Near Field Dictionary Design and Channel Estimation Using Discrete Fresnel Transform

Two prominent trends in 6G multi-antenna technology are the use of extremely large-scale antenna arrays (ELAAs) and higher frequencies. These trends necessitate near-field spherical-wave propagation modeling, moving beyond the classical far-field planar-wave model. In the millimeter-wave band, where wavelengths are small relative to the array aperture, many propagation phenomena resemble optics. Drawing inspiration from Fresnel diffraction, we propose a Discrete Fresnel Transform (DFnT)-based dictionary for effectively modeling and sparsely representing the channel vector in both near and far-field scenarios. By discretizing and parameterizing the Fresnel Transform, we adapt it to ELAA codewords. Our simulations demonstrate that the DFnT dictionary outperforms existing far-field and Polar dictionaries for channel estimation using Orthogonal Matching Pursuit, a compressive channel estimation algorithm dependent on sparse representations.