WaveComp: Wavelet-Domain Computation for Reliable Data Fusion in IoT Networks

Over-the-air computation (AirComp) is a promising technique that leverages the superposition property of wireless channels for distributed data aggregation. However, its performance can be severely affected by synchronization errors, spectral leakage, and cyclic-prefix (CP) overhead. To address these challenges, this work proposes a wavelet-domain AirComp framework, termed WaveComp, which employs an orthonormal wavelet basis to achieve joint time-frequency localization, mitigate spectral leakage, and operate without explicit CP insertion under the considered channel model. A unified mean-squarederror (MSE) formulation is developed under both perfect and imperfect channel-state-information (CSI) conditions, providing analytical insight into the robustness of WaveComp relative to OFDM-based AirComp, and system behavior is evaluated under several practical power-allocation strategies. Simulation results demonstrate that WaveComp achieves up to 3 dB lower MSE and up to a 25% reduction in error floor compared with OFDMbased AirComp across a wide range of SNRs and device densities under both CSI regimes.