Two-dimensional and high-order directional information modulations for secure communications based on programmable metasurface

The paper addresses the challenge of physical-layer security in next-generation wireless systems that demand higher data rates, low latency, and low error rates. Traditional cryptographic approaches at upper layers increase overhead and require key exchanges, which can be problematic for ultra-low-latency, high-bandwidth links. Existing physical-layer methods (e.g., beamforming with phased arrays, cooperative jamming) aim to increase the SNR disparity between intended and unintended receivers but still radiate undistorted signals omnidirectionally, leaving vulnerabilities to sensitive eavesdroppers. Directional information modulation (DIM) seeks to send correct constellation symbols only along desired directions and distort them elsewhere, enhancing security. However, current DIM implementations are constrained by bulky, power-hungry, and costly hardware, typically supporting only 1D transmissions with limited array sizes, and, for time-modulated arrays, risk information leakage via harmonics. Programmable metasurfaces (PMs) have emerged as a promising platform for DIM due to their low-cost, low-power, and highly integrated architectures, yet prior PM-based demonstrations predominantly used only amplitude or phase, lacked support for high-order modulations such as QAM, relied on external RF sources, and were not easily compatible with standard transceiver operations. The study proposes a 2D PM-based DIM architecture with an efficient discrete optimization algorithm to achieve multi-user, high-order directional modulations while maintaining low profile and power consumption.

Prior physical-layer security approaches include phased-array beamforming and cooperative jamming/artificial noise, rooted in Wyner’s wiretap model that quantifies secrecy by capacity differences between legitimate and eavesdropper channels. Directional modulation has been implemented via: (1) phased arrays achieving single-channel QPSK, but requiring expensive RF chains and heuristic algorithms; and (2) time-modulated arrays (TMA), which realize DIM at harmonics using switching devices and periodic sequences, yet involve parasitic harmonics that carry information and create security risks, alongside high energy costs. PM-based systems have demonstrated near-field multi-channel ASK, dual-channel far-field QPSK, and dual-channel ASK, but typically used either phase or magnitude only, did not support high-order QAM, had large profiles with external RF sources, and lacked bidirectional (transmit/receive) compatibility. These gaps motivate a PM-based, 2D, high-order DIM solution with efficient discrete optimization.

Hardware: The authors design a low-profile 2-bit programmable metasurface (PM) element of size 13 × 13 × 2.5 mm (≈0.48 × 0.48 × 0.09λ at 11 GHz). Each meta-element has a radiation layer with dual PIN diodes bridging patches, a DC bias layer sandwiched between ground planes to shield bias lines, and a feed network layer with a two-port reflection-type phase shifter integrating two PIN diodes. Phase states S1–S4 produce approximately −90°, 0°, 90°, 180° without external phase shifters. Magnitude responses for all states are near unity across 10.7–11.7 GHz, with ~90° phase spacing across the band. For receiving-mode capability and reduced interference, the design improves the feed network using a Wilkinson power divider with high isolation and replaces varactors with PIN diodes to avoid high tuning voltages and complex controls. System architecture: The PM-based DIM system includes multi-channel bit streams, an MCU for imposing coding sequences, the PM acting as a transmitter or receiver, and user equipment in different directions. A phase-coding library is precomputed via discrete optimization to map target constellation symbols to PM coding states. During transmission, bit streams are translated to symbols and mapped to PM codes; UEs recover bits by comparing received signals to reference constellations (with uniform phase compensation for propagation). Channel and optimization model: With an N-element PM serving K users, the received signal at user k is y_k = h_k^H x + n_k, where h_k encodes path-dependent phases, element gain pattern G(θ_k, φ_k), and geometry. The optimization targets coding sequence x ∈ X^N (P-bit discrete phase set) and a scaling factor β to minimize ||s − β H x||^2 + κ β^2 σ^2 subject to discrete constraints. This non-convex finite-resolution precoding problem is addressed via an ADMM-based discrete optimization. By introducing an auxiliary variable and forming an augmented Lagrangian with penalty parameter ρ and dual vector u, the problem is split into alternating updates with closed-form steps: projection of x onto discrete phase set, linear solve for relaxed variable, update of β to match symbol magnitude, and dual ascent. The algorithm exhibits low complexity and fast convergence, scaling to larger arrays. Details of update equations, computational complexity, and comparisons to branch-and-bound and other DIM algorithms are provided (with derivations in supplementary material). Experimental setup: Measurements are performed in a far-field anechoic chamber. The fabricated 8 × 8 PM (overall 144 × 144 × 2.5 mm³) is excited by a sinusoidal carrier via an SMA port; coding sequences are imposed via an STM32F103C8T6 MCU. A horn antenna (HZ-90HA20NZJL) and VNA (Agilent N9010A) record signals. Received signals are rescaled using power normalization and β, with a uniform phase bias added for propagation compensation. Single-channel and dual-channel experiments validate 8PSK, 64QAM, and 16QAM transmissions in specified directions. EVM is used to quantify performance and define secure zones. Crosstalk is measured via a newly defined K × K matrix using controlled symbol transmissions across users.

- The PM-based DIM generates correct high-order constellation symbols in desired directions and distorted symbols elsewhere, enabling directional physical-layer security. - Single-channel demonstrations: 8PSK symbols transmitted toward (θ, φ) = (−19°, 0°) and 64QAM toward (θ, φ) = (21.5°, 0°) show measured phases and magnitudes closely matching references. - EVM-based validation: For 8PSK and 64QAM cases, EVM distributions show low EVM in intended directions and high EVM in unintended directions, confirming directional security. Secure zones are defined by EVM thresholds separating users from eavesdroppers. - Dual-channel 2D 16QAM: Simultaneous and independent transmission to two users at (θ1, φ1) = (28.5°, 0°) and (θ2, φ2) = (28.5°, 90°) achieves measured constellations matching references. Radiation patterns form main-lobe clusters aligned with target directions; main-lobe powers correlate with symbol magnitudes, evidencing effective energy allocation. - Low inter-user interference: Measured crosstalk matrix for the dual-user 16QAM shows a maximum cross-talk value of 0.12 (−18.4 dB), indicating acceptable channel independence. - Secure-zone characteristics: Around the target directions, received symbols cluster near the reference constellations for 8PSK, 64QAM, and 16QAM, while other directions show distorted constellations. - Broadband operation: Correct constellation structures are maintained across wide frequency ranges—8PSK: 10.3–11.8 GHz; 64QAM: 10.7–11.6 GHz; 16QAM (φ = 0° and φ = 90° cases): 10.6–11.4 GHz—supporting high-throughput communications. - Hardware features: The 2-bit PM element offers near-unity magnitude and ~90° phase spacing over 10.7–11.7 GHz. The 8 × 8 PM maintains low profile, cost, and power consumption, and can operate in both transmit and receive modes. - Algorithm performance: The ADMM-based discrete optimization scales efficiently with low complexity and fast convergence, enabling larger arrays (details in supplementary material).

The study demonstrates that a 2-bit programmable metasurface, combined with an efficient discrete optimization algorithm, can realize two-dimensional, high-order directional information modulation with multi-user support. By mapping desired symbols to discrete phase codes that shape beams and field phases, correct constellations are formed only along intended directions, while signals are distorted elsewhere, effectively addressing the security vulnerability of omnidirectional radiation. The experimental EVM maps, constellation diagrams, and crosstalk measurements confirm reliable symbol recovery in target directions and incorrect structures outside secure zones. The dual-channel 16QAM results verify 2D multi-user capability with low inter-user interference, while radiation power-symbol magnitude correlations validate energy-efficient allocation. The broadband performance across GHz-wide ranges indicates robustness suitable for next-generation high-throughput links. Collectively, these outcomes substantiate DIM as a practical physical-layer security mechanism using compact, low-power PM hardware compatible with conventional transceiver roles.

This work introduces a low-profile, low-cost PM-based DIM scheme that supports 2D, high-order modulations and multi-user links using a 2-bit metasurface and an ADMM-based discrete optimization algorithm. Experiments validate single-channel 8PSK and 64QAM and dual-channel 16QAM with directional security, low EVM in desired directions, distorted symbols elsewhere, acceptable inter-user crosstalk (max 0.12, −18.4 dB), and broadband operation. The approach offers a pathway to endogenous secure communications at the physical layer and is compatible with transmitter and receiver roles. Future work includes advancing real-time communication systems, increasing phase quantization levels, scaling metasurface size to reduce multi-user interference, and improving channel models (e.g., incorporating mutual coupling) and exploring positional modulations to further mitigate DIM limitations.

- Experimental validation uses an 8 × 8 array with 2-bit phase quantization; higher quantization and larger arrays are expected to further reduce multi-user interference and improve performance. - The optimization and transmission assume a perfectly known scaling factor β (via pilot), which may be imperfect in practical deployments. - Dual-channel experiments show non-zero crosstalk (maximum 0.12 or −18.4 dB), indicating residual inter-user interference. - The demonstrated system focuses on far-field scenarios at ~11 GHz; while broadband performance is shown, performance outside measured ranges and in more complex channels (including mutual coupling effects) requires further study. - Real-time end-to-end communication and full integration into conventional systems are identified as future developments; current demonstrations are proof-of-concept measurements.