A continuum approach to dense wireless networks with cooperation

We consider a multi-hop wireless network in which a single source-destination pair communicates with the help of multiple cooperative relays. The relays deliver the source message by transmitting it in groups at every hop. The group transmissions increase the signal-to-noise ratio (SNR) of the received signal, and improve the range of communication. In this paper, we analyze the behavior of cooperative network with respect to the network parameters such as source/relay transmission powers and the decoding threshold (the minimum SNR required to decode a transmission). It is shown that if the decoding threshold is below a critical value, the message is delivered to the destination regardless of the distance between the source and the destination. Otherwise, the number of transmitting nodes diminishes at every hop, and the message does not reach to a destination far away. Our approach is based on the idea of continuum approximation, which is valid when the network density is high.