Utility Optimization for Over-the-air Computation Systems with Spectrum Sharing

Wireless data aggregation (WDA) is a pivotal enabling technique for Internet of Things (IoT). Recently, an emerging WDA technique, over-the-air computation (AirComp), has been proposed to perform fast data aggregation, with enhanced spectrum utilization and shortened transmission delay. AirComp leverages the superposition property of a wireless multiple access channel to accomplish functional computation of data, which can support the model aggregation in distributed machine learning and fusion of sensing data. In this paper, we consider a multi-cell AirComp system with spectrum sharing, in which every user in a multi-cell network shares a common part of the spectrum. The mean squared error (MSE) is used as the performance metric to quantify the computation accuracy at each access point (AP). With the aim of coordinating the MSEs among multiple APs, two different objective functions, weighted sum MSE and proportional fairness, are adopted. Accordingly, to minimize the weighted sum MSE, the block coordinate descent (BCD) method is employed. The analytical solutions are also provided. To minimize the proportional fairness, a tractable solution is developed, which is based on the successive convex approximation (SCA) technique. The effectiveness of the proposed schemes is validated by our numerical results.