1.2.1 Capacity of Single Antenna Channel For jointly random variables U,...U2,using the fact that hU,…,Ux)≤∑hU) k=1 with equality if and only if the U,are independent,we obtain I(X,…,XN;Y,…,Yw)≤∑[h(HsX+Z)-h(Z,…,Z)] Using then the fact suph(U)=log,(πeP) where the supremum is attained for U~N.(0,P),we further obtain x…,XxX,,X)sog((PlH.+-log,(meog+PH.） 1616 1.2.1 Capacity of Single Antenna Channel For jointly random variables U1 ,…U2 , using the fact that 1 ( , , ) ( ) N 1 N k k h U U h U    with equality if and only if the U1 are independent, we obtain   1 ( , , ; , , ) ( ) ( , , ) N 1 N 1 N k k k k k k I X X Y Y h H X Z h Z Z     + Using then the fact       2 2 sup log U P h U eP    where the supremum is attained for , we further obtain ~ ( , ) U N 0 P c       2 2 2 2 2 1 1 ( , , ; , , ) log ( 1) log ( ) = log 1 N N 1 N 1 N k k k k k k I X X Y Y e P H e P H          