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

Alternating Optimization Techniques for Power Allocation and Receiver Design in Multihop Wireless Sensor Networks