Amplify-and-Forward Compressed Sensing as an Energy-Efficient Solution in Wireless Sensor Networks

In this paper, we propose a novel distributed compressed sensing transmission scheme, which is referred to as amplify-and-forward compressed sensing (AF-CS), in order to improve the existing tradeoff among reconstruction error, energy consumption, and resource utilization. The goal is twofold. First, to take advantage of the time correlation in order to produce sparse versions of the signal vector, which collects the transmitted signals of all the sensors. Second, to benefit from the nature of the multiple access channel in order to perform random measurements of the signal vector. Additionally, a simple model that accurately approximates the distortion introduced by the proposed scheme is presented. This model is then used to select the number of active nodes and relays based on a cost function that controls the tradeoff between reconstruction error and energy consumption. Simulation results show that the AF-CS outperforms other techniques in terms of distortion and number of transmissions, providing simultaneously, energy savings and a significant reduction in the number of channel uses.