Most of the existing literature on performance evaluation of fading channels is concentrated on either the symbol error rate of the links, or the outage capacity. We present in this technical report approximation techniques for the packet error rate of quasi-static fading channels. This model applies when the channel coherence time is larger than the signaling time and leads to multiple symbols experiencing the same fading state during a packet transmission. We start by giving a closed-form upper bound on the asymptotic \emph{coding gain} of the packet error rate in quasi-static fading channels. Using the fact that the asymptotic formulation is inversible with respect to the mean signal-to-noise ration (SNR), we present a \emph{packet error outage} metric, with applications to channels where links are subject to both fading and log-normal shadowing effects simultaneously. We then show that a \emph{unit step approximation} can be derived for the packet error rate of block fading channels, that closely matches the numerical computation of the packet error rate in a tractable closed-form expression. Using the asymptotic approximation method, we derive the optimal power allocation for different relaying protocols, especially when optimal combination of the symbols received at the destination may not be possible.
Approximations of the packet error rate under slow fading in direct and relayed links