This paper studies an multi-cluster over-the-air computation (AirComp) system, where an intelligent reflecting surface (IRS) assists the signal transmission from devices to an access point (AP). The clusters are activated to compute heterogeneous functions in a time-division manner. Specifically, two types of IRS beamforming (BF) schemes are proposed to reveal the performancecost tradeoff. One is the cluster-adaptive BF scheme, where each BF pattern is dedicated to one cluster, and the other is the dynamic BF scheme, which is applied to any number of IRS BF patterns. By deeply exploiting their inherent properties, both generic and lowcomplexity algorithms are proposed in which the IRS BF patterns, time and power resource allocation are jointly optimized. Numerical results show that IRS can significantly enhance the function computation performance, and demonstrate that the dynamic IRS BF scheme with half of the total IRS BF patterns can achieve near-optimal performance which can be deemed as a cost-efficient approach for IRS-aided multi-cluster AirComp systems.

翻译：本文研究了一个多集群空中计算（AirComp）系统，其中智能反射面（IRS）辅助设备向接入点（AP）传输信号。集群以时分方式激活以实现异构函数的计算。具体而言，提出了两种IRS波束成形（BF）方案以揭示性能与成本的权衡关系：一种是集群自适应波束成形方案，其中每个波束模式专用于一个集群；另一种是动态波束成形方案，可应用于任意数量的IRS波束模式。通过深入挖掘其固有特性，提出了通用算法和低复杂度算法，其中联合优化了IRS波束模式、时间和功率资源分配。数值结果表明，IRS能显著提升函数计算性能，并证明采用总IRS波束模式一半的动态IRS波束成形方案可实现接近最优的性能，可视为IRS辅助多集群空中计算系统中一种高性价比的方法。