Statistical Characterization and Block-EM Estimation of Frequency-Domain NSI for OFDM Systems in Bursty Impulsive Noise

Impulsive noise (IN), characterized by its high power and non-Gaussian distribution, poses a critical challenge in modern orthogonal frequency-division multiplexing (OFDM) systems, driven by the proliferation of electronic devices. Current IN mitigation techniques rely heavily on time-domain processing. These methods apply before the discrete Fourier transform (DFT), introducing additional complexity, failing to align with OFDM's inherent frequency-domain processing flow, and risking the destruction of subcarrier orthogonality due to imperfect IN subtraction. To address these limitations, we propose a frequency-domain, block-based framework for mitigating IN. The statistical representation of IN in the frequency domain is first derived using a transformed Gaussian mixture model. Based on this model, we develop an optimal receiver that leverages perfect noise state information (NSI), thereby identifying scenarios in which NSI is critical. We then propose an unsupervised block-based expectation-maximization (EM) framework for NSI estimation and develop three variants for evaluation. These include a simple symbol-by-symbol variance-updated EM, a sequence-based transition-updated EM, and a MAP-based EM that exploits a sparsity-promoting prior to automatically prune the number of states. Our frequency-domain design operates after the DFT, seamlessly integrates with the OFDM processing chain, preserves subcarrier orthogonality, and leverages the known IN block structure to achieve substantial performance gains without the immense complexity of time-domain impulse reconstruction.