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This paper considers the application of compressed sensing (CS) to a wireless sensor network for data measurement communication and reconstruction, where N sensor nodes compete for medium access to a single receiver. Sparsity of the sensor data in three domains due to time correlation, space correlation and multiple access are being utilized. We first provide an in-depth analysis on the CS-based medium access control schemes from a physical layer perspective and reveal the impact of communication signal-to-noise ratio on the reconstruction performance. We show the process of the sensor data converted to the modulated symbols for physical layer transmission and how the modulated symbols being recovered via compressed sensing. This paper further identifies the decision problem of distinguishing between active and inactive transmitters after symbol recovery and shows a comprehensive performance comparison between carrier sense multiple access and the proposed CS-based scheme. Second, a network data recovery scheme that exploits both spatial and temporal correlations is proposed. Simulation results validate the effectiveness of the proposed method in terms of communication throughput and show that enhanced performance can be obtained by utilizing the sensed signal's temporal and spatial correlations.