A Radio-Frequency-Based 2-D Convolutional Layer using Transmissive Intelligent Surfaces

A novel convolutional layer based on transmissive intelligent surfaces (TISs), which operates in the radio-frequency (RF) domain, is introduced for analog over-the-air (OTA) computation in this paper. To be specific, each RF convolutional layer comprises three TISs placed sequentially to perform a 2-D convolution operation. A method for designing TIS transmission coefficients, TIS locations, and TIS element spacing is proposed to execute the 2-D convolution of I ∗ K = O. The transmission coefficients of the second TIS encapsulate information about the kernel K, and the output (O) of the third TIS is the convolutional result of K and the input signal (I), which is the input to the first TIS. To validate the proposed design, a simple neural network featuring a single convolutional layer with one kernel is tested. The simulation results demonstrate that, with a practical size of the proposed design and adequate signal power transmitted to the TISs, the neural network incorporating the proposed TIS-based convolutional layer achieves a good approximation of performance compared to a neural network with the classic complex-valued convolutional layer. This validates the feasibility of the proposed design and the potential for offloading convolution operations from digital processors to the RF domain.