Wave Processing Unit: Closed-Form Matrix Synthesis for Wave Computing in Multiuser MIMO Communications
Abstract
Wave computing offers a compelling route to bypass the latency and energy bottlenecks of digital baseband processing. However, existing wave-domain processors rely on task-specific, non-convex iterative optimization, which incurs substantial configuration overhead and limits real-time applications. In this paper, we propose the wave processing unit (WPU), a programmable planar Mach--Zehnder interferometer (MZI) network that accelerates matrix--vector multiplications in MIMO communications. First, we model the tunable MZI element as a parameterized 2×2 unitary transformation, and establish a closed-form synthesis framework for the WPU that decomposes an arbitrary unitary matrix into a cascade of MZI elements arranged in a compact rectangular topology. To handle arbitrary complex-valued operators, we further extend the method through singular value decomposition (SVD) and a hardware-efficient semi-unitary synthesis, avoiding redundant hardware and reducing the compilation complexity. We then apply the WPU to multiuser downlink precoding by an efficient WPU synthesis method, and compare the proposed architecture with hybrid and wave-domain ones. Numerical results demonstrate machine-precision synthesis with negligible residuals for up to 64×64 operators, with approximately 380× faster configuration than iterative wave computing baselines. For 64-antenna, 8-user downlink precoding, WPU requires 87.5% fewer RF chains than the fully digital architecture while achieving the same sum rate under ideal hardware. These results highlight the potential of the WPU for precise, hardware-efficient wave-domain processing with rapid configuration.
Related
- Joint Beamforming for Continuous Transmissive RIS-Enabled Multiuser Communications
- Structured Positive-Definite Optimal Control Synthesis of Closed-Loop Recommendation Systems over Social Networks
- MAP-Based Task-Oriented Precoding for Multiuser Communication
- A Multiuser Channel Capacity Region
- Discrete Diffusion for Port Selection in Multiuser Pinching-Antenna Systems
BibTeX
@misc{teng2026wave,
title = {{Wave Processing Unit: Closed-Form Matrix Synthesis for Wave Computing in Multiuser MIMO Communications}},
author = {Xiaokun Teng and Yanqing Ren and Weicong Chen and Wankai Tang and Xiao Li and Shi Jin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29687},
eprint = {2610.29687},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29687},
}
RIS
TY - UNPB
TI - Wave Processing Unit: Closed-Form Matrix Synthesis for Wave Computing in Multiuser MIMO Communications
AU - Xiaokun Teng
AU - Yanqing Ren
AU - Weicong Chen
AU - Wankai Tang
AU - Xiao Li
AU - Shi Jin
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29687
UR - https://arxiv.org/abs/2610.29687
AB - Wave computing offers a compelling route to bypass the latency and energy bottlenecks of digital baseband processing. However, existing wave-domain processors rely on task-specific, non-convex iterative optimization, which incurs substantial configuration overhead and limits real-time applications. In this paper, we propose the wave processing unit (WPU), a programmable planar Mach--Zehnder interferometer (MZI) network that accelerates matrix--vector multiplications in MIMO communications. First, we model the tunable MZI element as a parameterized 2×2 unitary transformation, and establish a closed-form synthesis framework for the WPU that decomposes an arbitrary unitary matrix into a cascade of MZI elements arranged in a compact rectangular topology. To handle arbitrary complex-valued operators, we further extend the method through singular value decomposition (SVD) and a hardware-efficient semi-unitary synthesis, avoiding redundant hardware and reducing the compilation complexity. We then apply the WPU to multiuser downlink precoding by an efficient WPU synthesis method, and compare the proposed architecture with hybrid and wave-domain ones. Numerical results demonstrate machine-precision synthesis with negligible residuals for up to 64×64 operators, with approximately 380× faster configuration than iterative wave computing baselines. For 64-antenna, 8-user downlink precoding, WPU requires 87.5% fewer RF chains than the fully digital architecture while achieving the same sum rate under ideal hardware. These results highlight the potential of the WPU for precise, hardware-efficient wave-domain processing with rapid configuration.
ER -