Analysis and design of diversity schemes for ad hoc wireless networks

Diversity schemes permit efficient communication over fading channels but are often hard to analyze and design in networks with many nodes. For Rayleigh-fading channels, there exists an interesting relationship between resistive circuits and time and path diversity mechanisms in wireless ad hoc networks. A resistor-like network element, the erristor, representing the normalized noise-to-signal ratio, is introduced. Given an end-to-end packet delivery probability, the logarithmic mapping from link reception probabilities to erristor values greatly simplifies the problems of power allocation and the selection of time and path diversity schemes, which is illustrated in a number of examples. We focus on transmission strategies with selection combining and simple noncoherent "decode-and-forward" strategies, which is motivated by their practicality. Thanks to its conceptual simplicity, the formalism that is developed provides valuable insight into the benefits of diversity mechanisms.