Toward a circuit theory for sensor networks with fading channels

For Rayleigh fading wireless channels, there exists an interesting similarity between resistive circuits and time and path diversity mechanisms in multihop wireless sensor networks. A resistor-like circuit element, the erristor, representing the normalized noise-to-signal ratio, is introduced. Given an end-to-end packet delivery probability, the nonlinear mapping from link reception probabilities to erristor values greatly simplifies the problems of power allocation and the selection of time and path diversity schemes. Thanks to its simplicity, the formalism that is developed also provides valuable insight into the benefits of diversity mechanisms, and it reveals an interesting analogy to electric circuits as the signal-to-noise ratios exhibit resistor-like properties.