Skip to main content
Signal Processing

You are not logged in. Your edit will be placed in a queue until it is peer reviewed.

We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.

4
  • $\begingroup$ Great explanation & thank you immensely for going through that thesis. $\endgroup$ Commented May 29, 2015 at 15:40
  • $\begingroup$ I found an article univ-brest.fr/lest/tst/publications/pdf/… which says that for the Bernoulli Map, the mapping between symbol space and the number space is bijective. In that case, the mapping from $z_n$ to $s_n$ is bijective nad so $z_n$ can be recovered. I will have to study this more carefully from other sources as well. In case, it is bijective, then it may be possible to recover $z_n$ by CMA. Any thoughts on this? I really appreciate all your insights and helpful guidelines. $\endgroup$ Commented May 29, 2015 at 16:28
  • $\begingroup$ Although I am not quite sure if the mapping from $z_n$ to $s_n$ is not bijective. In the book : The Nonlinear Workbook: Chaos, Fractals, Cellular Automata, Neural Networks Under Section 1.1.15, there is a hint that we can inverse the mapping to obtain the real number (initial condition) from which the dynamical system was iterated. For example: as given in book notation, $x_0 = \sigma_0\sigma_1...$ and each $\sigma_i$ forms the BPSK input. Then if CMA can equalize to obtain the $\sigma_i$ then by doing the inverse of the symbolism we may get the number $x_0$. $\endgroup$ Commented May 29, 2015 at 20:34
  • $\begingroup$ @SKM: If the mapping from $z_n$ to $s_n$ is bijective, you can run the (unmodified) CMA to recover $s_n$ and then apply the inverse mapping to obtain $z_n$. There would still be no need to modify the CMA. $\endgroup$ Commented May 30, 2015 at 17:19