I am having difficulty in understanding how the Authors in this paper, *An EM based method for semi blind identification of linear systems driven by Chaotic signals*

have used the expressions derived from applying an EM_EKF estimation method when the driving process is a non-linear input. They have considered the noise model as AWGN.
They then apply their method for in equalization. They apply the estimators derived in Eq(12)--Eq(15) to estimate the MA process with Rayleigh fading coefficients. I have attached a picture of the method that they have used. 

[![picture][1]][1]


Question 1: It is not clear to me if they have applied equalization to BPSK or to QAM model. I want to know what the EQ(1) would be for QAM communication and if the expression for the estimators would change if I want to apply to QAM communication. 


Question 2:  The Authors say that they apply their estimators to equalize a Rayleigh fading channel where the channel impulse response is modeled as an MA process. I am confused what the channel noise model would be ? Would it still be AWGN or Rayleigh noise? As they have applied the same estimators, I think the noise model is still AWGN. But in may other papers, when we say rayleigh model then don't we mean that the noise is rayleigh distributed?


Question 3: Link http://www.raymaps.com/index.php/theoretical-ber-of-m-qam-in-rayleigh-fading/

gives theoretical expressions for BER in Rayleigh fading channel. Can I  use the expression for 64-QAM in this paper? The Authors have given a plot of the BER performance but there is no expression for it. So, I am unsure how to get the plot for Rayleigh case.


  [1]: https://i.sstatic.net/8lBUR.png