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In this paper, the authors study distributed gain allocation to maximize the achievable sum-rate in non-regenerative multihop networks with multiple users and multi-antenna nodes. The source and relay nodes are constrained to forward linear transformations of their input and calculate their transformation matrices based on locally available channel state information and limited feedback from the destination. They relax the optimization problem by imposing a norm constraint instead of a power constraint on each node, and devise a gain allocation scheme that is based on an approximation of the gradient of the sum-rate. By means of computer simulations, they show that the proposed algorithm achieves close to optimal solutions, if a good initialization is provided. This makes the scheme particularly useful for channel tracking in slow fading environments.
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