Fixed-Point Algorithms for the Blind Separation of Arbitrary Complex-Valued Non-Gaussian Signal Mixtures

Abstract

We derive new fixed-point algorithms for the blind separation of complex-valued mixtures of independent, noncircularly symmetric, and non-Gaussian source signals. Leveraging recently developed results on the separability of complex-valued signal mixtures, we systematically construct iterative procedures on a kurtosis-based contrast whose evolutionary characteristics are identical to those of the FastICA algorithm of Hyvarinen and Oja in the real-valued mixture case. Thus, our methods inherit the fast convergence properties, computational simplicity, and ease of use of the FastICA algorithm while at the same time extending this class of techniques to complex signal mixtures. For extracting multiple sources, symmetric and asymmetric signal deflation procedures can be employed. Simulations for both noiseless and noisy mixtures indicate that the proposed algorithms have superior finitesample performance in data-starved scenarios as compared to existing complex ICA methods while performing about as well as the best of these techniques for larger data-record lengths.

New Negentropy Optimization Schemes for Blind Signal Extraction of Complex Valued Sources

“…2 satisfies all properties of the MM maximization methods with L corresponding to J and Q corresponding to I. Meanwhile, the convergence conditions (13) and (14) can also be satisfied by (12) and the convexity of criterion. Thereby, one can see that Alg.…”

“…Many contrasts relying on higher-order statistics (e.g. the kurtosis contrast) have been easily extended from the real to the complex domain [11][12][13]. However, using these contrast functions generally results in an estimate sensitive to outliers [14].…”

Extraction of a weak co-channel interfering communication signal using complex Independent Component Analysis

“…[6], the complex fixed-point algorithm (CFPA) by Douglas [7], and the RobustICA by Zarzoso et al [8]. We applied these algorithms to extract a weak co-channel …”

“…The algorithm's iteration update is based on an approximate Newton optimization and is shown in [7] to be given by…”

“…Again, the update is similar to that found in cFastICA, except for the third term which takes into account potential non-circular source properties [7]. The algorithm is applied in the same manner as in CMN and follows the same steps by prewhitening using SVD, sequential extraction, and sequentially orthogonalizing the resulting un-mixing vectors.…”