occupancy bounds and tractable bilevel optimization (Jin et al., 27 Oct 2025). This approach is essential for next-generation autonomous vehicle and situational awareness platforms optimizing both throughput and navigational safety.