Convergence of MSE
Next we consider the convergence of the output MSE. Let 
denote the mean output energy at time i and 
[i] denote the MSE
at time i:
Equation 7.205
Equation 7.206
Since [i] and differ only by a constant P, we can focus on the behavior of the mean output
energy :
Equation 7.207
Since E{q[i} 
0, as i 
, the last
term in (7.207) is a transient term.
Therefore, for large 
, where 
is the
average excess MSE at time i. We are interested
in the asymptotic behavior of the excess MSE. Premultiplying both sides of (7.200) by Rr and
then taking the trace on both sides, we obtain
Equation 7.208
Since l2 + (1-l2) < [l + (1 - l)]2 = 1, the term tr{RrK[i]} converges.
The steady-state excess mean-square error is then given by
Equation 7.209
Again we see that the convergence of the MSE and the
steady-state misadjustment are independent of the eigenvalue distribution of the
data autocorrelation matrix, in contrast to the situation for the LMS version of
the blind adaptive algorithm [183].
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