The rapid deployment of mega-constellations is driving the long-term vision of space data centers (SDCs), where interconnected satellites form in-orbit distributed computing and learning infrastructures. Enabling distributed federated learning in such systems is challenging because iterative training requires frequent aggregation over inter-satellite links that are bandwidth- and energy-constrained, and the link conditions can be highly dynamic. In this work, we exploit over-the-air computation (AirComp) as an in-network aggregation primitive. However, conventional coherent AirComp relies on stringent phase alignment, which is difficult to maintain in space environments due to satellite jitter and Doppler effects. To overcome this limitation, we propose OptiVote, a robust and communication-efficient non-coherent free-space optical (FSO) AirComp framework for federated learning toward Space Data Centers. OptiVote integrates sign stochastic gradient descent (signSGD) with a majority-vote (MV) aggregation principle and pulse-position modulation (PPM), where each satellite conveys local gradient signs by activating orthogonal PPM time slots. The aggregation node performs MV detection via non-coherent energy accumulation, transforming phase-sensitive field superposition into phase-agnostic optical intensity combining, thereby eliminating the need for precise phase synchronization and improving resilience under dynamic impairments. To mitigate aggregation bias induced by heterogeneous FSO channels, we further develop an importance-aware, channel state information (CSI)-free dynamic power control scheme that balances received energies without additional signaling. We provide theoretical analysis by characterizing the aggregate error probability under statistical FSO channels and establishing convergence guarantees for non-convex objectives.

翻译：巨型星座的快速部署正推动着空间数据中心（SDCs）的长期愿景，其中互联卫星构成在轨分布式计算与学习基础设施。在此类系统中实现分布式联邦学习具有挑战性，因为迭代训练需要通过星间链路频繁聚合，而这些链路受带宽和能量限制，且链路条件可能高度动态。在本工作中，我们利用空中计算（AirComp）作为一种网络内聚合原语。然而，传统的相干AirComp依赖于严格的相位对齐，这在空间环境中由于卫星抖动和多普勒效应而难以维持。为克服此限制，我们提出了OptiVote，一个面向空间数据中心的鲁棒且通信高效的非相干自由空间光（FSO）AirComp联邦学习框架。OptiVote将符号随机梯度下降（signSGD）与多数投票（MV）聚合原理及脉冲位置调制（PPM）相结合，其中每颗卫星通过激活正交的PPM时隙来传输本地梯度符号。聚合节点通过非相干能量累积执行MV检测，将相位敏感的场叠加转换为相位无关的光强合并，从而消除了对精确相位同步的需求，并提高了动态损伤下的鲁棒性。为减轻异构FSO信道引起的聚合偏差，我们进一步开发了一种无信道状态信息（CSI）的重要性感知动态功率控制方案，该方案可在无需额外信令的情况下平衡接收能量。我们通过刻画统计FSO信道下的聚合错误概率，并为非凸目标建立收敛保证，提供了理论分析。