Low-complexity remote compressive sensing for machine-to-machine networks with stochastic sources

In recent years, machine-to-machine (M2M) networks have been widely considered in wireless communication systems. Machines typically have constrained power, and their processing and communication capabilities are limited. To avoid the transmission of redundant information in order to save the transmission power, compressive sensing (CS) is a promising tool to consider. In this paper, under the two-tier architecture, we propose a remote CS scheme for the M2M networks with stochastic sources. We first formulate a stochastic CS problem and verify that the selected power exponential model for the stochastic source is compressible, i.e., satisfies the power law. Then we propose to use the minimum mean square error (MMSE) estimator at the gateway to transform the problem into a noiseless stochastic CS one where a low-complexity sensing matrix is adopted. After that we derive an estimation error upper bound for the proposed scheme and prove that it is asymptotically optimal in the MMSE sense compared to the one without CS. We then use simulation to show that the proposed system is still approximately optimal when the observation length is finite.