Artificial-Noise Aided Design for Movable-Antenna Enabled Physical-Layer Service Integration

Abstract: This paper pioneers a novel scheme for artificial-noise (AN)-aided movable-antenna (MA)-enabled physical-layer service integration (PLSI) to harmonize the simultaneous delivery of multicast and confidential messages. By jointly exploiting the spatial reconfiguration capability of MAs and the interference shaping capability of AN, we aim to enhance secrecy performance while guaranteeing multicast reliability. The joint design of MA positions and transmit variables results in a highly coupled and non-convex optimization problem. To address this, we first provide key insights into the role of spatial degrees of freedom in AN design. We then characterize the AN direction under a structured transmission design and derive a closed-form expression for the AN-to-confidential power allocation ratio, which significantly simplifies the overall design. To solve the resulting problem, we further develop a low-complexity block coordinate ascent (BCA)-based scheme that alternates between transmit design and MA position optimization. Numerical results demonstrate that the proposed scheme achieves significant secrecy performance gains with low computational complexity and fast convergence, highlighting its effectiveness for MA-enabled PLSI systems.

• The paper demonstrates that jointly optimizing movable antenna positions and artificial noise allocation significantly enhances secrecy and multicast reliability in physical-layer service integration.
• A block coordinate ascent algorithm is employed to iteratively optimize antenna positioning and beamforming with closed-form solutions for power allocation and noise direction.
• Numerical results show that the combined MA and AN approach substantially improves secrecy rates in multipath channels compared to fixed-antenna systems.

Artificial-Noise Aided Design for Movable-Antenna Enabled Physical-Layer Service Integration

Introduction and Problem Setting

This paper addresses secure wireless transmission in service-integrated systems leveraging the unique reconfigurability of movable antennas (MAs). Specifically, it considers physical-layer service integration (PLSI), where a transmitter must simultaneously broadcast a multicast message to multiple legitimate users while keeping a confidential message secure from potential eavesdroppers within the same group of users. In the PLSI context, ensuring multicast reliability and the secrecy of confidential information presents intrinsic tradeoffs due to power/resource coupling.

The work advances the state of the art by jointly incorporating artificial noise (AN) and MA positioning for secrecy enhancement. The central premise is that movable antennas, capable of re-optimizing spatial positions, provide new spatial degrees of freedom (DoFs) for spatial interference shaping. Although MAs have previously been shown to offer channel reconfiguration benefits, the optimal integration with AN schemes for PLSI has not been systematically investigated.

System Model and Problem Formulation

The system comprises a base station equipped with $M$ movable antennas within a physically constrained aperture, communicating with two single-antenna user equipments ($U_1$, $U_2$). $U_1$ is the intended recipient of a confidential message, while both $U_1$ and $U_2$ receive a multicast message. Notably, $U_2$ is a legitimate user for multicast but an eavesdropper for the confidential message.

The channel is modeled as geometric multipath with position-dependent phase shifts, and the signal model incorporates confidential, multicast, and AN signal components with respective beamforming vectors. The secrecy rate at $U_1$ is defined as $R_s = [R_1 - R_E]^+$, following the conventional wiretap model, with multicast SINR constraints enforced at both users. The joint optimization goal is to maximize $R_s$ over antenna positions (matrix $U_1$0) and all transmit variables, subject to physical, power, and service reliability constraints.

Analytical Insights

Single-MA Case

For a single-movable-antenna ($U_1$1), the system reduces to a single-input configuration. The paper confirms—consistent with established results—that allocating power to artificial noise is strictly suboptimal, i.e., $U_1$2. This is due to the lack of spatial DoFs precluding effective AN spatial nulling towards the intended user.

Multi-MA Case

With $U_1$3, MAs enable transmit-side spatial shaping:

• AN Directionality: Under the constraint that AN causes zero leakage to $U_1$4, the optimal AN direction aligns with the projection of the eavesdropper's channel onto the null space of the intended user's channel. Mathematically, if $U_1$5, $U_1$6 are linearly independent, optimal $U_1$7 satisfies

$U_1$8

with $U_1$9 being the projection matrix onto the orthogonal complement of $U_2$0.

• AN-to-Confidential Power Ratio: The optimal allocation ratio $U_2$1 is derived in closed form, parameterized by relative channel strengths and AN projection efficacy (quantities $U_2$2, $U_2$3, $U_2$4). A nonzero $U_2$5 is beneficial only when the channel to $U_2$6 is not significantly stronger than the channel to $U_2$7, and AN can be projected to $U_2$8 efficiently.

These results establish that the joint spatial control via MAs fundamentally augments the utility of AN, as opposed to fixed-antenna systems.

Algorithmic Design

The highly coupled, non-convex nature of the joint optimization over MA positions and transmit variables is handled via a block coordinate ascent (BCA) framework:

• Transmit Variable Update: For given MA positions, a structured beamforming strategy is used. Multicast and confidential beamformers adopt maximum-ratio and parameterized sum directions between user channels. With the closed-form expressions for the optimal AN direction and power ratio, power allocation is reduced to a one-dimensional search.
• MA Position Update: For given transmit variables, an antenna-wise local search is performed using candidate points in the neighborhood, evaluated according to secrecy rate performance and system constraints. Damping and adaptive search radius ensure robustness and convergence.

The overall complexity is polynomial in the number of antennas and candidate points; empirical results show rapid convergence within a few iterations.

Numerical Results

Key numerical findings include:

• Secrecy Rate vs. AN-to-Confidential Power Ratio: The derived closed-form $U_2$9 achieves observed optimal secrecy rates, with a clear non-monotonic relationship reflecting the tradeoff between eavesdropper jamming (AN) and intended signal strength.
• Convergence Behavior: The BCA-based solution converges quickly (few iterations) and stably to locally optimal secrecy rates in multipath scenarios.
• Number of MAs: Significant secrecy gain is observed as $U_1$0 increases, particularly in the small-$U_1$1 regime; gains saturate due to aperture saturation at large $U_1$2. The combined MA+AN scheme consistently outperforms fixed-antenna and MA-only baselines.
• Multipath Richness: Environments with more paths (higher $U_1$3) are better exploited by MAs, further increasing secrecy rates, a property not present in fixed-antenna systems.

Empirical results corroborate strong claims that MA reconfiguration synergizes with AN spatial shaping for secrecy enhancement under PLSI.

Implications and Future Directions

The integration of AN with MA positioning delivers robust, low-complexity secrecy enhancement in service-integrated downlink systems. The closed-form design principles derived for power allocation and AN directionality facilitate scalable implementation. The proposed BCA framework is modular and compatible with extensions to larger user sets, higher-dimensional antenna structures, or constraints such as imperfect CSI.

Potential future research avenues include:

• Extending to multi-user, multi-class confidential/multicast service settings, invoking more general resource allocation frameworks.
• Integration with other physical-layer techniques (e.g., intelligent reflecting surfaces) to further exploit spatial DoFs.
• Addressing robustness to partial or outdated CSI, accounting for mobility and real-world positioning errors.
• Hardware prototyping and practical deployment studies to quantify real-world benefits and constraints of MA spatial control.

Conclusion

This work establishes rigorous theoretical and algorithmic foundations for artificial-noise-aided, movable-antenna-based PLSI. Leveraging new spatial DoFs, the joint optimization of MA positions and transmit variables—guided by analytically tractable design rules—enables considerable and scalable improvements in secrecy performance under service integration constraints. The proposed approaches are suited for next-generation (6G) secure wireless networks with stringent confidentiality and reliability requirements.

Reference:

"Artificial-Noise Aided Design for Movable-Antenna Enabled Physical-Layer Service Integration" (2605.00306)