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Closed-Form Power Allocation for Analog AirComp Over Dimming-Constrained IM/DD VLC
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DOI：10.1109/lcomm.2026.3710988.png)
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Abstract
En 中文
Direct-analog over-the-air computation (AirComp) over indoor visible light enables brightness-controlled overhead organic light-emitting diode (OLED) lighting/sensing panels to aggregate local measurements at a common photodetector in one channel use. We consider <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> panels that embed normalized scalars as zero-mean intensity variations around prescribed optical outputs while a receiver in their shared illumination region recovers a weighted aggregate. Under intensity modulation/direct detection (IM/DD), non-negativity, peak optical-output, and prescribed-brightness constraints jointly impose a per-panel bound on the received slope. We derive a boundary-complete closed-form mean-squared-error (MSE)-optimal allocation: a sorted prefix saturates at the optical bound while the remaining users follow strict received-coefficient alignment. The rule has <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {O}(K\log K)$ </tex-math></inline-formula> complexity without iteration or tuning, and the optimal receiver denoiser is the inverse allocation multiplier. We also characterize a closed-form MSE gap relative to projected strict alignment. An independent multi-start constrained optimizer that does not encode the active-set form matches the closed-form MSE over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4{\,}320$ </tex-math></inline-formula> operating points, with maximum relative difference <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7.91\!\times \!10^{-14}$ </tex-math></inline-formula>. Across <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$21{\,}600$ </tex-math></inline-formula> hardware-anchored OLED-VLC operating cells, the closed-form normalized MSE (NMSE) matches Monte Carlo to a median relative error of 0.37%, and the allocation yields a paired median MSE gain of 1.93 dB (35.9% MSE reduction) over projected strict alignment.
Keywords:
Visible light communication
over-the-air computation
intensity modulation/direct detection
power allocation
active-set method
dimming constraint
mean-squared error
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4.4
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1.2W
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2.2W
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