Over-the-Air Computation with Multiple Receivers: A Space-Time Approach

Over-the-air (OtA) computation is a newly emerged concept for achieving resource-efficient data aggregation over a large number of wireless nodes. Current research on this topic only considers the standard star topology with multiple senders transmitting information to one receiver. In this work, we investigate how to achieve OtA computation with multiple receivers, and we propose a novel communication design by exploiting joint precoding and decoding over multiple time slots. The optimal precoding and decoding vectors are determined by solving an optimization problem that aims at minimizing the mean squared error of aggregated data under the unbiasedness condition and the power constraints. We show that with our proposed multi-slot design, we can save communication resources (e.g., time slots) and achieve smaller estimation error as compared to the baseline approach of separating different receivers over time.