Adapting Compressed Sensing Algorithms to Discrete Sparse Signals

In sensor networks, many sensors with very low duty cycles transmit their discrete-valued data independently to a fusion center. This central instance has to estimate the individual data symbols. Assuming a great number of sensors and a much lower number of antennas at the fusion center, the reconstruction has to be done based on an underdetermined system of linear equations. Since the transmit symbol vector is assumed to be sparse, a Compressed Sensing task is present. However, as the data is discrete-valued, Compressed Sensing algorithms for discrete sparse signals are requested. A possible approach is the concatenation of a standard (real-valued) Compressed Sensing algorithm and the Sphere Decoder. In this paper, we give a deeper insight into existing approaches and optimize them in order to improve performance and/or to lower the computational complexity. Thereby, a class of algorithms for the recovery of discrete sparse signals, beneficial also for other applications in digital communications, like peak-power reduction or radar detection, is designed.