# Iterative Receiver Design for the Estimation of Gaussian Samples in Impulsive Noise +
###### Abstract  
Impulsive noise is the main limiting factor for transmission over channels affected by electromagnetic interference. We study the estimation of (correlated) Gaussian signals in an impulsive noise scenario. In this work, we analyze some of the existing, as well as some novel estimation algorithms. Their performance is compared, for the first time, for different channel conditions, including the Markov-Middleton scenario, where the impulsive noise switches between different noise states. Following a modern approach in digital communications, the receiver design is based on a factor graph model and implements a message passing algorithm. The correlation among signal samples, as well as among noise states brings about a loopy factor graph, where an iterative message passing scheme should be employed. As is well known, approximate variational inference techniques are necessary in these cases. We propose and analyze different algorithms and provide a complete performance comparison among them, showing that the expectation propagation, transparent propagation, and parallel iterative schedule approaches reach a performance close to optimal, at different channel conditions. Keywords:communications engineering; impulsive noise; variational Bayesian inference +
Footnote †: This paper is an extended version of a paper published in 43 rd International Conference on Telecommunications and Signal Processing (TSP), Milan, Italy, 7–9 July 2020. Footnote †: These authors contributed equally to this work. Footnote †: This paper is an extended version of a paper published in 43 rd International Conference on Telecommunications and Signal Processing (TSP), Milan, Italy, 7–9 July 2020. Footnote †: These authors contributed equally to this work. Different impulsive noise models have been proposed in the past years, the simplest being a Bernoulli-Gaussian model [3], where a background Gaussian noise with given power switches to another (usually much larger) power level, during an impulsive event. These events induce a larger noise variance and model the onset of an external source of EMI. Clearly, the sources of EMI that can independently switch are usually more than one, so that the Middleton class \(A\) model [4] was proposed later to account for a variable number \(k\) of Gaussian interferers, with \(k\) following a Poisson distribution, whereas the Bernoulli distribution accounted for one or no interferes (only background noise). Impulsive noise events, however, usually occur in bursts, whose average duration is related to the timing characteristics of the interfering EMI events, while the models cited above are instead memoryless. In order to introduce Markovianity between successive noise samples, a Markov-Gaussian model [5] and a Markov-Middleton model [6] were later proposed, extending the accuracy of the Bernoulli-Gaussian and the Middleton class \(A\) models, so as to capture the bursty nature of the impulsive noise. On PLC systems, while the Middleton class \(A\) is regarded as a suitable model [8], the Markov-Middleton model is still a more general and accurate representation for impulsive noise [9]. Regarding the information signal, an adequate model to represent multicarrier transmission over PLC channels is a sequence of Gaussian samples [7]; the same author analyzed Gaussian samples' estimation in Middleton class \(A\) noise, in [10]. In a similar impulsive noise scenario, modeled as Markov-Gaussian [5], [PERSON], [PERSON], and [PERSON] tackled the problem of estimating a sequence of independent Gaussian samples in impulsive noise with memory [11; 12]. Both in the transmission of discrete symbols [13] and in distributed sensing applications with continuous samples [10], there is a correlation among successive signal samples, so that a first-order autoregressive (AR(1)) model can be used to establish a short-term memory in the transmitted signal [14]. The presence of memory in both signal and noise significantly complicates the detection/estimation problem.