  This paper presents joint power allocation and interference mitigation
techniques for the downlink of spread spectrum systems 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 an individual power constraint 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 linear receivers.
In order to solve the proposed optimization problem efficiently, we develop
joint adaptive power allocation and interference suppression algorithms that
can be implemented in a distributed fashion. The proposed stochastic gradient
(SG) and recursive least squares (RLS) algorithms mitigate the interference by
adjusting the power levels across the relays and estimating the parameters of
the linear receiver. SG and RLS channel estimation algorithms are also derived
to determine the coefficients of the channels across the base station, the
relays and the destination terminal. The results of simulations show that the
proposed techniques obtain significant gains in performance and capacity over
non-cooperative systems and cooperative schemes with equal power allocation.
