Beamforming Design for Continuous Aperture Array (CAPA)-Based MIMO Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915397350981632 |
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| author | Wang, Zhaolin Ouyang, Chongjun Liu, Yuanwei |
| author_facet | Wang, Zhaolin Ouyang, Chongjun Liu, Yuanwei |
| contents | An efficient beamforming design is proposed for continuous aperture array (CAPA)-based point-to-point multiple-input multiple-output (MIMO) systems. In contrast to conventional spatially discrete array (SPDA)-MIMO systems, whose optimal beamforming can be obtained using singular-value decomposition, CAPA-MIMO systems require solving the eigendecomposition of a Hermitian kernel operator, which is computationally prohibitive. To address this challenge, an explicit closed-form expression for the achievable rate of CAPA-MIMO systems is first derived as a function of the continuous transmit beamformer. Subsequently, an iterative weighted minimum mean-squared error (WMMSE) algorithm is proposed, directly addressing the CAPA-MIMO beamforming optimization without discretization approximation. Closed-form updates for each iteration of the WMMSE algorithm are derived via the calculus of variations (CoV) method. For low-complexity implementation, an equivalent matrix-based iterative solution is introduced using Gauss-Legendre quadrature. Our numerical results demonstrate that 1) CAPA-MIMO achieves substantial performance gain over the SPDA-MIMO, 2) the proposed WMMSE algorithm enhances performance while significantly reducing computational complexity compared to state-of-the-art Fourier-based approaches, and 3) the proposed WMMSE algorithm enables practical realization of parallel, non-interfering transmissions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_00181 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Beamforming Design for Continuous Aperture Array (CAPA)-Based MIMO Systems Wang, Zhaolin Ouyang, Chongjun Liu, Yuanwei Information Theory An efficient beamforming design is proposed for continuous aperture array (CAPA)-based point-to-point multiple-input multiple-output (MIMO) systems. In contrast to conventional spatially discrete array (SPDA)-MIMO systems, whose optimal beamforming can be obtained using singular-value decomposition, CAPA-MIMO systems require solving the eigendecomposition of a Hermitian kernel operator, which is computationally prohibitive. To address this challenge, an explicit closed-form expression for the achievable rate of CAPA-MIMO systems is first derived as a function of the continuous transmit beamformer. Subsequently, an iterative weighted minimum mean-squared error (WMMSE) algorithm is proposed, directly addressing the CAPA-MIMO beamforming optimization without discretization approximation. Closed-form updates for each iteration of the WMMSE algorithm are derived via the calculus of variations (CoV) method. For low-complexity implementation, an equivalent matrix-based iterative solution is introduced using Gauss-Legendre quadrature. Our numerical results demonstrate that 1) CAPA-MIMO achieves substantial performance gain over the SPDA-MIMO, 2) the proposed WMMSE algorithm enhances performance while significantly reducing computational complexity compared to state-of-the-art Fourier-based approaches, and 3) the proposed WMMSE algorithm enables practical realization of parallel, non-interfering transmissions. |
| title | Beamforming Design for Continuous Aperture Array (CAPA)-Based MIMO Systems |
| topic | Information Theory |
| url | https://arxiv.org/abs/2504.00181 |