Multiuser detection in asynchronous on-off random access channels using lasso

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This paper considers on-off random access channels where users transmit either a one or a zero to a base station. Such channels represent an abstraction of control channels used for scheduling requests in third-generation cellular systems and uplinks in wireless sensor networks deployed for target detection. This paper introduces a novel convex-optimization-based scheme for multiuser detection (MUD) in asynchronous on-off random access channels that does not require knowledge of the delays or the instantaneous received signal-to-noise ratios of the individual users at the base station. For any fixed number of temporal signal space dimensions N and maximum delay τ in the system, the proposed scheme can accommodate M ≲ exp(O(N1/3)) total users and k ≲ N/ logM active users in the system—a significant improvement over the k ≤ M ≲ N scaling suggested by the use of classical matched-filtering-based approaches to MUD employing orthogonal signaling. Furthermore, the computational complexity of the proposed scheme differs from that of a similar oracle-based scheme with perfect knowledge of the user delays by at most a factor of log(N+τ). Finally, the results presented in here are non-asymptotic, in contrast to related previous work for synchronous channels that only guarantees that the probability of MUD error at the base station goes to zero asymptotically in M.