Joint Logarithmic Hyperbolic Cosine Robust Sparse Adaptive Algorithms

Recently, the logarithmic hyperbolic cosine adaptive filter (LHCAF) was proposed and was seen to demonstrate excellent robustness against impulsive interference. However, for the modelling of sparse systems, it may not provide optimal performance as it does not take into account the sparse nature of the system. To improve the modelling accuracy and convergence performance, a sparsity aware zero attraction LHCAF (ZA-LHCAF) and a reweighted zero attraction LHCAF (RZA-LHCAF) is proposed. To further improve the performance for modelling of sparse systems in impulsive environments, a joint logarithmic hyperbolic cosine function (JLHCF) is proposed as the cost function. The corresponding update rule, called the joint logarithmic hyperbolic cosine adaptive filter (JLHCAF) is deduced and the bound on learning rate is derived. A room equalization scenario is also considered and an improved sparsity aware robust algorithm based on JLHCF, namely the filtered-x JLHCAF (Fx-JLHCAF) is proposed for the same. Extensive simulation studies carried out for different system identification scenarios, under Gaussian and non-Gaussian disturbances and a room equalization scenario, demonstrate the superior performance achieved by JLHCAF over existing sparsity aware robust adaptive filters.