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Let P1 and P2 two distinct output signals that are generated by a common input signal S. If you want to estimate S using multichannel blind system identification algorithms, you have to specify the channel length L. How can I determine the best choice for L?

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  • $\begingroup$ Can you just measure the channel ? $\endgroup$
    – Hilmar
    Aug 12 at 11:53
  • $\begingroup$ I can only measure P1 and P2. There are several multichannel blind system identification algorithms to estimate S from P1 and P2, but in all cases, you have to choose a value for the channel length L. The result S depends obviously on the choice of L. $\endgroup$ Aug 12 at 13:36
  • $\begingroup$ The usual approach to questions about order (or length) is to use something like the Akaike Information Criterion or [Minimum Description Length](Minimum Description Length) approaches that are parameterized by $L$. $\endgroup$
    – Peter K.
    Aug 12 at 15:29
  • $\begingroup$ Thank you very much for your suggestion, Peter. I understand that you can use Akaike Information Criterion to determine the order of a transfer function between two signals and the criterion is e.g. implemented in Matlab. But is the situation of a multichannel blind system identification algorithm not slightly different where you need the length of the channel, i.e. of the impulse response of the channel? Could you therefore be more precise, please? $\endgroup$ Aug 16 at 11:00
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If I understand correctly, the Akaike Information Criterion leads to the following algorithm:

Fix an L. Calculate S from P1 and P2 (and L) and determine the impulse responses h1 and h2. Then calculate the estimated signals P1est and P2est from S and h1 and h2 resp. The Criterion is therefore given by the sum of the errors e1i and e2i at the sample points i=1:length(P1)=N, divided by 2N, minus the penalty term of the Akaike Information Criterion. Repeat the calculations for other choices of L and compare the resulted values of the criterion.

This is a possibility to determine the optimal choice of L, but this needs a lot of computations and it is expensive. Is there not an easier way to determine the best choice for L?

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