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Integrated Sensing, Communication, and Computation Over-the-Air: MIMO Beamforming Design
Xiaoyang Li, Fan Liu, Ziqin Zhou, Guangxu Zhu, Shuai Wang, Kaibin Huang, Yi Gong
TL;DR
The paper addresses how to combine radar sensing, communication, and over-the-air computation in IoT networks while jointly optimizing their coupled MIMO beamformers. It develops the ISCCO framework and a semidefinite-relaxation-based solution, then demonstrates target-location estimation in simulation.
Problem
The paper addresses the need to integrate sensing, communication, and computation while jointly optimizing coupled MIMO beamformers for their non-convex design problem.
Method
The paper develops ISCCO with shared and separated beamforming schemes and solves the joint design using semidefinite relaxation.
Results
Simulation demonstrates target-location estimation based on ISCCO and reports sensing–AirComp MSE relationships for the shared and separated schemes.
Takeaways & Limitations
ISCCO provides a framework for simultaneously supporting radar sensing and AirComp in an IoT system.
Abstract
from arXiv · showhide
To support the unprecedented growth of the Internet of Things (IoT) applications, tremendous data need to be collected by the IoT devices and delivered to the server for further computation. By utilizing the same signals for both radar sensing and data communication, the integrated sensing and communication (ISAC) technique has broken the barriers between data collection and delivery in the physical layer. By exploiting the analog-wave addition in a multi-access channel, over-the-air computation (AirComp) enables function computation via transmissions in the physical layer. The promising performance of ISAC and AirComp motivates the current work on developing a framework called integrated sensing, communication, and computation over-the-air (ISCCO). The performance metrics of radar sensing and AirComp are evaluated by the mean squared errors of the estimated target response matrix and the received computation results, respectively. The design challenge of MIMO ISCCO lies in the joint optimization of beamformers for sensing, communication, and computation at both the IoT devices and the server, which results in a non-convex problem. To solve this problem, an algorithmic solution based on the technique of semidefinite relaxation is proposed. The use case of target location estimation based on ISCCO is demonstrated in simulation to show the performance superiority.
I. INTRODUCTION
The paper proposes ISCCO, which unifies sensing, communication, and computation over a shared wireless transmission. It jointly designs beamformers for shared and separated schemes and evaluates their sensing–AirComp tradeoffs, including target-location estimation.
- I. INTRODUCTION: ISCCO integrates radar sensing, communication, and AirComp within a single signal-transmission framework for IoT systems.Sensors transmit radar signals and data symbols to a multi-antenna server, which performs data fusion via AirComp.
- I. INTRODUCTION: The shared scheme uses one sensor beamformer for a dual-purpose radar pulse and data carrier, while the separated scheme assigns distinct antenna groups and beamformers.The shared scheme also uses a server aggregation beamformer; the separated scheme separately designs radar and data-transmission beamformers.
- I. INTRODUCTION: Sensing and AirComp MSEs are naturally coupled, creating a beamforming tradeoff that requires joint radar, transmission, and aggregation design.The separated scheme additionally faces radar-signal interference at the server, making its optimization more complex.
- I. INTRODUCTION: The paper formulates the shared-scheme joint design as a semidefinite program and applies semidefinite relaxation under sensing and per-sensor power constraints.The objective is to minimize AirComp computation error while satisfying radar sensing requirements.
- I. INTRODUCTION: Simulations compare shared and separated schemes and demonstrate ISCCO through target-location estimation aggregated from local sensor estimates.The server compares the averaged estimated target location with ground truth.
II. BACKGROUND OF AIRCOMP AND ISAC
AirComp computes functions through simultaneous analog transmissions whose wave addition performs aggregation at the server. The background reviews its function class, efficiency benefits, MIMO extensions, applications, and the open integration of sensing data.
- A. AirComp: AirComp computes nomographic functions by exploiting simultaneous analog transmissions and multi-access-channel wave addition, with the result received directly at the server.Examples include averaging and geometric mean.
- A. AirComp: Simultaneous transmission gives AirComp low latency independent of device count and saves spectrum resources.
- A. AirComp: MIMO AirComp uses spatial degrees of freedom to multiplex multiple function computations and reduce computation errors through noise suppression.Related extensions include wireless-power transfer, reduced-dimension designs, blind operation without CSI, and power control for fading channels.
- A. AirComp: AirComp has been applied to IoT settings including federated edge learning, RIS-assisted communication, UAV communication, autonomous driving, and edge-cloud MapReduce.
- A. AirComp: Despite broad AirComp applications, incorporating data sensing remains an uncharted area that motivates the paper’s ISCCO framework.
B. ISAC
ISAC integrates radar sensing and communication by sharing spectrum, waveforms, or system resources, but prior approaches often leave computation outside the integrated design. This motivates combining ISAC with AirComp for simultaneous sensing, communication, and physical-layer computation.
- Earlier coexistence schemes may prevent radar and communication from operating simultaneously, motivating methods such as null-space projection for concurrent operation.
- Null-space projection can harm radar beamforming optimality and cause radar-sensing performance loss.
- Some coexistence designs require frequent exchange of CSI, probing waveforms, and modulation formats, while control-center coordination adds implementation complexity.
- ISAC research has developed shared radar-communication designs spanning dual-functional waveforms, MIMO beamforming, spectrum sharing, and application-specific systems.
- Because ISAC literature often overlooks data computation, AirComp provides a physical-layer mechanism for integrating sensing, communication, and computation.
III. SYSTEM MODEL
The system model considers synchronized MIMO sensors that simultaneously probe a common target and transmit data symbols to an access point for AirComp. Radar sensing and computation quality are modeled through mean-squared estimation errors under shared transmission and aggregation beamforming.
- Each sensor simultaneously transmits probing signals for target detection and data symbols to the access point for AirComp over synchronized time slots.
- The model assumes block-fading channels, per-sensor transmit-power limits, and independent zero-mean unit-variance data symbols across sensors and functions.
- The shared scheme uses all sensor antennas for both sensing and communication, with a transmit beamformer generating signals that serve dual functions.
- Radar sensing estimates the target response matrix from matched-filtered observations, with sensing quality evaluated by the MSE of the estimate.
- At the access point, a data aggregation beamformer combines sensor transmissions, and AirComp accuracy is measured by the MSE between the estimated function value and the ground truth.
B. Separated Scheme
The separated scheme partitions each sensor’s antennas into dedicated radar-sensing and data-transmission groups. It therefore uses distinct radar and communication beamformers while modeling their effects on sensing and AirComp reception separately.
- The separated scheme divides each sensor’s antennas into radar-sensing and data-transmission groups, with radar transmission and reception assigned to dedicated antenna subsets.
- Each sensor uses a data transmission beamformer W_m and a radar sensing beamformer F_m under a transmit-power constraint.
- The separated-scheme sensing model includes target-response, direct-radar, data-reflection, and direct-data channels alongside additive noise.
- Radar estimation and AirComp computation quality are evaluated using their respective MSE expressions in the separated architecture.
- The access point receives both data-transmission and radar-sensing components through separate channels before aggregation with its beamformer.
IV. DUAL-FUNCTIONAL SHARED BEAMFORMING DESIGN
The shared scheme jointly designs sensor transmission and server aggregation beamformers for radar sensing and AirComp, but their coupling makes the problem non-convex. Semidefinite relaxation converts the design into a convex problem, followed by Gaussian randomization to recover a feasible beamformer.
- Problem formulation: The joint beamforming problem is non-convex because the transmission and aggregation beamformers are coupled.The formulation combines power and sensing-quality constraints with the coupled beamformer design.
- Beamformer optimization: Given the aggregation beamformer, the optimal sensor transmission beamformer minimizes computation error under the shared design.This result is stated as Proposition 1 for the shared beamforming design.
- Semidefinite relaxation: Introducing  = AAH and applying semidefinite relaxation yields a convex formulation that can be solved with a convex problem solver.The convex formulation produces a globally optimal relaxed solution Â*.
- Semidefinite relaxation: Gaussian randomization extracts a feasible rank-K aggregation beamformer from the relaxed solution when its rank exceeds K.The algorithm samples candidate matrices and selects the one with the minimum objective.
- Problem formulation: The shared scheme uses one transmission beamformer at each sensor to support both radar sensing and AirComp, coupled with the server aggregation beamformer through zero-forcing.This coupling requires satisfying sensing MSE requirements while preserving AirComp accuracy.
V. DUAL-FUNCTIONAL SEPARATED BEAMFORMING DESIGN
The separated scheme independently designs data-transmission, radar-sensing, and aggregation beamformers, while radar signals create extra AirComp error. It uses semidefinite relaxation and Gaussian randomization to address the resulting non-convex optimization.
- Separated beamforming design: The separated scheme jointly optimizes data transmission, radar sensing, and data aggregation beamformers rather than using one dual-functional transmission beamformer.Its radar beamformer is constrained to be an orthogonal matrix represented as Fm = √αmDm.
- Problem formulation: The separated formulation is non-convex because the radar sensing beamformer Fm and aggregation beamformer A are coupled in the objective.The data transmission beamformer uses zero-forcing to minimize AirComp MSE.
- Semidefinite relaxation: After semidefinite relaxation, the separated problem becomes a convex optimization with linear objective and convex constraints.Gaussian randomization then converts the relaxed solution into a feasible rank-K solution of the original problem.
- Separated beamforming design: Radar signals introduce an additional AirComp error, so the radar beamformers are designed to meet sensing requirements with maximum tolerance.The radar-sensing scaling factor αm increases MSE, motivating its minimum feasible value.
VI. TARGET LOCATION ESTIMATION BASED ON ISCCO
The ISCCO location-estimation use case has each sensor estimate a target from reflected radar signals and transmit its local location estimate to the AP via AirComp. The AP obtains an averaged target location from these sensor estimates.
- Local target estimation: Each sensor estimates target distance and angle from reflected radar signals, then forms a local target-location estimate from those parameters and its own position.The local estimate is denoted by ẑm = [x̂m, ŷm]T.
- Over-the-air aggregation: The sensors transmit their estimated target locations to the server through AirComp, enabling the AP to obtain an averaged estimate.The received computation result is converted into an averaged target location using the statistics of the x- and y-coordinates.
- Radar observation model: The target-response matrix is modeled as Gmm = βmΦ(θm), combining a complex amplitude with a phase-delay matrix determined by angle.The phase-delay elements depend on transmitting and receiving antenna time delays.
- Parameter estimation: The angle estimate has no closed-form expression, so grid search or golden-section search is used while obtaining the beamformer by solving problem (P1).This numerical step follows the angle-dependent part of the likelihood objective.
A. Baseline Schemes
The experiments compare optimized shared and separated schemes with antenna-selection baselines across AP antennas, sensor antennas, sensors, and computed functions. AirComp error generally rises with sensing or computation demands, while optimized beamforming outperforms antenna selection.
- AP antenna scaling: Normalized AirComp MSE decreases as the number of AP antennas increases because the aggregation beamformer exploits diversity gain.The trend is evaluated for both shared and separated schemes.
- Baseline comparison: Both optimized shared and separated schemes achieve lower AirComp MSE than antenna-selection baselines, verifying the value of beamformer optimization.The separated scheme performs better than the shared scheme under the reported system settings.
- Sensor antenna scaling: Normalized AirComp MSE increases with more antennas at each sensor because larger target-response matrices impose stricter sensing constraints.The added sensing burden sacrifices AirComp performance, although the shared scheme becomes better than the separated scheme as sensor antennas increase.
- Number of sensors: Normalized AirComp MSE increases with the number of sensors because equalizing channels across more connected sensors makes aggregation beamformer design harder.The increase is more pronounced for the separated scheme because additional sensors exacerbate radar interference.
- Number of computed functions: Normalized AirComp MSE increases with the number of computed functions, indicating a throughput–accuracy trade-off.The separated scheme consistently outperforms the shared scheme across the tested function counts and is therefore more robust to function-number variation.
C. Radar Sensing Performance of ISCCO
Simulation evaluates ISCCO sensing and target-location estimation, showing antenna-dependent sensing behavior and improved location accuracy relative to ISAC and conventional AoA, with degradation under strong channel noise.
- Averaged sensing MSE decreases with more AP antennas in the shared scheme because the aggregation beamformer gains degrees of freedom.
- More antennas per sensor increase shared-scheme sensing MSE because the target response matrix dimension becomes larger.
- Separated-scheme sensing MSE remains unchanged with AP or sensor antenna counts because tighter radar constraints mitigate radar-signal interference.
- Target Location Estimation based on ISCCO: AirComp averaging alleviates the deviation in individual-sensor ISAC location estimates.
- Target Location Estimation based on ISCCO: The estimated target location from ISCCO is closer to ground truth than estimates from conventional AoA.
- Target Location Estimation based on ISCCO: Under −59.5 dBm data-channel noise, AirComp deteriorates and single-sensor estimation can outperform aggregation, motivating sensor scheduling.
APPENDIX
The appendix analyzes Gaussian noise and convexity properties underlying the optimization, including a zero-forcing structure that achieves equality in a derived bound.
- The appendix models the transformed noise vector as Gaussian with covariance determined by the linear transformation of vec(N_r).
- For any data aggregation beamformer A, the zero-forcing structure for W_m achieves equality in the stated AirComp MSE bound.
- Problem (P4) is convex because its objective and constraints are linear over the lifted variables, while the inverse-trace term is convex by composition.