Performance analysis of direction-of-arrival estimation using the decentralized root-MUSIC

In this paper, we propose a decentralized implementation of the root-MUSIC algorithm over a network of nodes based on averaging consensus (AC) protocol. In our implementation, the nodes compute a sufficient statistic of their measurements, namely the signal subspace, in a decentralized fashion and sent it to a fusion center (FC), which performs the direction-of-arrival (DOA) estimation using the root-MUSIC algorithm. The proposed decentralized implementation reduces the required communication with the FC and the computational cost at the FC. Moreover, we derive an analytical expression for the asymptotic behaviour of the mean square error (MSE) for DOA estimation using our proposed algorithm, which we refer to as the decentralized root-MUSIC algorithm. Based on our performance analysis we show that the decentralized root-MUSIC algorithm is not a consistent estimator of the DOAs. Nevertheless, we demonstrate by simulations that the decentralized root-MUSIC algorithm achieves the Cramér Rao bound (CRB) for small number of snapshots and low SNRs.