This work presents joint iterative power allocation and interference suppression algorithms for spread spectrum networks which employ multiple hops and the amplify-and-forward cooperation strategy for both the uplink and the downlink. 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 linear minimum mean-squared error (MMSE) expressions for the parameter vectors that determine the optimal power levels across the relays and the linear receivers. In order to solve the proposed optimization problems, we develop cost-effective algorithms for adaptive joint power allocation, and estimation of the parameters of the receiver and the channels. An analysis of the optimization problem is carried out and shows that the problem can have its convexity enforced by an appropriate choice of the power constraint parameter, which allows the algorithms to avoid problems with local minima. A study of the complexity and the requirements for feedback channels of the proposed algorithms is also included for completeness. Simulation results show that the proposed algorithms obtain significant gains in performance and capacity over existing non-cooperative and cooperative schemes.