We are often presented with the problem of having multiple signals mixed together that we would like to isolate. BSS consists of techniques for doing this without prior knowledge of either the signals or the way in which they are mixed. The underlying assumption is that the signals are statistically independent. This allows us to analyze the statistical properties of the mixed signals in order to separate out the original signals. We will consider the case where there are m desired signals s1,…, sm, and they are mixed with Gaussian white noise n to form m signals,x1,…, xm via xi = ai 1 s1 +…+ ai m sm + n, where ai j represents the unknown channel information.

Our method for BSS involves two steps. First, we will perform a Linear Prediction (LP) analysis on the signals jointly. This will allow us to remove the auto-correlation from each captured signal xi, and focus on the values of t that give xi(l), and xj(l+t) the highest correlation. In many situations, a correlation cutoff value would have to be carefully chosen so as to ensure detection of the lag values that should be included while preventing the inclusion of inappropriate lags. For this algorithm, we are more worried about getting a false negative than a false positive at this stage, so we set a relatively low threshold for inclusion .

In the second step, we apply PSO to determine the coefficients of optimal Finite Impulse Response (FIR) unmixing filters based upon the taps found in the first step. We will perform the optimization in such a way so as to minimize the correlation between pairs of signals xi and xj. This is where any incorrectly chosen lags from the first step can be dealt with. In minimizing the correlation, we will end up setting the coefficients of any unnecessary lags close to zero, thus effectively eliminating them from consideration. In fact, if we find that the swarm has converged for that coefficient, i.e. every particle has that coefficient less than a given cutoff, we can remove that lag and continue the swarm optimization in a lower dimensional space. We would simply restart the optimization in the lower dimension, and project the current positions of the particles onto the lower dimensional space for the initial seeds. Once the FIR filters have been found and applied, what will be left is ŝi =si + n’i where n’i is residual noise that can be diminished by using noise reduction techniques. This technique has many applications including wireless networks where it can be used to separate the different signals that are received.

Blind Signal Separation (BSS) is used in many digital signal processing applications where signal separation using blind methods is applicable, including acoustics, radio communications, as well as image processing. Please contact us to discuss your specific application requirements.

Blind Signal Separation

Blind Signal Separation or Blind Source Separation is the separation of a set of signals from a set of mixed signals without the aid of information (or with very little information) about the signal source or the mixing process.

Blind source separation relies on the assumption that the source signals do not correlate with each other. For example, a set of signals may be statistically independent or decorrelated. Because of this independence, the set can be separated into another signal set, such that the regularity of each resulting signal is maximized, and the regularity between the different signals is minimized (i.e. statistical independence is maximized).

Applications of BSS

Signal separation using these blind techniques has found many applications in acoustics, where different sound sources are recorded simultaneously either with individual microphones or microphone arrays. These sources may be speech or music, or an underwater signal recorded with passive sonar. In these cases it can be especially useful for noise reduction processing where the signals of interest are isolated from interferes and other noise sources.

Other applications for blind source separation include radio communications, where it is used to differentiate the mixtures of communication signals received by antenna arrays. The method has also been applied to image processing as well as used in the processing of biomedical markers like electrocardiogram (EKG/ECG), electromyogram (EMG) and other bio-potentials.

BSS Methods

Typical methods for blind source separation include:

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