Abstract—We present a reduced-dimension multiuser detector (RD-MUD) structure for synchronous systems that significantly decreases the number of required correlation branches at the receiver front end, while still achieving performance similar to that of the conventional matched-filter (MF) bank. RD-MUD exploits the fact that, in some wireless systems, the number of active users may besmallrelativetothetotalnumberofusersinthesystem. Hence, the ideas of analog compressed sensing may be used to reduce the number of correlators. The correlating signals used by each correlator are chosen as an appropriate linear combination of the users’ spreading waveforms. We derive the probability of symbol error when using two methods for recovery of active users and their transmitted symbols: the reduced-dimension decorrelating (RDD) detector, which combines subspace projection and thresholding to determine active users and sign detection for data recovery, and the reduced-dimension decision-feedback (RDDF) detector, which combines decision-feedback matching pursuit for active user detection and sign detection for data recovery. We derive probability of error bounds for both detectors, and show that the number of correlators needed to achieve a small probability of symbol error is on the order of the logarithm of the number of users in the system. The theoretical performance results are validated via numerical simulations. Index Terms—Compressed sensing, demodulation, multiuser detection. I
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