Compressive Rate Estimation With Applications to Device-to-Device Communications

We consider the pairing problem in network-assisted device-to-device communications. The pairing problem is stated as a rate estimation problem. To this end, we develop a framework that we call compressive rate estimation. We assume that the composite channel gain matrix (i.e., the matrix of all channel gains between all network nodes) is compressible and develop a novel sensing and reconstruction protocol for the estimation of achievable rates. The proposed sensing protocol exploits the superposition principle of the wireless channel and enables the receiving nodes to obtain non-adaptive random measurements of columns of the composite channel matrix. The random measurements are fed back to a central controller who decodes the composite channel gain matrix (or parts of it) and estimates individual user rates. We analyze the rate loss gap for a linear and a non-linear decoder and find the scaling laws according to the number of non-adaptive measurements.