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A possible future application in communications is the wireless uplink transmission in sensor networks. This application is mainly characterized by sporadic transmission over a random access channel. Since each sensor has a low activity probability, the signal for Multi-User Detection (MUD) is sparse. Compressive Sensing (CS) theory introduces detectors that are able to recover sparse signals reliably. When applied to MUD, CS detectors perform a joint detection of both data and user activity. This allows for less control signaling, since information about the activity state of each user no longer need to be signaled. Additionally, CS detectors are able to reliably detect sparse signals even in under-determined systems.
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