Adaptive Exposure-Aware Beamforming

• Adaptive exposure-aware beamforming is a technique that dynamically shapes transmission beams to maximize link performance while ensuring EM exposure remains within safe, regulatory limits.
• It employs real‐time methods such as computer vision-based beam avoidance, Lyapunov optimization, and RIS-aided equalization to balance high SNR with reduced human exposure.
• Performance evaluations demonstrate that these methods achieve near-optimal communication metrics, leveraging multi-modal sensing and rigorous EM and thermal modeling for mmWave, massive MIMO, and RIS networks.

Adaptive exposure-aware beamforming design refers to a class of spatial signal processing methodologies in wireless systems that dynamically shape transmission beams to maximize communication performance while ensuring electromagnetic (EM) exposure at human-relevant and regulatory-critical locations stays within predefined limits. Modern exposure-aware approaches exploit fine-grained environment and user state sensing—including computer vision (CV), EM field modeling, and bioheat transfer dynamics—to optimize beam selection or weight adaptation in real time. These techniques are particularly pertinent in millimeter-wave (mmWave), massive MIMO, and reconfigurable intelligent surface (RIS)-aided networks, where the potential for localized EM exposure is significant due to high directivity and large antenna arrays (Xiang et al., 2020, Awarkeh et al., 2022, Zhou et al., 27 Jan 2026).

1. Physical Foundations and Channel Modeling

Adaptive exposure-aware beamforming is grounded in rigorous electromagnetic field theory and human tissue interaction models. The radiated field from each antenna array element, including mutual coupling and polarization effects, is modeled from Maxwell's equations. In mmWave uplink scenarios, the field at any observation point is represented as

$$\boldsymbol{\mathcal E}(\mathbf r) = \frac{j\eta I_m}{2\pi d} \frac{\cos(kh\cos\psi)-\cos(kh)}{\sin\psi} e^{-jkd} \hat{\boldsymbol\rho}(\hat{\mathbf r})$$

with parameters reflecting antenna geometry, propagation loss, and polarization (Zhou et al., 27 Jan 2026). For arrays, mutual impedance $\mathbf Z$ is accounted for, coupling current distributions across elements. The equivalent MIMO channel $\mathbf H$ includes these fine-grained electrodynamic effects and forms the basis for subsequent beamforming and exposure calculations.

In RIS-aided systems, propagation channels between base station, RIS panels, and user equipment are similarly parameterized, with phase-tunable surface elements included in the composite channel model (Awarkeh et al., 2022).

2. Exposure Metrics and Human Safety Models

Metrics for exposure-aware design typically comprise both electromagnetic field properties and physiological absorption indicators:

• Power Density (PD): The instantaneous incident field energy per unit area at a point $(\theta, \phi, d)$ from the array is

$$E(\theta, \phi, d) = \frac{P_t}{4\pi d^2} | \mathbf{w}^H\mathbf{a}(\theta, \phi)|^2$$

where $P_t$ is total transmit power and $\mathbf{w}$ is the beamforming weight vector (Xiang et al., 2020).

• Specific Absorption Rate (SAR): Absorbed power per unit tissue mass

$$\mathrm{SAR}_i = \frac{\sigma_i}{\rho_i} E(\theta_i, \phi_i, d_i)$$

with $\sigma_i$ the absorption cross-section and $\rho_i$ tissue density.

Thermal compliance is addressed via the Pennes Bioheat Transfer Equation (BHTE), which models tissue temperature $T(\mathbf{r},t)$ in response to incident PD, tissue conductivity, perfusion cooling, and boundary conditions. The effective temperature rise under periodic exposure integrates both heating and bio-thermal inertia (Zhou et al., 27 Jan 2026).

3. Optimization Formulations

Exposure-aware beamforming is formalized as a constrained optimization balancing communication objectives (rate, SNR) against exposure metrics:

• Instantaneous Constraint Formulation:

$$\min_{w \in \{ \mathbf{w}_1, ..., \mathbf{w}_{N_g} \} } \alpha R(w)^{-1} + \beta \sum_i E_i(w)$$

subject to $E_i(w) \leq E_{\max,i}$, $\|w\|^2 \leq P_t$, where $\alpha,\beta$ govern rate versus exposure trade-off (Xiang et al., 2020).

• Thermal-Aware Long-Term Formulation:

$$\max_{\{\mathbf{w}[n]\}} \frac{1}{N}\sum_{n=1}^N \| \mathbf{H}[n]\mathbf{w}[n] \|^2$$

subject to average transmit power and

$\frac{1}{N}\sum_{n=1}^N T_m[n] \leq T_{\rm th}$

for all thermal sampling points $m$ (Zhou et al., 27 Jan 2026).

RIS- and proximity-based constraints are similarly posed; exposure at any point outside a regulatory exclusion region must remain below threshold, requiring joint optimization of transmit power and beam pattern (Awarkeh et al., 2022).

4. Adaptive Beamforming Algorithms

Key algorithmic advances enable real-time adaptation to environmental and user condition dynamics:

• CV-Aided Beam Avoidance: Camera-based pose estimation identifies vulnerable body parts (e.g., head, eyes). The system disables beam codebook entries whose main lobes would intersect vulnerable directions above a preset threshold, then selects the optimal remaining beam maximizing communication performance (Xiang et al., 2020). Finer beam codebook granularity reduces SNR loss for a given exposure reduction.
• Lyapunov-Based Online Optimization: Virtual queues $Q_m[n]$ for each sampled exposure point track thermal "debt," and a drift-plus-penalty objective combines instantaneous SNR and cumulative exposure cost. In each slot, the per-slot beamforming vector is the top eigenvector of

$$\mathbf{A}[n] = V \mathbf{H}[n]^H\mathbf{H}[n] - \frac{\xi_0}{2\eta} \sum_m Q_m[n] \Phi_m[n]^H\Phi_m[n]$$

ensuring both high performance and temperature stabilization (Zhou et al., 27 Jan 2026).

• RIS-Aided Channel Equalization: The RIS is configured to "flatten" the phase profile of paths, creating an angularly equalized virtual propagation channel. Maximum Ratio Transmission is then applied to this channel, and transmit power is scaled to ensure that at all test points outside a regulatory circle, field strength is below threshold (Awarkeh et al., 2022). This achieves near-MRT throughput with full compliance and reduced complexity relative to truncated beamforming.

5. Performance Evaluation and Trade-Offs

Simulation studies demonstrate that:

• Disabling beams within a fixed angular footprint can force head exposure below 0.3 mW/cm², with SNR penalties highly dependent on codebook granularity (3–5 dB with 3 dB spacing, 1–2 dB with 0.5 dB spacing) (Xiang et al., 2020).
• Lyapunov-based thermal-aware resource allocation enables protocol-defined average SNR to approach the unconstrained upper bound within 1–2 dB, outperforming PD-constrained and per-slot optimal schemes by up to 3 dB (Zhou et al., 27 Jan 2026).
• In RIS-aided systems, equalized beamforming matches or exceeds SNR performance of reduced beamforming under full regulatory compliance. Use of RIS enables SNR increases of approximately 4 dB at 100% compliance rates (Awarkeh et al., 2022).

A robust conclusion is that by leveraging spatial, temporal, and physical diversity, adaptive exposure-aware designs reduce required derating of communication links versus brute-force power back-off strategies. Exposure modeling at the physiological (thermal) level permits trade-offs that exploit tissue cooling rates and EM field dispersal across space and time.

6. Implementation Considerations and Extensions

Accurate implementation depends on:

• Exposure Manifold Calibration: Construction of exposure array manifolds $\Phi_m$ requires detailed EM field mapping (empirical or simulated) for each potential exposure point (Zhou et al., 27 Jan 2026).
• Real-Time Environment and Pose Sensing: Approaches based on CV (Xiang et al., 2020) or channel direction estimation (Awarkeh et al., 2022) presume measurement and state tracking with adequate spatial and temporal fidelity.
• Algorithmic Complexity: Principal eigenvector computation per slot dominates in Lyapunov-based algorithms ($\mathcal{O}(N_t^3)$), while codebook-based approaches scale with codebook size and beam search operations.
• Extension to Multi-User and Downlink Scenarios: Multi-queue structures per user and block-coordinate descent methods allow generalizations to downlink and multi-user exposure-aware beamforming (Zhou et al., 27 Jan 2026).

A notable practical challenge is reconciling model assumptions (homogeneous tissue, adiabatic boundary) with biological variability and regulatory validation requirements.

7. Comparative Summary Table

Approach	Performance vs. SNR	Compliance Rate	Algorithmic Complexity
CV-Aided Exposure Avoidance (Xiang et al., 2020)	1–5 dB SNR loss	100%	Codebook Search
Lyapunov Thermal-Aware (Zhou et al., 27 Jan 2026)	≤2 dB from optimal	100%	$\mathcal{O}(N_t^3)$
RIS-Aided Equalized BF (Awarkeh et al., 2022)	≈4 dB gain over Reduced BF	100%	Moderate (no DFT)

While the specific trade-off envelopes depend on parametric choices (codebook size, RIS elements, channel state), adaptive exposure-aware methods consistently provide operational regimes with near-optimal link performance and robust safety compliance. A plausible implication is that practical communication system design should incorporate multi-modal sensing, physics-informed modeling, and online adaptive optimization for exposure-critical scenarios.