A Generalized Lorentzian–Rational M-Estimator for Robust Channel Estimation in Impulsive Noise

Robust channel estimation is essential for wireless communication systems operating in non-Gaussian, impulsive noise environments. While classical M-estimators such as Huber and Hampel provide robustness against outliers, they often rely on non-differentiable or piecewise-defined influence functions, which may lead to algorithmic instability. In this paper, we propose the Generalized Lorentzian–Rational (GLR) M-estimator, which employs a smooth, redescending influence function parameterized by only two shape parameters. The proposed estimator is infinitely differentiable and admits a stable iteratively reweighted least-squares (IRLS) implementation. We analyze key robustness properties of the GLR estimator, including influence behavior and asymptotic efficiency, and apply it to pilot-assisted channel estimation under impulsive noise modeled by a two-term Gaussian mixture distribution. Simulation results demonstrate that the proposed GLR-based channel estimator consistently outperforms least-squares and classical robust estimators in terms of normalized mean-squared error across a wide range of signal-to-noise ratio (SNR).