problem understanding LMS noise whitening alg.

Hi.

I am self-studying adaptive signal processing.
I've read C.R. Johnson's Adaptive Signal Processing, and some parts of
Haykin's. 

I am reading this paper "Self adaptive decision feedback equalization:
Application to high order QAM signal"
In the paper, adaptive whitening filter is applied to the received
signal.
The whitened signal is then fed to another adaptive FFE equalizer to
recover the transmitted symbol.

I got the FFE adaptation part, where the adaptation is
W(k+1) = W(k)+mu*e(k)*Y(k), where W is the vector of filter coefficient,
and Y(k) is the data array, mu is stepsize, and e(k) is D-y where D is
desired signal.

Here is the noise whitening part,

x(k)---->H(z) ----->y(k)
where H(z)is all pole whitening filter, and H(z) = 1/(1+A(z)), where A(z)
is a fir system.


Adaptation eq.
H(k+1) = H(k)+mu*y(k)*Y(k), 
The author choose cost function to be E{x(k)^2}, then derive the above eqn
using LMS alg.

Why is the E{y(k)^2} chosen to be the cost function of whitening filter?

I'd appreciate if someone could explain to me or point me to a text book
that I should read. I've scanned through Haykin, but coulnt find the
answer to this.

Regards,
Sam Wo