Optimal transmit power allocation in wireless sensor networks performing field reconstruction

In our previous work, we developed efficient field reconstruction methods in wireless sensor networks. In this paper, we use an amplify-and-forward to transmit the sensor measurements to the fusion center and we derive the mean square error (MSE) of the reconstructed field as a function of the measurement and receive SNR and of the sensor positions. We propose to allocate the sensor node transmit powers such that the sum power is minimized subject to an MSE target and we phrase this approach as a convex optimization problem that can be numerically solved in an efficient manner. For the case of critical sampling we derive a closed-form expression for the optimal power allocation. We illustrate the power savings achieved with the proposed power allocation schemes both for Gaussian and Rayleigh fading channels.