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Bit-Interleaved Coded Modulation: Fundamentals, Analysis and Design by Alex Alvarado, Leszek Szczecinski

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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.,

Further, we average the CDF with respect to c05-math-0730, and obtain the PDF of the L-values by differentiating with respect to c05-math-0731, i.e.,

5.142 equation
5.143 equation

where, similarly to (5.141), we define

i.e., the dependence of c05-math-0736 on the c05-math-0737 is made explicit.

Having changed the order of differentiation and integration, the PDF of the L-values for fading channels ...

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