Over-the-Air ISCC Network

• Over-the-air ISCC networks are integrated frameworks that combine sensing, communication, and computation using analog waveform superposition.
• They leverage dual-functional signal design and joint optimization of beamformers, power allocation, and aggregation to meet strict fidelity and latency constraints.
• Practical implementations using MIMO and OFDM platforms enable low-latency, spectrum-efficient operations for applications like edge intelligence and real-time inference.

Over-the-Air-Empowered ISCC Network

An over-the-air-empowered integrated sensing, communication, and computation (ISCC) network is an architecture wherein distributed devices (e.g., sensors, IoT terminals, edge nodes) simultaneously perform environmental sensing, wireless data communication, and distributed function computation using the physical-layer property of analog waveform superposition (@@@@1@@@@, AirComp). Both dual-functional signal design and analog computation enable simultaneous data collection, delivery, and on-the-fly aggregation under unified resource constraints, providing large-scale, low-latency, and spectrum-efficient operation suitable for edge intelligence and perception-centric service requirements. The ISCC framework typically employs joint optimization of device/server beamformers, power allocation, and function aggregation strategies, often formulated as nonconvex MIMO or OFDM resource allocation problems with stringent sensing and computation fidelity constraints (Li et al., 2022, Zhuang et al., 2023, Wen et al., 21 Aug 2025, Li et al., 2022).

1. Signal Models and Network Architecture

ISCC networks can be instantiated in MIMO or OFDM topologies depending on application requirements. In MIMO settings, sensor arrays share antennas for both radar probing and AirComp transmission; alternatively, subarray splitting partitions resources for dedicated sensing and communication (shared vs. separated antenna schemes) (Li et al., 2022). The transmit signal at device $m$ is $x_m[t] = W_m s_m[t]$ for shared antennas, with $W_m$ denoting the joint beamformer. At the access point (AP), the AirComp receive statistic is $$\hat{z}[t] = A^H \sum_{m=1}^M H_m W_m s_m[t] + A^H n_c[t]$$, where $A$ is the receive beamformer matrix.

For OFDM-based ISCC, each feature dimension or function aggregates on a distinct subcarrier. Multi-device data is locally mapped as $C_{k,n}$ on subcarrier $n$, transmitted as $X_{k,n} = B_{k,n} C_{k,n}$, and the AP applies $W_n$ for aggregation: $\widehat{F}_n = W_n^H Y_n$ (Dong et al., 7 Mar 2025).

A typical ISCC node alternates among sensing, local computation (e.g., feature extraction, gradient calculation), and communication. Aggregation at the server or fusion center exploits analog waveform addition, allowing one-shot nomographic function computation (e.g., arithmetic mean, soft-data fusion) (Li et al., 2022). The design challenge centers around joint optimization across all phases under physical-layer constraints.

2. Performance Metrics: Sensing, Communication, Computation

Radar sensing fidelity is quantified by the mean squared error (MSE) of target matrix estimation or the Cramér-Rao bound (CRB) on physical parameters (e.g., angle, range, velocity):

$$\mathrm{MSE}_s = E[\|G_{mm} - \hat{G}_{mm}\|_F^2] = \frac{N_{rx} \sigma_r^2}{T} \operatorname{tr}[(W_m W_m^H)^{-1}]$$

(Shared antenna; $W_m$ replaced by $F_m$ for separated antennas) (Li et al., 2022).

AirComp aggregation fidelity (summed function estimate deviation) is evaluated via:

$$\mathrm{MSE}_a = E[\|\hat{z}[t] - \sum_m s_m[t]\|^2] = \sum_m \operatorname{tr}[(A^H H_m W_m - I)(A^H H_m W_m - I)^H] + \sigma_c^2 \operatorname{tr}(A A^H)$$

In OFDM, the per-subcarrier computation error is:

$$\mathrm{MSE}_n = \left| \sum_{k=1}^K W_n^H H_{k,n} B_{k,n} - 1 \right|^2 + |W_n|^2 \sigma^2$$

and total MSE is averaged over all $N$ subcarriers (Dong et al., 7 Mar 2025).

In edge inference contexts, discriminant gain (DG), representing KL-divergence–based class separability, is introduced as a composite metric connecting feature-space separation to resource allocation:

$$G_{l,l'}(\hat{\mathbf x}) = \sum_{k=1}^K \frac{|\sum_{u=1}^U \mathbf w_k^H \mathbf h_{u,k} v_{u,k}|^2 \psi_{l,l',k}} {\delta_k^2 \sum_{u=1}^U |\mathbf w_k^H \mathbf h_{u,k} v_{u,k}|^2 + \frac{\sigma_c^2}{2} \|\mathbf w_k\|^2 }$$

(Xu et al., 1 Jan 2026).

ISCC-enabled federated learning leverages convergence bounds capturing distortion in sensing ($\Delta_{sense}$), communication ($\Delta_{comm}$), and computation ($\Delta_{comp}$), explicitly quantifying the impact on overall learning rate (Wen et al., 21 Aug 2025).

3. Beamforming and Resource Optimization

Simultaneous high-fidelity sensing and accurate AirComp requires the joint optimization of device/server transmit and receive beamformers, energy allocation, and aggregation strategies. The canonical ISCC design problem is nonconvex due to bilinearities and summed-ratio objectives:

$$\min_{A,\{W_m\}} \sum_{m=1}^M \operatorname{tr}[(A^H H_m W_m - I)(A^H H_m W_m - I)^H] + \sigma_c^2 \operatorname{tr}(A A^H)$$

subject to radar-sensing MSE and power constraints (Li et al., 2022).

Solving for beamformers and aggregation weights under these constraints is typically approached via semidefinite relaxation (SDR), difference-of-convex (DC) programming, or alternating block coordinate methods. In SDR, the relaxation to $\bar{A} = A A^H \succeq 0$ yields a convex SDP whose solutions are randomized to recover feasible rank-$K$ beamformers.

For OFDM ISCC, the problem is split between alternating optimization: closed-form updates for $W_n$ (aggregator side), and convex QCQP for per-device transmit vectors $B_{k,n}$, using Taylor approximation for nonconvex sensing constraints; subsequent ADMM-based refinement recovers feasibility (Dong et al., 7 Mar 2025).

Edge inference ISCC networks maximize class-discriminant gain via alternating transmit/receive precoder updates—e.g., block coordinate ascent with matrix inversion and QCQP subproblems (Xu et al., 1 Jan 2026).

In federated learning, alternating optimization over batch size, sensing power, communication power, and CPU frequency efficiently balances resource trade-offs under per-device latency and energy budgets (Wen et al., 21 Aug 2025).

4. Task-Oriented Design and Algorithms

Recent research emphasizes task-oriented ISCC design. For classification via edge AI, maximizing the minimum pairwise discriminant gain ($G_{min}$) instead of mean or sum objectives improves worst-case separability and downstream inference accuracy. The associated optimization explicitly couples sensing power, AirComp precoding, and receive beamforming such that improvements in sensor energy allocation can be directly traced to class-separability gains (Zhuang et al., 2023).

DC programming and successive convex approximation (SCA) techniques linearize nonconvex denominators in discriminant gain constraints; primal–dual updates are deployed for closed-form resource allocation. Pseudocode typically involves initialization, convex surrogate construction, closed-form KKT multiplier update, and repeated reference updates until convergence.

For federated learning, batch size control intertwines with sensing power: allocating more sensing power enables larger batches at the same distortion level and vice versa. Optimal computation speed is the minimal feasible value under latency constraints, and communication power directly decreases AirComp distortion (Wen et al., 21 Aug 2025).

Multi-tier DNN partitioning across device–edge–cloud is optimized via cross-entropy learning for partition selection, and inner-layer resource allocation employs Karush-Kuhn-Tucker closed-form solutions for CPU and beamforming variables, including iterative MM–WMMSE beamformer updates and orthogonal Procrustes problems for beampattern matching (Liu et al., 30 Apr 2025).

5. Practical Implementation and Experimental Platforms

Recent open-source platforms, such as OpenISAC, support real-time ISCC experimentation with robust over-the-air synchronization via OFDM waveforms. Bistatic operations—where remote user equipment (UE) perform delay-Doppler sensing coordinated by base stations (BS)—require precise compensation for carrier-frequency offset (CFO), sampling-interval offset (SIO), and timing offset (TO).

A typical pipeline includes:

• Sliding-correlation for coarse TO/CFO estimation
• Weighted least-squares pilot autocorrelation for fine CFO/SIO estimation
• Quinn’s estimator for fractional timing correction
• Sliding-window tracking for SIO drift
• FFT-based Doppler/range estimation and phase compensation

Hardware uses multi-channel USRP radios with stable OCXO references, and real-time FFT/IFFT processing in C++ with algorithm prototyping in Python. Experimental validation demonstrates near-wired synchronization accuracy, Doppler resolution ($\sim$500 Hz), micro-Doppler spectrograms, and high communication throughput ($\sim$90 Mbit/s) (Zhou et al., 7 Jan 2026).

Extending OTA synchronization to large-scale ISCC networks requires careful protocol design (star/hierarchical or mesh topologies, periodic sync bursts, group consensus clock alignment) and tuning of OFDM parameters.

6. Representative Applications and Insights

Air-ISCC networks enable applications such as environmental monitoring (joint pollutant mapping and concentration averaging), smart factory vibration monitoring (concurrent fault detection and health-score aggregation), vehicular platooning (joint ranging and velocity averaging), cooperative spectrum sensing (semantic DNN compression with AirComp-based global detector computation), edge intelligence (real-time feature extraction with aggregated inference), and closed-loop over-the-air control (direct actuator feedback with stability region expansion) (Li et al., 2022, Park et al., 2021).

Key practical insights include:

• Dual-functional waveform design and analog computation maximize hardware and spectrum reuse.
• Joint beamforming and aggregation allow fine-grained trade-off between sensing fidelity and aggregation accuracy.
• Flexibility in antenna/resource split (shared vs. separated, multi-tier computation) accommodates interference management, mobility, and multi-target scenarios.
• Task-oriented metrics (DG, $G_{min}$) outperform naive amplitude-based averaging designs, improving robustness for multi-class inference.
• Over-the-air computation provides $K$-fold reduction in latency/resource usage for aggregation.
• Stability and error bounds exhibit favorable scaling with device count and resource budgets.

7. Challenges and Future Directions

Principal challenges include scalability to dense networks, robust OTA synchronization in urban multipath environments, optimal resource allocation under compounded latency/energy constraints, and real-time adaptation for dynamic scheduling, target tracking, and mobility. Extensions to distributed semantic encoding, federated learning, sensor scheduling, and multi-target tracking are active research avenues (Li et al., 2022, Wen et al., 21 Aug 2025, Yi et al., 2023).

The ISCC framework, through unified beamforming, analog computing, and joint task-oriented design, forms a foundation for 6G systems integrating wireless perception, ultra-reliable low-latency communication, and distributed edge intelligence.