# Iterative Receiver Design for the Estimation of Gaussian Samples in Impulsive Noise +
###### Abstract
This is a typical situation where, as commonly done in recent years, approximate inference techniques and graphical model-based algorithms are effectively borrowed or adapted from the machine learning literature (see, e.g., [15]) to solve complicated estimation problems with many random variables. In particular, novel receivers, designed based on a factor graph (FG) approach, are an efficient solution to jointly estimate the correlated Gaussian samples and detect the correlated states of channel impulsive noise, as done for the first time in [16], in the case of Markov-Gaussian impulsive noise, later extended to Markov-Middleton impulsive noise [17]. Receivers based on message passing algorithms [18] work iteratively, to guarantee convergence on a loopy FG. Moreover, the message passing between discrete channel states and continuous (Gaussian) observations produces (Gaussian) mixture messages with exponentially increasing complexity [19]. In [16; 17], hard decisions were made on the states of impulsive noise (i.e., the number of interfering devices); as a consequence, the mixture messages were approximated as one of their terms (the one with the largest likelihood). This is a suboptimal approach that neglects part of the information carried by messages [12]. A more sophisticated approach--that promises close to optimal performance--is based on mixture reduction. Approximate variational inference algorithms adopt the Kullback-Leibler (KL) divergence, or other divergence measures, to minimize the approximation error in mixture reduction [20] and achieve good performance at a reasonable computational cost. This is the case of the celebrated expectation propagation (EP) algorithm proposed by [PERSON] [21], which is based on KL divergence. The EP algorithm and a similar algorithm called transparent propagation (TP) were recently applied to signal estimation in impulsive noise channels, showing good performance [22; 23]. In this paper, we provide, for the first time, a comprehensive study of signal estimation over bursty impulsive noise channels, modeled either as Markov-Gaussian or as Markov-Middleton noise with memory, where the signal is modeled as a correlated (AR(1)) sequence of Gaussian samples, as representatives of multicarrier signals or of a Gaussian sensing source with memory. We analyze different estimation algorithms and provide a performance comparison between several suboptimal and close-to-optimal techniques, in various channel conditions. In particular, this paper is an extension of our recent work [23], where EP and TP were applied for the first time to a channel with Markov-Middleton impulsive noise. Besides describing these algorithms in more detail, here, we critically review the channel model and compare it with the simpler Markov-Gaussian model. In addition, for both impulsive noise channel models, we compare EP and TP to a simpler suboptimal algorithm (PIS), which was introduced previously, and motivate the differences in their performances. The paper is organized as follows. In Section 2, we introduce the system model along with the Markov-Gaussian and Markov-Middleton noise models. Its related FG and the basics of message passing algorithms are introduced in Section 3. A brief introduction to KL divergence is given in Section 3.1, while Section 4 describes different estimation strategies, whose performance is compared in Section 5. Conclusions are drawn in Section 6.