# Stacked Intelligent Metasurface Performs a 2D DFT in the Wave Domain for DOA Estimation

arXiv: https://arxiv.org/abs/2310.09861 · HTML: https://mlsanity.com/paper/2310.09861/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2023.

## Built on by (most cited first, 3 of 3)

- [Artificial General Intelligence (AGI)-Native Wireless Systems: A Journey Beyond 6G](https://mlsanity.com/paper/2405.02336/) (2024)
- [Over-the-Air Semantic Alignment with Stacked Intelligent Metasurfaces](https://mlsanity.com/paper/2512.05657/) (2025)
- [Over-The-Air Extreme Learning Machines with XL Reception via Nonlinear Cascaded Metasurfaces](https://mlsanity.com/paper/2601.17749/) (2026)

## Abstract (arXiv)

Staked intelligent metasurface (SIM) based techniques are developed to perform two-dimensional (2D) direction-of-arrival (DOA) estimation. In contrast to the conventional designs, an advanced SIM in front of the receiving array automatically performs the 2D discrete Fourier transform (DFT) as the incident waves propagate through it. To arrange for the SIM to carry out this task, we design a gradient descent algorithm for iteratively updating the phase shift of each meta-atom in the SIM to minimize the fitting error between the SIM's response and the 2D DFT matrix. To further improve the DOA estimation accuracy, we configure the phase shifts in the input layer of SIM to generate a set of 2D DFT matrices having orthogonal spatial frequency bins. Extensive numerical simulations verify the capability of a well-trained SIM to perform 2D DFT. Specifically, it is demonstrated that the SIM having an optical computational speed achieves an MSE of 10-4 in 2D DOA estimation.