Fluid antenna arrays (FAAs), support multiuser downlink transmission by activating a subset of reconfigurable ports. The activation mask jointly determines the effective channel and the sparse radiating aperture, which requires a balance among sum rate, sidelobe suppression, hardware constraints, and online complexity. Channel driven selection can cluster active ports and increase sidelobes, whereas sidelobe oriented synthesis is typically channel independent and can sacrifice sum rate. This paper proposes learned blockwise port activation (L-BPA), for real time sidelobe aware FAA downlink beamforming. L-BPA activates a fixed number of ports in each aperture block, which supports grouped switching hardware and limits port clustering. A lightweight convolutional network scores ports using multiuser channel features, port coordinates, and user power statistics. Training combines blockwise straight through masks with a differentiable peak sidelobe level (PSLL), surrogate. During inference, learned scores are combined with multiscale geometric repulsion, followed by regularized zero forcing precoding over the reduced effective channel. L-BPA reduces the average PSLL by 3.26 dB relative to uniform sparse activation while achieving a slightly higher sum rate. It also reduces the PSLL by 8.13 dB and 10.10 dB relative to greedy and gain based selection, respectively, without iterative online search.

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