Major effects of the modification o Makes the theoretical convergence analysis dramatically more complex o The effect in the allowable step-size o Excess MSE or mismatch. (n+l)-wpr=(n）-Wo+ +u(d"(n)-u(n)(w(n)-woo))u(n)-Lu"(n)wopu(n) =(I-Hu(n)u"(n))(w(n)-wop)+ +u(d"(n)-u(n)wu(n) 2020-01-18 16
2020-01-18 16 Major effects of the modification Makes the theoretical convergence analysis dramatically more complex The effect in the allowable step-size Excess MSE or mismatch. * * ˆ ( 1) ( ) ˆ ( ) ( )( ( ) ) ( ) ( ) ( ) ˆ ( ) ( ) ( ( ) ) ˆ ( ) ( ) ( ) opt opt H H opt opt H opt H opt n n d n n n n n n n n n d n n n w w w w u w w u u w u I u u w w u w u
Orthogonality principle o Take the expected value of both sides of the equation. o The last term then vanishes because of the orthogonality principle. E[(n+1-ww] =E[(I-m(m)u“(mj(()-w)】 2020-01-18 17
2020-01-18 17 Orthogonality principle Take the expected value of both sides of the equation. The last term then vanishes because of the orthogonality principle. ˆ ( 1) ( ) ( ) ( ( ) ) ˆ opt H opt E n E n n n w w I u u w w