Channel-Aware Constellation Design for Digital OTA Computation

Over-the-air (OTA) computation has emerged as a promising technique for efficiently aggregating data from massive numbers of wireless devices. OTA computations can be performed by analog or digital communications. Analog OTA systems are often constrained by limited function adaptability and their reliance on analog amplitude modulation. On the other hand, digital OTA systems may face limitations such as high computational complexity and limited adaptability to varying network configurations. To address these challenges, this paper proposes a novel digital OTA computation system with a channel-aware constellation design for demodulation mappers. The proposed system dynamically adjusts the constellation based on the channel conditions of participating nodes, enabling reliable computation of various functions. By incorporating channel randomness into the constellation design, the system prevent overlap of constellation points, reduces computational complexity, and mitigates excessive transmit power consumption under poor channel conditions. Numerical results demonstrate that the system achieves reliable NMSE performance across a range of scenarios, offering valuable insights into the choice of signal processing methods and weighting strategies under varying computation point configurations, node counts, and quantization levels. This work advances the state of digital OTA computation by addressing critical challenges in scalability, transmit power consumption, and function adaptability.