MAP-Optimal Hierarchical Quantization and Amplitude-Shift QAM for Reliable Digital Over-the-Air Computation

This paper presents a digital over-the-air (OTA) computation architecture that reliably aggregates nomographic functions, e.g., sum, product, maximum, and sum-of-squares—over a fading multiple-access channel. Every sensor quantises its reading through a multiple-level amplitude-shift modulation (ASM) hierarchy whose rectangular QAM grids are jointly optimised by a level-wise, maximum-a-posteriori (MAP) search. The optimisation weighs quantization distortion against MAP–detection error, producing