Exponential Noise Robustness of Type-Based Multiple Access for Over-the-Air Computation

This paper studies the robustness of type-based multiple access (TBMA) in over-the-air computation (AirComp) under nonparametric estimation, where no prior knowledge of the data distribution is available. While conventional AirComp approaches rely on amplitude modulations and suffer from noise sensitivity, TBMA enables the use of more structured modulation formats that can be exploited for improved performance. We show that the superposition of transmitted signals in TBMA induces a discrete lattice structure in the received signal space, where each lattice point corresponds to the number of devices accessing a given channel resource. By exploiting this structure through nearest-lattice-point projection, noise effects can be substantially suppressed. The proposed technique achieves an exponential decay of the mean squared error (MSE) with respect to the energy-to-noise spectral density ratio, whereas in conventional techniques the MSE only scales inversely with this ratio. Simulation results validate the theoretical findings and demonstrate that TBMA provides a fundamental robustness advantage over traditional AirComp.