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.