# Geometry-Informed Optimization of Binary RIS Configurations for Communication and Sensing

arXiv: https://arxiv.org/abs/2608.04133 · HTML: https://mlsanity.com/paper/2608.04133/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 31 references that are in the map.
- First posted on arXiv 4 Aug 2026.

## Builds on (most cited first, 16 of 16)

- [Intelligent Reflecting Surface Enhanced Wireless Network via Joint Active and Passive Beamforming](https://mlsanity.com/paper/1810.03961/) (2018)
- [Towards Smart and Reconfigurable Environment: Intelligent Reflecting Surface Aided Wireless Network](https://mlsanity.com/paper/1905.00152/) (2019)
- [Integrating Over-the-Air Federated Learning and Non-Orthogonal Multiple Access: What Role can RIS Play?](https://mlsanity.com/paper/2103.00435/) (2021)
- [Reconfigurable Intelligent Surfaces for Localization: Position and Orientation Error Bounds](https://mlsanity.com/paper/2009.02818/) (2020)
- [Target Sensing with Intelligent Reflecting Surface: Architecture and Performance](https://mlsanity.com/paper/2201.09091/) (2022)
- [Beamforming Optimization for Intelligent Reflecting Surface with Discrete Phase Shifts](https://mlsanity.com/paper/1810.10718/) (2018)
- [Intelligent Reflecting Surface-Assisted Cognitive Radio System](https://mlsanity.com/paper/1912.10678/) (2019)
- [Asymptotically Optimal Closed-Form Phase Configuration of 1-bit RISs via Sign Alignment](https://mlsanity.com/paper/2407.13510/) (2024)
- [Foundations of MIMO Radar Detection Aided by Reconfigurable Intelligent Surfaces](https://mlsanity.com/paper/2105.09250/) (2021)
- [Intelligent Reflecting Surface with Discrete Phase Shifts: Channel Estimation and Passive Beamforming](https://mlsanity.com/paper/1911.03916/) (2019)
- [Joint Localization and Environment Sensing by Harnessing NLOS Components in RIS-aided mmWave Communication Systems](https://mlsanity.com/paper/2305.12332/) (2023)
- [RIS-Assisted High Resolution Radar Sensing](https://mlsanity.com/paper/2407.11726/) (2024)
- [Reconfigurable Intelligent Surfaces for 6G and Beyond: A Comprehensive Survey from Theory to Deployment](https://mlsanity.com/paper/2506.19526/) (2025)
- [RIS-Assisted 3D Spherical Splatting for Object Composition Visualization using Detection Transformers](https://mlsanity.com/paper/2511.02573/) (2025)
- [Intelligent Reflecting Surfaces for Integrated Sensing and Communications: From System Coexistence to Networked Mutualism](https://mlsanity.com/paper/2511.10990/) (2025)
- [A Tutorial on Controlling Metasurfaces from the Network Perspective](https://mlsanity.com/paper/2601.12118/) (2026)

## Abstract (arXiv)

Practical Reconfigurable Intelligent Surfaces (RISs) often support only a small number of phase states, making their configuration inherently discrete. For a 1-bit RIS with N elements, direct optimization requires searching among 2N binary configurations. This work shows that this exponential configuration space is not unstructured. By reformulating 1-bit RIS optimization as the maximization of the norm of a signed sum of channel-dependent vectors, we prove that every globally optimal configuration must be induced by the signs of their projections onto a common direction. This geometric characterization restricts the class of configurations that can contain global optima and leads to different algorithmic consequences depending on the signal-space dimension. For general Multiple-Input-Multiple-Output (MIMO) systems, we develop a geometry-informed sampling method that evaluates only structurally admissible configurations. For Single-Input-Single-Output (SISO) systems, the same principle reduces to a two-dimensional angular partition, allowing the complete candidate set to be characterized and the global optimum to be recovered through polynomial-time enumeration, by evaluating at most N+1 out of the 2N configurations. Finally, we apply the same binary optimization principle to an Integrated Sensing and Communication (ISAC) scenario, where communication enhancement and target localization reduce to the same underlying geometric problem. The proposed framework therefore provides a unified approach for exploiting the structure of practical 1-bit RIS configurations across communication and sensing functionalities.