Approximations of the packet error rate under quasi-static fading in direct and relayed links

The packet error rate (PER) is a metric of choice to compute the practical performance of communication systems experiencing block fading, e.g., fading processes whose coherence time is relatively slow when compared to the symbol transmission rate. For these types of channels, we derive a closed-form asymptotic expression which approximates the value of the PER for high signal-to-noise ratio (SNR). We also provide another approximation based on a unit-step formulation of the symbol error rate (SER). We show that the two approximations are related and may be derived from one another, thereby allowing us to obtain closed-form approximations of the block fading PER in both coded and uncoded systems. We then show how these approximations may be used in practice, through the derivation of a packet error outage (PEO) metric covering the case where the links experience shadowing on top of block fading, as well as asymptotically optimal power allocations in relay channels under a block fading hypothesis.