Optimal sensor placement for linear decentralized estimation with coherent and orthogonal multiple access channels

The design of wireless sensor networks requires cross layer optimization of sensing, signal processing and communication. We consider the linear decentralized estimation model in which low complex sensors sense, amplify, and forward the noisy and scaled observation of a source variable via a multiple-access channel (MAC) to the fusion center (FC), where the FC has perfect channel state information. We study the optimal placement of sensors located between the source and the FC. Using majorization, we prove for the orthogonal MAC, that an equidistant placement of the sensors between source and FC is optimal. For the general coherent MAC, the same behavior is explained and observed. Bounds on the loss due to suboptimal sensor placement are derived. The clear behavior changes if the outage probability is used for sensor placement. At high SNR, the average distortion is Schur-convex while for small SNR, it is Schur-concave. Numerical simulations illustrate the theoretical findings.