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Tri-Hybrid Beamforming Design for DMA-Aided Secure ISAC Systems
Siyi Li, Zhuoming Li, Mohammadali Mohammadi, Jiajun He, Hien Quoc Ngo, Michail Matthaiou
TL;DR
Secure ISAC must balance target sensing with confidential communication in the presence of an eavesdropper, while existing work had not addressed tri-hybrid beamforming for this setting. The paper optimizes a DMA-aided tri-hybrid design by first finding a fully digital solution and then alternating updates of its beamformers. The resulting design improves sensing performance over the reported comparison schemes under the stated conditions.
Problem
Prior work addressed tri-hybrid communication design or physical-layer security with conventional hybrid architectures, but secure tri-hybrid ISAC had not been investigated to the authors’ knowledge.
Source: §I · p. 1Method
The design maximizes sensing SNR subject to SSE, transmit-power, and hardware constraints, using SDR and SCA for a fully digital solution followed by triple alternating optimization of digital, analog, and DMA beamformers.
Source: §I · pp. 1–2, §III · p. 5Results
The proposed design achieves higher sensing SNR and improved CRB performance than conventional hybrid beamforming at the same aperture and tri-hybrid beamforming with fixed DMA design under the same SSE requirement.
Source: §I · p. 2Takeaways & Limitations
The numerical results show that optimizing the DMA electromagnetic response improves sensing performance relative to a tri-hybrid design with fixed response.
Source: §IV · p. 6
Abstract
from arXiv · showhide
This paper proposes a tri-hybrid beamforming scheme for secure integrated sensing and communication (ISAC) with a dynamic metasurface antenna (DMA) architecture, where the base station (BS) is capable of communicating with legitimate users and sensing the target. There is also an eavesdropper in the system intending to eavesdrop on the confidential information. The tri-hybrid beamforming design problem is formulated with the objective of maximizing the sensing signal-to-noise ratio (SNR) under the constraints of secrecy spectral efficiency (SSE), transmit power, and physical structure limitations. We first solve the problem and obtain the optimized fully-digital beamforming solution through successive convex approximation (SCA) and semidefinite relaxation (SDR) approaches. A triple alternating optimization scheme is then developed to iteratively optimize the digital, analog, and DMA beamformers, progressively approximating the fully-digital solution. Numerical results demonstrate that the proposed secure tri-hybrid beamforming design for DMA-aided ISAC improves the sensing SNR by approximately 3 dB compared to a tri-hybrid beamforming scheme with a fixed DMA electromagnetic design.
I. Introduction
Tri-hybrid beamforming offers design flexibility for large-array ISAC, but secure design combining that architecture with physical-layer security had not been investigated. This work formulates and solves a DMA-aided secure design problem and reports improved sensing performance over the stated baselines.
I. Introduction
- Large antenna arrays support robust sensing and communication but conventional fully digital architectures consume substantial power and face size and deployment-flexibility limitations.Source: §I · p. 1
- Sensing-directed beams can raise leakage risk to eavesdroppers, while dedicated sensing waveforms can be designed to interfere with an eavesdropper without carrying communication information.Source: §I · p. 1
- Existing studies separately emphasize tri-hybrid communication performance or physical-layer security with conventional hybrid architectures, leaving secure tri-hybrid ISAC uninvestigated to the authors’ knowledge.Source: §I · p. 1
- The work formulates DMA-assisted secure ISAC to maximize sensing SNR subject to SSE, transmit-power, and physical-structure constraints, and derives the CRB for performance evaluation.Source: §I · pp. 1–2
- A triple alternating optimization scheme designs digital, analog, and DMA beamformers to approximate a fully digital solution obtained using SDR and SCA.Source: §I · p. 2
- The proposed design achieves higher sensing SNR and improved CRB performance than conventional hybrid beamforming at the same aperture and tri-hybrid beamforming with fixed DMA design, under the same SSE requirement.Source: §I · p. 2
A. Tri-Hybrid Beamforming Model
The model uses a DMA-assisted tri-hybrid base station to communicate with legitimate users while sensing a target in the presence of an eavesdropper. Its signal and sensing models account for the beamformer layers, DMA structure, user and Eve links, and sensing performance measures.
A. Tri-Hybrid Beamforming Model
- The base station serves K legitimate UEs and senses a target while an Eve attempts to intercept confidential information; its DMA has Nw waveguides with Nr radiating elements each.Source: A. Tri-Hybrid Beamforming Model · p. 2
- The tri-hybrid transmitter combines digital, analog, and DMA beamformers; the analog layer uses a fully connected phase-shifter architecture with constant-modulus elements.Source: A. Tri-Hybrid Beamforming Model · p. 2
- The DMA beamformer is block diagonal because each waveguide feeds its own radiating-element subarray, and each element response is constrained by coupled amplitude and phase behavior.Source: A. Tri-Hybrid Beamforming Model · p. 2
- The digital beamformer assigns one column to sensing and one to each UE’s communication stream, while the UE channel is modeled as sparse geometric multipath.Source: A. Tri-Hybrid Beamforming Model · p. 2
- The communication model defines SINRs for legitimate UEs and Eve and uses their secrecy spectral efficiency to assess secure communication.Source: A. Tri-Hybrid Beamforming Model · p. 3
- Sensing uses a uniform planar array steering vector for the target and evaluates performance through sensing SNR and the trace of the CRB matrix for angle estimation.Source: A. Tri-Hybrid Beamforming Model · p. 3
B. Problem Formulation
The design jointly optimizes the DMA, analog, and digital beamformers to maximize sensing SNR under secrecy, power, and hardware constraints. Coupled variables and non-convex constraints make the problem difficult to solve directly.
B. Problem Formulation
- The tri-hybrid design jointly optimizes DMA, analog, and digital beamformers to maximize sensing SNR under practical constraints.The constraints cover analog and DMA hardware structure, secrecy spectral efficiency (SSE), and total transmit power.Source: B. Problem Formulation · p. 3
- The optimization includes constraints on SSE performance, total transmit power, and the hardware structures of the analog and DMA beamformers.Source: B. Problem Formulation · p. 3
- Coupled variables, a non-convex SSE constraint, analog constant-modulus constraints, and DMA structural constraints prevent direct solution of P1.Source: B. Problem Formulation · p. 3
III. Tri-Hybrid Beamforming Design
The design first obtains a fully digital target by relaxing the analog and DMA hardware constraints, then fits the tri-hybrid beamformers to that target. SDR, SCA, and alternating updates address the optimization and hardware constraints.
Fully-digital target
- Relaxing the analog and DMA hardware constraints yields a freely optimized fully digital beamformer that serves as the tri-hybrid design's target.Source: §III · pp. 3–4
Fully-digital optimization
- SDR relaxes the rank-1 constraint, while auxiliary variables and SCA linearization turn the SSE constraints into a tractable convex form.The exponential terms are linearized at the preceding iteration's points.Source: §III · p. 4
- Gaussian randomization recovers a feasible rank-one solution satisfying the original problem's constraints.Source: §III · p. 4
Alternating optimization
- The three beamformers are updated sequentially; with analog and DMA fixed, the digital beamformer minimizes squared fitting error to the target.Source: §III · p. 4
Analog beamformer
- With the digital and DMA beamformers fixed, gradient descent updates the analog beamformer, using backtracking for step size and projection to enforce constant modulus.Source: §III · p. 4
DMA beamformer
- With the analog and digital beamformers fixed, coordinate descent searches each DMA phase over [0, 2π) to minimize approximation error against the target.The target matrix entries and equivalent beamforming vector define the corresponding per-element fit.Source: §III · pp. 4–5
Iteration and refinement
- The DMA, analog, and digital updates repeat until fitting-error change falls below a threshold or the iteration limit; the digital beamformer is then refined to satisfy SSE and power constraints.The SCA-based fully digital optimization and subsequent block updates are described as convergent.Source: §III · p. 5
IV. Numerical Results
The numerical results compare the proposed secure tri-hybrid design with fixed-EM, conventional hybrid, and fully digital alternatives. They report sensing SNR and CRB advantages, alongside sensing-SNR gains as transmit power and waveguide count increase.
- The proposed architecture achieves lower CRB than fully digital and hybrid architectures with the same aperture, and greater CRB improvement than fixed-EM tri-hybrid beamforming.The comparison indicates that the added DMA EM-design complexity is justified by the resulting sensing-performance gain.Source: Figure 3 · p. 6, §IV · p. 6
- Sensing SNR improves with transmit power and with more waveguides, which allow more accurate focusing of the transmit beam toward the target.The power sweep uses an SSE threshold of 1 bit/s/Hz.Source: Figure 4 · p. 6, §IV · p. 6
- The proposed tri-hybrid design achieves higher sensing SNR than fully digital and hybrid designs with the same array aperture and tri-hybrid beamforming with fixed EM response.Source: §IV · p. 6
V. Conclusion
The paper proposes secure tri-hybrid beamforming for DMA-aided ISAC and jointly optimizes its digital, analog, and DMA beamformers. Numerical results report advantages over conventional same-aperture designs and a fixed-EM tri-hybrid design.
- The proposed DMA-aided secure ISAC design jointly optimizes the digital, analog, and DMA beamformers through a triple optimization algorithm.Source: §V · p. 6
- The design maximizes sensing SNR subject to SSE and analog- and DMA-beamformer physical constraints, and derives CRB for system evaluation.Source: §V · p. 6
- Numerical results show better performance than conventional fully digital and hybrid designs with the same array aperture and tri-hybrid beamforming with fixed EM design.Source: §V · p. 6