Combining AF-based Relay and Multiantenna for Over-the-Air Computation

Over-the-air computation has attracted much attention in wireless data aggregation, which collects and processes data simultaneously with high efficiency. Different propagation distances from nodes to the sink or channel fading may lead to misalignment in signal magnitude and result in computation error. In our previous work, amplify and forward (AF) based relay has been investigated. With multiantenna available at the sink, it is possible to achieve better performance by the misalignment allowed optimization (Miso), compared with zero forcing (ZF) which requires all signals aligned in signal magnitude. But Miso does cause many signals misaligned in signal magnitude, leading to a biased result. Aiming to further improve system performance, in this work, we study how to combine the AF based relay with Miso by a joint optimization, and solve it with an iterative algorithm. Extensive simulations verify the effectiveness of the proposed method.