Optimization of the amplify-and-forward in a wireless sensor network using compressed sensing

In this paper, we study a novel compressed sensing technique applied to wireless sensor networks with a star topology. In particular, we propose a amplify-and-forward transmission scheme to achieve a distributed compressed sensing framework. The key idea is twofold; the first is to take advantage of time correlation properties present in most of the physical sensing scenarios and produce a sparse version of the measured signal. The second one is to perform random projections by means of the channel matrix that models the path among transmitters, relays and receivers. To reconstruct the signal at the fusion center, we follow a l
¹
-norm minimization approach. The simulation results show that our proposed distributed algorithm performs close to centralized compressed sensing techniques, presenting a reduction of the number of channel uses and significant energy savings. Furthermore, the trade-off between savings and the mean square error in the reconstruction is evaluated.