Can compressed sensing be efficient in communication with sparse data?

L User Equipments (mobile stations) transmit signals with sparsity S and their signals are compressively sensed to M samples by Z remote samplers (a distributed antenna arrangement) and the uplink channel is estimated by a central processor (the “central brain”). For a given system signal to noise ratio, retained samples M and sparsity S, we approximate the loss in sum mutual information due to imperfect knowledge of the channel. The approximation is premised on a lower bound of the mutual information which accounts for the power in the channel estimation error. Also, throughput results are given for adaptively adjusting the sparsity of multiple users´ transmit signals based on channel fading.