Exploiting Sparsity in Widely Linear Estimation

The distribution of complex random signals is typically improper. It has recently been established that conventional strictly linear models are only second order optimum for signals with proper distributions, while so called “widelylinear models” are optimum for the generality of complex signals, both proper and improper. Widely-linear models, however, are over-parameterised when the underlying system is strictly-linear, requiring twice the number of parameters to be estimated compared to strictly-linear models. This effects widely-linear adaptive algorithms, such as the augmented complex least mean square (ACLMS) and augmented complex recursive least squares (ACRLS), and leads to slow convergence. We here address the problem of the over-parameterisation of the ACLMS through the use of regularised cost error functions, and illustrate its effects through analysis and simulations.