On the Efficient Design of Stacked Intelligent Metasurfaces for Secure SISO Transmission

Recently, stacked intelligent metasurfaces (SIMs) have aroused widespread discussions as an innovative technology for directly processing electromagnetic (EM) wave signals. By stacking multiple programmable metasurface layers, an SIM has the ability to provide additional spatial degrees of freedom without the introduction of expensive radio-frequency chains, which may outperform reconfigurable intelligent surfaces (RISs) with single-layer structures. For the sake of alleviating information leakage risks in wireless communications, artificial noise (AN) has arisen as a physical-layer security technology with severe hardware constraints, which is impracticable in single-input single-output (SISO) systems. Therefore, we deploy an SIM at the transmitter (Alice) to accomplish joint modulation, beamforming, and AN in SISO systems. As such, an artificial neural network structured SIM aims to convert an input carrier signal into a desired output signal. Subsequently, we formulate the fitting problem between the actual output signal and the desired signal. Moreover, we introduce a regularization parameter to improve the energy efficiency. In order to tackle this resultant non-convex problem, we provide an alternating optimization algorithm to iteratively determine each variable. For the sake of reducing the computational complexity, we derive closed-form expressions for each phase shift and transmit power. Furthermore, we theoretically analyze the secrecy rate and computational complexity. By considering the signal deviation introduced by SIM, we derive upper and lower bounds of the secrecy rate to provide fundamental insights. Finally, simulation results demonstrate that the SIM-aided SISO system is capable of realizing secure communications efficiently, while the introduced power regularization parameter saved over 2 dB transmit power for a 5-layer SIM without amplifying the fitting error.