In a stereo echo cancellation system, the echo path for the far-end-signal in the near-end room is estimated by an adaptive filter. Since the same signal is transmitted by two similar far-end paths, the input signals to the filter are correlated. This causes a problem because of the non-uniqueness of the solution to the adaptive filtering problem. The solution depends also on the far-end transfer paths.

At the moment, I am not considering a decorrelation unit, because I would like to understand how the non-uniqueness problem. I understand that multiple linear combinations of the far-end impulse responses lie in the null space of the autocorrelation matrix of input signal to the adaptive filter, but what does that really mean?

In particular, when the far-end paths remain constant due to a stationary source position in the far-end room, why does the filter adaption result in a suboptimal solution?

(I am unsure whether it would help to include a drawing and/or mathematical notation, please let me know in the comments if you think this is the case.)

TLDR My questions are:

  • Is there an intuitive explanation on why the non-uniqueness of the solution in stereo echo cancellation has a negative influence on filter convergence?
  • Why does it impair filter adaption if the far-end source has a stationary position?

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