PER Approximation for Cross-Layer Optimization under Reliability and Energy Constraints

The vision of connecting billions of battery operated devices to be used for diverse emerging applications calls for a wireless communication system that can support stringent reliability and latency requirements. Both reliability and energy efficiency are critical for many of these applications that involve communication with short packets which undermine the coding gain achievable from large packets. In this paper, we first revisit the packet error rate (PER) performance of uncoded schemes in block fading channels and derive a simple and accurate PER expression. Specifically, we show that the waterfall threshold in the PER upper bound in Nakagami-$m$ block fading channels is tightly approximated by the $m$-th moment of an asymptotic distribution of PER in AWGN channel. This PER expression gives an explicit connection between the parameters of both the physical and link layers and the PER. We utilize this connection for cross-layer design and optimization of communication links. To this end, we optimize signal-to-noise ratio (SNR) and modulation order at physical layer, and the packet length and number of retransmissions at link layer with respect to distance under the prescribed delay and reliability constraint.