Bit-Interleaved Coded Modulation: Fundamentals, Analysis and Design

5.4 Fading Channels

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.,

5.141

Further, we average the CDF with respect to , and obtain the PDF of the L-values by differentiating with respect to , i.e.,

5.142

5.143

5.144

where, similarly to (5.141), we define

5.145

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 ...