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：本文研究了一种多簇空中计算（AirComp）系统，其中智能反射面（IRS）辅助设备向接入点（AP）传输信号。各簇以时分方式激活，用于计算异构函数。具体而言，本文提出了两种IRS波束成形（BF）方案以揭示性能与成本之间的权衡：其一是簇自适应波束成形方案，每个波束成形模式专用于一个簇；其二是动态波束成形方案，该方案可应用于任意数量的IRS波束成形模式。通过深入挖掘其固有特性，本文提出了通用算法与低复杂度算法，联合优化了IRS波束成形模式、时间及功率资源分配。数值结果表明，IRS能显著提升函数计算性能，并证明使用总数一半IRS波束成形模式的动态波束成形方案可实现接近最优的性能，可视为IRS辅助多簇AirComp系统中一种具有成本效益的方法。