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This work presents joint iterative power allocation and interference suppression algorithms for DS-CDMA networks which employ multiple relays and the amplify and forward cooperation strategy. We propose a joint constrained optimization framework that considers the allocation of power levels across the relays subject to individual and global power constraints and the design of linear receivers for interference suppression. We derive constrained minimum mean-squared error (MMSE) expressions for the parameter vectors that determine the optimal power levels across the relays and the parameters of the linear receivers. In order to solve the proposed optimization problems efficiently, we develop recursive least squares (RLS) algorithms for adaptive joint iterative power allocation, and receiver and channel parameter estimation. Simulation results show that the proposed algorithms obtain significant gains in performance and capacity over existing schemes.