Fourier Transform-based Wavenumber Domain 3D Imaging in RIS-aided Communication Systems

TL;DR

This work introduces a Fourier-transform-based 3D imaging framework for RIS-aided communication systems, turning RIS into an imaging aperture by recovering the equivalent UE-to-RIS channel response (ECR) through tailored RIS phase shifts. The method then applies FT-based wavenumber-domain imaging to reconstruct the ROI, complemented by k-space DRL analysis that accounts for near-field bistatic geometry. To address limited pilots, the authors propose pseudo-inverse and block RIS schemes and develop an integrated FT-CS algorithm that uses FFT/IFFT-based forward/backward operators to replace large sensing matrices. Numerical results show fast, memory-efficient imaging with DRLs aligning well with theoretical predictions, while the FT-CS integration achieves CS-like performance with substantially lower computational burden. The proposed approach enables real-time 3D radio imaging in RIS-enabled systems and provides design guidelines for RIS deployment, imaging distance, and pilot budgeting.

Abstract

Radio imaging is rapidly gaining prominence in the design of future communication systems, with the potential to utilize reconfigurable intelligent surfaces (RISs) as imaging apertures. Although the sparsity of targets in three-dimensional (3D) space has led most research to adopt compressed sensing (CS)-based imaging algorithms, these often require substantial computational and memory burdens. Drawing inspiration from conventional Fourier transform (FT)-based imaging methods, our research seeks to accelerate radio imaging in RIS-aided communication systems. To begin, we introduce a two-stage wavenumber domain 3D imaging technique: first, we modify RIS phase shifts to recover the equivalent channel response from the user equipment to the RIS array, subsequently employing traditional FT-based wavenumber domain methods to produce target images. We also determine the diffraction resolution limits of the system through k-space analysis, taking into account factors including system bandwidth, transmission direction, operating frequency, and the angle subtended by the RIS. Addressing the challenge of limited pilots in communication systems, we unveil an innovative algorithm that merges the strengths of both FT- and CS-based techniques by substituting the expansive sensing matrix with FT-based operators. Our simulation outcomes confirm that our proposed FT-based methods achieve high-quality images while demanding few time, memory, and communication resources.

Figures (11)

• Figure 1: Illustration of the considered RIS-aided communication system.
• Figure 2: Data stream on the $t$-th subcarrier, where $\widehat{b}_t(y_u, z_v)$, $\widehat{B}_t(k_y, k_z)$, $\widehat{B}'_{t}(k_y,k_z)$, $\widehat{\sigma}_t(x_{n_{\rm{x}}},y,z)$, and $\widehat{\sigma}_t(x,y,z)$ represent estimated discrete functions.
• Figure 3: Illustration of the $k$-space coverage in the considered system, where $k_{{\rm{t,min}}}$ and $k_{{\rm{r,min}}}$ ($k_{{\rm{t,max}}}$ and $k_{{\rm{r,max}}}$) represent the transmitting $k$-space vector from the UE to the point target and the scattering $k$-space vector from the point target to the RIS array at the minimum (maximum) subcarrier frequency, respectively.
• Figure 4: NLOS imaging scenarios with and without a RIS.
• Figure 5: Illustration of the block-controlled RIS phase shift configuration, where each small square represents a RIS element, and various colors denote different phase shifts.

Theorems & Definitions (4)

• Remark 1
• Remark 2
• Remark 3
• Remark 4