GMM-based Symbol Error Rate Analysis for Multicarrier Systems with Impulsive Noise Suppression

Theoretical analysis of orthogonal frequency division multiplexing (OFDM) systems, equipped at the receiver by a non-linear impulsive noise suppressor, is very challenging. Indeed, although an exact closed-form expression for the output signal-to-noise ratio (SNR) of such OFDM systems is available for widely used impulsive noise models, theoretical analysis of the associated symbol error rate (SER) is still open. The analytical SER available in the literature, exploit a Gaussian approximation of the non-linear distortion noise, which however holds true only under specific conditions. Conversely, this work develops an accurate analytical closed-form expression of the distortion noise distribution at the nonlinearity output, as well as its approximation by a Gaussian mixture model (GMM). By using GMMs we unify the SER analysis for communication systems equipped by non-linear impulsive noise suppressors, typically also used in vehicular communications. Closed form expressions for the SER are derived both for non-fading and frequency-selective Rayleigh/Rician fading channels affected by impulsive noise, which is also modeled by a GMM, including Bernoulli-Gaussian (BG), Middleton Class-A, and alpha-stable noises. Theoretical SER performance are compared with simulations, showing very good agreement for all the impulsive noise scenarios and the non-linear suppressors.