  In this paper, we consider a multihop wireless sensor network with multiple
relay nodes for each hop where the amplify-and-forward scheme is employed. We
present algorithmic strategies to jointly design linear receivers and the power
allocation parameters via an alternating optimization approach subject to
different power constraints which include global, local and individual ones.
Two design criteria are considered: the first one minimizes the mean-square
error and the second one maximizes the sum-rate of the wireless sensor network.
We derive constrained minimum mean-square error and constrained maximum
sum-rate expressions for the linear receivers and the power allocation
parameters that contain the optimal complex amplification coefficients for each
relay node. An analysis of the computational complexity and the convergence of
the algorithms is also presented. Computer simulations show good performance of
our proposed methods in terms of bit error rate and sum-rate compared to the
method with equal power allocation and an existing power allocation scheme.
