Abstract
As the best-known scheme in the field of Blind Source Separation (BSS), Independent Component Analysis (ICA) has been intensively used in various domains, including biomedical and acoustics applications, cooperative or non-cooperative communication, etc. While sensor arrays are involved in most of the applications, the influence on the performance of ICA of practical factors therein has not been sufficiently investigated yet. In this manuscript, the issue is researched by taking the typical antenna array as an illustrative example. Factors taken into consideration include the environment noise level, the properties of the array and that of the radiators. We analyze the analytic relationship between the noise variance, the source variance, the condition number of the mixing matrix and the optimal signal to interference-plus-noise ratio, as well as the relationship between the singularity of the mixing matrix and practical factors concerned. The situations where the mixing process turns (nearly) singular have been paid special attention to, since such circumstances are critical in applications. Results and conclusions obtained should be instructive when applying ICA algorithms on mixtures from sensor arrays. Moreover, an effective countermeasure against the cases of singular mixtures has been proposed, on the basis of previous analysis. Experiments validating the theoretical conclusions as well as the effectiveness of the proposed scheme have been included.
Highlights
The fundamental goal of Blind Source Separation (BSS) is to recover the original signals from their mixtures when the mixing process is unknown
Since |cosθ 2 cosφ2 –Dcosθ 1 cosφ1 | P (0,D). This indicates that so long as the element spacing of the array is smaller than wavelengths of the sources, the cases of singular mixtures can be well prevented for sources with diverse carriers and from all possible directions
The analytic connection between the environment noise variance, the source variance, the condition number of the mixing matrix and the optimal signal to interference-plus-noise ratio is deduced in Equation (20)
Summary
The fundamental goal of BSS is to recover the original signals from their mixtures when the mixing process is unknown. Limitations and performance bounds of certain ICA algorithms have been indicated in these works, but little attention has been paid to the actual performance under different situations depicted by the mixing processes, the sources as well as the environment, while the issue is significant for the applications. Analysis of the performance of several ICA algorithms under varied conditions was referred to in the scenario of blind suppression of interfering signals in direct sequence spread spectrum communication systems [33], but the work was mainly based on computer simulations with little in the way of analytical expression and conclusions. We think it is of great significance to analyze the performance of ICA algorithms under varied conditions depicted by the mixing matrix, the sources as well as the environment, since conclusions (especially quantitative ones) from such analysis may act as guidance for the applications of wide variety.
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