Compressive Forwarding for Jointly Sparse Signals in Amplify-and-Forward Gaussian Relay Networks

This paper considers the problem of applying compressed sensing ideas to relay networks in order to increase the network throughput. We present a new method to perform forwarding which, when the signals transmitted by several sources are jointly sparse, enables to send a vector of dimension higher than the min-cut of the network. First, the jointly sparse source signals are mapped to a signal of lower dimension which can be transmitted over the network. Second, we allow source nodes to send at a so called single-source min-cut rate which is such that each node transmits without considering other sources transmitting simultaneously. Finally, sinks use compressed sensing in order to recover the transmitted sparse signal. Algebraically, the source signal is multiplied by a network matrix which needs to have the restricted isometry property to provide perfect reconstruction. We present algorithms to choose the network matrix coefficients as well as simulation results to show the validity of our approach.