On the Discrete Concavity of Packet Reception Ratio Utility Functions

The wireless channel often shows high complexity in the attempt to analyze theoretically the network layer parameters. A parameter of this layer is the Packet Reception Ratio (PRR). The PRR is a practical metric, which when analyzed theoretically, exhibits high complexity. Its optimization results in high throughput and a reduction in the interference and collisions of transmissions. In theory, PRR is described with a sigmoid function, which conveys a very hard problem to solve. In this paper, we will reduce this complexity by transforming PRR and transmission power function to a discrete concave-up one; thus, allowing fast algorithms, which locate the globally optimal solutions, to be applied. We do this transformation utilizing networking terms, which come into play to reduce the complexity of a PRR optimization process.