# Iterative Receiver Design for the Estimation of Gaussian Samples in Impulsive Noise +
## 6 Conclusions  
We proposed different algorithms to estimate correlated Gaussian samples in a bursty impulsive noise scenario, where successive noise states are highly correlated. The receiver design was based on a factor graph approach, resulting in a loopy FG due to the correlation among signal samples, as well as among noise samples [18]. Due to the joint presence of continuous and discrete random variables (namely, signal samples and impulsive noise channel states), as typically occurs in these cases, the resulting iterative sum-product algorithm has an intractable complexity [20]. The bursty impulsive noise is in fact modeled either as Markov-Gaussian [5] or as Markov-Middleton [6]; hence, the channel is characterized by (dynamically switching) states that count the sources of electromagnetic interference, at every time epoch [4]. Although belonging to the broad class of switching linear dynamical systems [19], the system considered here exhibits remarkable symmetry properties that allow an effective estimation of the signal samples through approximate variational inference. A simple parallel iterative schedule (PIS) of messages, including dynamically updated hard decisions on the channel states [16], was shown to provide a satisfactory, although suboptimal, performance, for many different channel conditions [17]. The more computationally costly expectation propagation (EP) [21] is also applicable to this problem albeit affected by its usual instability problems during the iterations, which can however be solved by known methods in the literature [27]. For this reason, an alternative transparent propagation (TP) algorithm was introduced, which has a lower computational complexity (compared to EP) and is inherently stable [22]. Both EP and TP reach a performance that is close to the optimal one, i.e., that of a receiver with perfect channel state information. For the first time, we applied all of these algorithms to bursty impulsive noise channels with a very large number (up to 15) of independently switching interferers [23]. The results demonstrate that, for a given SNR, the degradation induced by many (e.g., 15) interferers, with limited power, is similar to that produced by fewer (e.g., three) stronger interferers with correspondingly larger power. Hence, few-state channel models, or even the binary Markov-Gaussian model, are adequate to predict the performance with any of the algorithms discussed here, both suboptimal (PIS) and close to optimal (EP,TP). Conceptualization, A.M., A.V., and G.C. ; methodology, A.M., A.V., G.C., R.P., and L.V. ; software, A.M. and R.P. ; validation, A.M., A.V., and R.P. ; formal analysis, A.M., A.V., and G.C. ; investigation, A.M. and A.V. ; resources, G.C. and L.V. ; data curation, A.M.; writing, original draft preparation, A.M. and A.V. ; writing, review and editing, A.M., A.V., G.C., R.P., and L.V. ;  
Figure 6: Signal estimation in Markov–Middleton noise with \(M=4\) states and \(\Gamma=0.01\) (as in Figure 5a). Different values of the average number of interferers \(A\) are considered. visualization, A.M. and A.V. ; supervision, G.C. ; project administration, A.V. ; funding acquisition, G.C. All authors read and agreed to the published version of the manuscript. This research received no external funding. Data Availability Statement: Data sharing not applicable. The authors declare no conflict of interest. The following abbreviations are used in this manuscript: