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We consider the uplink transmission in multiuser wireless systems with multiple single-antenna transmitting users and a multiantenna receiver. We address two problems in this paper. The first problem is user admission, i.e., given a large number of users, how to admit the maximum number of users that can simultaneously satisfy quality of service (QoS) and power constraints. The second problem is how to distribute the data among the users when they are allowed to share data before transmission. The aim is to minimize the total data exchange cost. Such a problem is called user clustering. We formulate those problems into sparsity-maximization problems, which are NP-hard. Inspired by compressive sensing techniques, we propose a common framework to tackle those problems by first applying the \ell1 -norm relaxation and then solving them with convex optimization methods. Simulations show that the proposed algorithms achieve excellent performance. For user admission, the numbers of admitted users by the proposed algorithms are close to the optimum numbers of admitted users obtained by exhaustive search (ES) . For user clustering, the total data exchange cost is reduced by more than 10% after only a few iterations. When the QoS requirement is low, the user data exchange can be avoided using the proposed method, which achieves the optimum result obtained by ES. [ABSTRACT FROM PUBLISHER]