1.2.1 Capacity of Single Antenna Channel Definition: Channel capacity is the e maximum i rate at which information can be communicated across a noisy channel with arbitrary reliability. The maximum rate at which one may possibly communicate over the time interval 1,...N]is given by C=maxR≤ sup IX1,XxY,…X） Let us compute: I(X,…,Xw;Y,…,Yv)=h(Y,…,Yx)-h(Y,…,Yx|X,…,XN) =h(H1X1+Z,…,HwXw+Zx)-h(H1X1+Z,…,HwXN+Zw|X,…,XN) =h(HX,+Z,…,HvXN+Zw)-h(Z,,Zx|X,…,XN) =h(HX+Z,…,HwXw+Zw)-h(Z,…,ZN) 1515 1.2.1 Capacity of Single Antenna Channel Definition: Channel capacity is the maximum rate at which information can be communicated across a noisy channel with arbitrary reliability. The maximum rate at which one may possibly communicate over the time interval [ 1, … , N ] is given by 2 1 P 1 1 =max sup ( , , ; , , ) N k k 1 N 1 N X N C R I X X Y Y N             Let us compute: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ( , , ; , , )= ( , , ) ( , , | , , ) ( , , ) ( , , | , , ) ( , , ) ( , , | , , ) ( , , ) ( , , ) 1 N 1 N 1 N 1 N 1 N N N N N N N 1 N N N N N 1 N N N N N I X X Y Y h Y Y h Y Y X X h H X Z H X Z h H X Z H X Z X X h H X Z H X Z h Z Z X X h H X Z H X Z h Z Z        + + + + + + + +