Up to now, we considered the case of transmission over fixed-gain channels. To address the problem of finding the distribution of the L-values in fading channels, we define the CDF in (5.31) explicitly conditioned on the SNR, i.e.,
Further, we average the CDF with respect to , and obtain the PDF of the L-values by differentiating with respect to , i.e.,
where, similarly to (5.141), we define
i.e., the dependence of on the is made explicit.
Having changed the order of differentiation and integration, the PDF of the L-values for fading channels ...