Optimal symmetric low-rank BD-RIS configuration maximizing the determinant of a MIMO link
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918438707920896 |
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| author | Santamaria, Ignacio Soleymani, Mohammad Gutierrez, Jesus Jorswieck, Eduard |
| author_facet | Santamaria, Ignacio Soleymani, Mohammad Gutierrez, Jesus Jorswieck, Eduard |
| contents | Beyond-diagonal reconfigurable intelligent surfaces (BD-RISs) significantly improve wireless performance by allowing tunable interconnections among elements, but their design in multiple-input multiple-output (MIMO) systems has so far relied on complex iterative algorithms or suboptimal approximations. This work introduces a simple yet powerful approach: instead of directly maximizing the achievable rate, we maximize the absolute value of the determinant of the equivalent MIMO channel. We derive a closed-form symmetric unitary scattering matrix whose rank is exactly twice the channel's degrees of freedom ($2r$). Remarkably, this low-rank solution achieves the same determinant value as the optimal unitary BD-RIS. Using log-majorization theory, we prove that the rate loss relative to the optimal unitary BD-RIS vanishes at high signal-to-noise ratio (SNR) or when the number of BD-RIS elements becomes large. Moreover, the proposed solution can be perfectly implemented using a $q$-stem BD-RIS architecture with only $q=2r-1$ stems, requiring a minimum number of reconfigurable circuits. The resulting Max-Det solution is orders of magnitude faster to compute than existing iterative methods while achieving near-optimal rates in practical scenarios. This makes high-performance BD-RIS deployment feasible even with large surfaces and limited computational resources. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09335 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal symmetric low-rank BD-RIS configuration maximizing the determinant of a MIMO link Santamaria, Ignacio Soleymani, Mohammad Gutierrez, Jesus Jorswieck, Eduard Signal Processing Beyond-diagonal reconfigurable intelligent surfaces (BD-RISs) significantly improve wireless performance by allowing tunable interconnections among elements, but their design in multiple-input multiple-output (MIMO) systems has so far relied on complex iterative algorithms or suboptimal approximations. This work introduces a simple yet powerful approach: instead of directly maximizing the achievable rate, we maximize the absolute value of the determinant of the equivalent MIMO channel. We derive a closed-form symmetric unitary scattering matrix whose rank is exactly twice the channel's degrees of freedom ($2r$). Remarkably, this low-rank solution achieves the same determinant value as the optimal unitary BD-RIS. Using log-majorization theory, we prove that the rate loss relative to the optimal unitary BD-RIS vanishes at high signal-to-noise ratio (SNR) or when the number of BD-RIS elements becomes large. Moreover, the proposed solution can be perfectly implemented using a $q$-stem BD-RIS architecture with only $q=2r-1$ stems, requiring a minimum number of reconfigurable circuits. The resulting Max-Det solution is orders of magnitude faster to compute than existing iterative methods while achieving near-optimal rates in practical scenarios. This makes high-performance BD-RIS deployment feasible even with large surfaces and limited computational resources. |
| title | Optimal symmetric low-rank BD-RIS configuration maximizing the determinant of a MIMO link |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2604.09335 |