This work proposes a novel distributed joint communication-acquisition scheme for the compressive sensing (CS)-based wireless sensor networks (WSN)s over fast fading wireless communication channels. The proposed scheme requires a sensor to transmit its measurement only on a fraction of the available transmission times. This work investigates the optimization of this transmission time fraction with respect to the minimal latency and total transmit energy. The resulting scheme, which naturally uses the fast fading wireless channels for generating random sensing projections required in the CS framework, is simple to implement, completely distributed, and other than a rough time synchronization, involves no additional overhead costs, such as scheduling. The efficiency of the proposed scheme in sensing the global environmental phenomena is evaluated via analysis and simulations assuming practical half duplex radios, and generic channel estimation procedure.