Massive MIMO for decentralized estimation over coherent multiple access channels

We consider a decentralized multisensor estimation problem where L sensor nodes observe noisy versions of a possibly correlated random source. The sensors amplify and forward their observations over a fading coherent multiple access channel (MAC) to a fusion center (FC). The FC is equipped with a large array of N antennas, and adopts a minimum mean square error (MMSE) approach for estimating the source. We optimize the amplification factor (or equivalently transmission power) at each sensor node in two different scenarios: 1) with the objective of total power minimization subject to mean square error (MSE) of source estimation constraint, and 2) with the objective of minimizing MSE subject to total power constraint. For this purpose, we apply an asymptotic approximation based on the massive multiple-input-multiple-output (MIMO) favorable propagation condition (when L ≪ N). We use convex optimization techniques to solve for the optimal sensor power allocation in 1) and 2). In 1), we show that the total power consumption at the sensors decays as 1/N, replicating the power savings obtained in Massive MIMO mobile communications literature. Through numerical studies, we also illustrate the superiority of the proposed optimal power allocation methods over uniform power allocation.