Globally convergent blind source separation based on a multiuser kurtosis maximization criterion
- 1 December 2000
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Signal Processing
- Vol. 48 (12), 3508-3519
- https://doi.org/10.1109/78.887044
Abstract
We consider the problem of recovering blindly (i.e., without the use of training sequences) a number of independent and identically distributed source (user) signals that are transmitted simultaneously through a linear instantaneous mixing channel. The received signals are, hence, corrupted by interuser interference (IUI), and we can model them as the outputs of a linear multiple-input-multiple-output (MIMO) memoryless system. Assuming the transmitted signals to be mutually independent, i.i.d., and to share the same non-Gaussian distribution, a set of necessary and sufficient conditions for the perfect blind recovery (up to scalar phase ambiguities) of all the signals exists and involves the kurtosis as well as the covariance of the output signals. We focus on a straightforward blind constrained criterion stemming from these conditions. From this criterion, we derive an adaptive algorithm for blind source separation, which we call the multiuser kurtosis (MUK) algorithm. At each iteration, the algorithm combines a stochastic gradient update and a Gram-Schmidt orthogonalization procedure in order to satisfy the criterion's whiteness constraints. A performance analysis of its stationary points reveals that the MUK algorithm is free of any stable undesired local stationary points for any number of sources; hence, it is globally convergent to a setting that recovers them all.Keywords
This publication has 41 references indexed in Scilit:
- Unconstrained optimization criteria for blind equalization of multichannel linear systemsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Kurtosis-based criteria for adaptive blind source separationPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Extraction of independent components from hybrid mixture: KuicNet learning algorithm and applicationsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Blind separation of independent co-channel signalsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Reply to "Comments on 'self-adaptive source separation, part I: convergence analysis of a direct linear network controled by the Herault-Jutten algorithm"IEEE Transactions on Signal Processing, 2000
- Stationary points of a kurtosis maximization algorithm for blind signal separation and antenna beamformingIEEE Transactions on Signal Processing, 2000
- On the surface characteristics of a mixed constant modulus and cross-correlation criterion for the blind equalization of a MIMO channelSignal Processing, 1999
- Criteria for blind deconvolution of multichannel linear time-invariant systemsIEEE Transactions on Signal Processing, 1998
- Self-adaptive source separation. II. Comparison of the direct, feedback, and mixed linear networkIEEE Transactions on Signal Processing, 1998
- Adaptive blind separation of independent sources: A deflation approachSignal Processing, 1995