I have few conceptual questions related to application of chaos in communications. In few application such as radar Chaotic signal reconstruction with application to noise radar system, cryptography, the noise considered is chaotic in nature. Why does MLE not work?
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The answer to your question is provided in the abstract of the paper you cited (and the title of your question):
Since a chaotic signal is inherently deterministic ...
So, MLE is not applicable in this case given that they are assuming that the signal/noise is deterministic, and therefore not random (an essential assumption in the context of maximum likelihood estimation). Whether or not this is a sensible assumption is open to debate.
