A useful lemma for capacity analysis of fading interference channels

This paper presents a simple new expression for the exact evaluation of averages of the form E [ln (1+x
₁
+...x
_N
/y
₁
+...+y
_M
+1)], where x
₁
,..., x
_N
, y
₁
..., y
_M
are arbitrary non-negative random variables, in terms of the joint moment generating functions of these random variables. Application examples are given for the ergodic capacity evaluation of some multiuser wireless communication systems which are difficult to solve by the known classical methods.