Spatial wideband effects are known to affect channel estimation and localization performance in millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems. Based on perturbation analysis, we show that the spatial wideband effect is in fact more pronounced than previously thought and could significantly degrade performance if not properly considered in the algorithm design, even at moderate bandwidths. We propose a novel channel estimation method based on multidimensional ESPRIT algorithms per subcarrier, combined with unsupervised learning for pairing across subcarriers, which shows significant performance gain over existing schemes under wideband conditions. © 2023 IEEE