Efficient Optimization of Reference-Based Negentropy for Noncircular Sources in Complex ICA

Bingham proposed a complex fast independent component analysis (c-FastICA) algorithm to approximate the nengentropy of circular sources using nonlinear functions. Novey proposed extending the work of Bingham using information from a pseudo-covariance matrix for noncircular sources, particularly for sub-Gaussian noncircular signals such as binary phase-shift keying signals. Based on this work, in the present paper we propose a new reference-based contrast function by introducing reference signals into the negentropy, upon which an efficient optimization FastICA algorithm is derived for noncircular sources. This new approach is similar to Novey’s nc-FastICA algorithm, but differs in that it is much more efficient in terms of the computational speed, which is significantly notable with a large number of samples. In this study, the local stability of our reference-based negentropy is analyzed and the derivation of our new algorithm is described in detail. Simulations conducted to demonstrate the performance and effectiveness of our method are also described.