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 $2\times2$ 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 $64\times64$ operators, with approximately $380\times$ 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.

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