Distribution of max-log metrics for QAM-based BICM in fading channels

In this letter we derive closed-form expressions for the probability density functions (PDFs) of the bits' reliability metrics (L-values) in bit-interleaved coded modulation (BICM) transmission over fully-interleaved fading channels. The expressions are valid for the relevant case of quadrature amplitude modulation (QAM) with Gray mapping when the metrics are calculated via the so-called max-log approximation. Using the developed expressions, the performance of coded BICM transmissions is efficiently evaluated, i.e., without resorting to otherwise required two-dimensional numerical integration. The BICM capacity for different fading channels and constellation sizes is also evaluated.