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We propose a joint approach for multiuser receiver design and power allocation. Inter-user interference is modeled by an axiomatic framework, based on parameter-dependent coupling matrices. We consider the problem of total power minimization subject to QoS constraints. Properties of the optimum are discussed, and a monotone iterative algorithm is proposed. We exploit the uniqueness of the optimal power allocation in order to prove component-wise convergence of each transmit power to the global optimum. Since the QoS functions are described by an abstract model, the results can be applied to a wide range of system designs.