Iterative receiver design for the estimation of Gaussian samples in impulsive noise

Impulsive noise is the main limiting factor for transmission over channels affected by elec-tromagnetic 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 propa-gation, and parallel iterative schedule approaches reach a performance close to optimal, at different channel conditions

Optimal State Estimation with Measurements Corrupted by Laplace Noise

Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the state is approximated using a randomized method. The method relies on that the Laplace noise can be rewritten as Gaussian noise scaled by Rayleigh random variable. The probability of the event that the distance between the approximation and the best estimate is smaller than a constant is determined as function of the number of parallel Kalman filters that is used in the randomized method. This estimator is then compared with the optimal linear estimator, the maximum a posteriori (MAP) estimate of the state, and the particle filter

A Novel Family of Adaptive Filtering Algorithms Based on The Logarithmic Cost

We introduce a novel family of adaptive filtering algorithms based on a relative logarithmic cost. The new family intrinsically combines the higher and lower order measures of the error into a single continuous update based on the error amount. We introduce important members of this family of algorithms such as the least mean logarithmic square (LMLS) and least logarithmic absolute difference (LLAD) algorithms that improve the convergence performance of the conventional algorithms. However, our approach and analysis are generic such that they cover other well-known cost functions as described in the paper. The LMLS algorithm achieves comparable convergence performance with the least mean fourth (LMF) algorithm and extends the stability bound on the step size. The LLAD and least mean square (LMS) algorithms demonstrate similar convergence performance in impulse-free noise environments while the LLAD algorithm is robust against impulsive interferences and outperforms the sign algorithm (SA). We analyze the transient, steady state and tracking performance of the introduced algorithms and demonstrate the match of the theoretical analyzes and simulation results. We show the extended stability bound of the LMLS algorithm and analyze the robustness of the LLAD algorithm against impulsive interferences. Finally, we demonstrate the performance of our algorithms in different scenarios through numerical examples.Comment: Submitted to IEEE Transactions on Signal Processin