Multistage cooperative broadcast using amplify-and-forward relays

In this work we study the propagation of the signal in a cooperative network where a single source message is retransmitted by multiple stages (levels) of relays. Relays are assumed to have limited computational abilities and hence adopt the amplify-and-forward scheme. At each node, cooperative diversity is obtained by combining the signals from the multiple levels of relays (in different time slots) using a matched filter. The levels are not predetermined and are formed based on the local decisions, hence the network is distributed. The retransmission criterion is based on the SNR (Signal-to-Noise Ratio) of the signal after the matched filtering operation. If the received SNR is greater than the SNR threshold then the signal is retransmitted. The parameter SNR threshold plays a critical role in determining the broadcast rate. We provide the expressions for received signal at each node as the message is forwarded in the network. We study the channel and noise statistics for a specific realization of a network. We also recursively characterize the effective channel, accumulated noise and their statistics. Through these formulations, we study the effects of noise accumulation, the number of levels used in the signal combination, the decoding and retransmission threshold on the number of nodes that successfully receive the message.