The increasing demand for higher data rates, lower latency, and reduced error rates in next-generation wireless communication systems necessitates higher carrier frequencies and extremely large-scale antenna arrays. However, this progress introduces a critical challenge: ensuring the security and resilience of these networks against eavesdropping. Traditional cryptographic methods at the network layer, while effective, increase message code length and transmission overhead, requiring key exchange and hindering the performance of high-bandwidth, ultralow-latency systems. Various physical-layer security methods have been developed to address this issue, including beamforming with phased arrays and cooperative jamming with artificial noise. Metasurface-coated devices offer a significant improvement over traditional beamforming by mitigating the trade-off between ultralow-power transmissions and secrecy capacity. These methods, rooted in Wyner’s wiretap model, aim to increase the signal-to-noise ratio (SNR) disparity between the main lobe (legitimate receiver) and side lobe (eavesdropper) beams. However, a fundamental security risk remains: the transmitter radiates undistorted signals indiscriminately, leaving information vulnerable to interception by eavesdroppers with sensitive receivers. This necessitates directional communication techniques. Directional information modulation (DIM) emerges as a promising physical-layer security technique. It uses the beamforming capabilities of multiple antennas to transmit correct constellation symbols to intended receivers while distorting them in undesired directions. Several DIM implementations exist, including phased arrays for single-channel QPSK modulation (expensive, uses heuristic algorithms) and time-modulated arrays (TMA) for DIM at harmonics (sensitive switching devices, pre-designed periodic waveforms). While powerful, these approaches suffer from high cost, energy consumption, limited dimensionality (primarily 1D), and security risks associated with parasitic harmonic signals carrying information. Programmable metasurfaces (PMs), offering advantages in integration, cost, and energy efficiency, have shown potential for DIM. However, previous PM-based DIM efforts are limited to low-order modulation schemes (ASK, QPSK) with a small number of channels, often relying on either phase or magnitude modulation of EM waves, resulting in high energy per bit due to low information capacity. This research proposes and experimentally demonstrates a novel DIM scheme that addresses these shortcomings.

The existing literature highlights the limitations of traditional cryptographic methods in securing high-bandwidth, low-latency wireless communication systems. The use of beamforming and cooperative jamming techniques, while effective to some degree, still suffers from the inherent vulnerability of indiscriminate signal radiation. Previous work on DIM explored phased arrays and time-modulated arrays, but these systems are often expensive, power-hungry, and limited in their ability to support high-order modulation and multi-directional transmission. The use of programmable metasurfaces for DIM has shown promise, offering a potential path towards more compact, efficient, and secure communication systems. However, existing metasurface-based DIM approaches have limitations in terms of the order of modulation achievable and the number of simultaneous communication channels supported. This research builds upon the existing body of work by demonstrating a more advanced and versatile DIM scheme that overcomes these limitations.

This study proposes a novel DIM scheme based on a two-dimensional (2D) programmable metasurface (PM). The system directly transmits digital information, comprising four parts: multi-channel bit streams, a microcontroller unit (MCU), a PM-based transmitter, and user equipment (UEs). The process begins with an efficient discrete optimization algorithm, based on the alternating direction method of multipliers (ADMM), determining the PM's phase coding library to generate specific modulation symbols in desired directions. Bit streams are translated into symbols, mapped to the PM's phase coding via library indexing, and imposed on the PM's tunable components via the MCU. UEs extract information by comparing received signals with the corresponding constellation symbols; desired UEs receive regular constellation diagrams (with phase shifts compensated), while undesired UEs receive distorted signals, preventing information acquisition. The PM's meta-element, measuring 13 × 13 × 2.5 mm (low-profile), uses dual PIN diodes to achieve 2-bit phase control (S1: -90°, S2: 0°, S3: 90°, S4: 180°), eliminating the need for external phase shifters. Simulations show consistent magnitude responses near unity and nearly 90° phase differences across the 10.7-11.7 GHz frequency range. The PM operates in both transmission and reception modes (with different coding patterns), facilitated by improvements in the feed network (Wilkinson power divider replacing the T-type divider) and the use of PIN diodes instead of varactors. The core of the algorithm involves optimizing the coding sequences (x) of the PM to minimize the difference between received signals (y) and reference constellation symbols (s). The optimization problem, formulated as minimizing ||s - βHx||² + κβ²σ², with discrete phase constraints on x, is non-convex. The ADMM framework decomposes this into simpler, convex subproblems which are solved iteratively: x is updated using a closed-form solution based on the current estimates of β and the dual variable u; β is updated to scale the magnitude of received signals; and u is updated using a gradient ascent method. This process iterates until convergence. The algorithm is shown to be computationally efficient and scalable to large arrays. The experimental setup involves a far-field anechoic chamber, a PM excited by a sinusoidal carrier signal, a horn antenna connected to a vector network analyzer (VNA) for signal detection, and an MCU for controlling the PM's coding sequences. The PM is an 8 × 8 element array (144 × 144 × 2.5 mm³). Received signals are normalized and have a uniform phase added for propagation compensation. Measurements are performed for single-channel 8PSK and 64QAM, and dual-channel 16QAM modes (four-channel DIM results are presented in the supplementary information). Error vector magnitude (EVM) is used to quantify performance, with lower values indicating better agreement between measured and reference symbols. A secure zone is defined based on EVM thresholds to separate desired and undesired users. The cross-talk between channels is analyzed by evaluating the EVM while transmitting different symbols to different users simultaneously, quantifying channel independence.

The experimental results demonstrate the successful implementation of the proposed 2D, high-order DIM scheme. Single-channel measurements for 8PSK and 64QAM showed excellent agreement between measured and reference constellation symbols in the desired directions, while signals in undesired directions were significantly distorted. This confirms the directional security of the system. Dual-channel 16QAM experiments successfully demonstrated independent and simultaneous transmission to two users, with low crosstalk values (maximum 0.12, -18.4 dB) indicating acceptable channel independence. The EVM analysis confirmed the existence of a secure zone around the desired directions where the received signals closely matched the reference constellation diagrams, emphasizing the robustness of the directional communication. Furthermore, experiments across a range of frequencies showed the broadband capabilities of this DIM scheme, indicating compatibility with next-generation high-throughput wireless communication systems. The optimized coding sequences for the 8x8 PM in the dual-channel 16QAM scenario were also presented, highlighting the algorithmic effectiveness in generating directional beams. The study also introduced a new method for calculating multi-user crosstalk in DIM systems, providing a quantitative metric for assessing channel independence.

This work successfully demonstrates a novel approach to achieve secure communication using a two-dimensional programmable metasurface. The ability to support high-order modulations (64QAM) and multiple channels simultaneously represents a significant advancement compared to existing DIM techniques. The low profile, low energy consumption, and inherent directional security features make this technology particularly promising for deployment in next-generation wireless communication networks. The successful implementation of the ADMM-based optimization algorithm showcases its effectiveness in generating precise coding sequences to achieve the desired directional modulation properties. The experimental validation confirms the practical feasibility of the proposed scheme and its potential to enhance security in various wireless applications. The relatively low cross-talk between channels suggests good independence, further strengthening the practical viability of the proposed system. The broadband capability of the system underscores its adaptability to different operating frequencies and its potential to integrate into existing high-throughput communication standards.

This paper presents a novel 2D, high-order DIM scheme based on a 2-bit programmable metasurface and a fast optimization algorithm. Experimental results successfully demonstrate multi-channel operation with 8PSK, 16QAM, and 64QAM modulations, achieving directional security with low crosstalk and broadband capabilities. This work contributes significantly to advancing physical-layer security in wireless communications. Future research could focus on developing real-time communication systems and exploring advanced modulation techniques to further improve the system's performance and security.

While the presented research demonstrates significant progress in 2D high-order DIM, certain limitations exist. The current implementation uses an 8x8 PM, and scaling to larger arrays could introduce challenges in terms of computational complexity and hardware limitations. The current algorithm assumes perfect knowledge of channel state information (CSI), which might not always be true in real-world scenarios. Furthermore, the impact of mutual coupling between elements within the PM was not explicitly considered, potentially affecting performance. Further investigation into these areas could enhance the robustness and applicability of this technology.