Asymptotic analysis of multistage cooperative broadcast in wireless networks

Cooperative broadcast aims to deliver a source message to a locally connected network by means of collaborating nodes. In traditional architectures, node cooperation has been at the network layer. Recently, physical layer cooperative schemes have been shown to offer several advantages over the network layer approaches. This form of cooperation employs distributed transmission resources at the physical layer as a single radio with spatial diversity. In decentralized cooperation schemes, collaborating nodes make transmission decisions based on the quality of the received signal, which is the only parameter available locally. In this case, critical parameters that influence the broadcast performance include the source/relay transmission powers and the decoding threshold (the minimum signal-to-noise ratio (SNR) required to decode a transmission). We study the effect of these parameters on the number of nodes reached by cooperative broadcast. In particular, we show that there exists a phase transition in the network behavior: if the decoding threshold is below a critical value, the message is delivered to the whole network. Otherwise, only a fraction of the nodes is reached, which is proportional to the source transmit power. Our approach is based on the idea of continuum approximation, which yields closed-form expressions that are accurate when the network density is high.