In this paper, direction-of-arrival (DOA) estimation using non-coherent processing for partly calibrated arrays composed of multiple subarrays is considered. The subarrays are assumed to compute locally the sample covariance matrices of their measurements and communicate them to the processing center. A sufficient condition for the unique identifiability of the sources in the aforementioned noncoherent processing scheme is presented. We prove that, under mild conditions, with the non-coherent system of subarrays, it is possible to identify more sources than identifiable by each individual subarray. This property of non-coherent processing has not been investigated before. We derive the Maximum Likelihood estimator (MLE) for DOA estimation at the processing center using the sample covariance matrices received from the subarrays. Moreover, the Cramér-Rao Bound (CRB) for our measurement model is derived and is used to assess the presented DOA estimators. The behaviour of the CRB at high signal-to-noise ratio (SNR) is analyzed. In contrast to coherent processing, we prove that the CRB approaches zero at high SNR only if at least one subarray can identify the sources individually.

In this paper, we consider performance analysis of the decentralized power method for the eigendecomposition of the sample covariance matrix based on the averaging consensus protocol. An analytical expression of the second order statistics of the eigenvectors obtained from the decentralized power method which is required for computing the mean square error (MSE) of subspace-based estimators is presented. We show that the decentralized power method is not an asymptotically consistent estimator of the eigenvectors of the true measurement covariance matrix unless the averaging consensus protocol is carried out over an infinitely large number of iterations. Moreover, we introduce the decentralized ESPRIT algorithm which yields fully decentralized direction-of-arrival (DOA) estimates. Based on the performance analysis of the decentralized power method, we derive an analytical expression of the MSE of DOA estimators using the decentralized ESPRIT algorithm. The validity of our asymptotic results is demonstrated by simulations.with a large communication overhead and latency. A performance analysis of the decentralized eigendecomposition which considers estimation errors introduced by the AC protocol is of wide interest for a large variety of applications.In [20], we presented a fully decentralized DOA estimation algorithm using partly calibrated arrays. Our DOA estimation algorithm combines the d-PM with the conventional ESPRIT algorithm [13] and is thus referred to as the decentralized ESPRIT (d-ESPRIT) algorithm. The numerical simulations carried out in [20] and [19] show that the d-ESPRIT algorithm achieves similar performance as the conventional ESPRIT algorithm when a large number of AC iterations is used. However, an analytical study of the performance of the d-ESPRIT algorithm which supports these simulations has not been considered so far. Moreover, the behavior of the d-ESPRIT algorithm when only a small number of AC iterations is carried out has not been studied before.The first and main contribution of this paper consists in the derivation of an analytical expression of the second order statistics of the eigenvectors for the sample covariance matrix computed using the d-PM. Based on this expression, we show that the d-PM is not a consistent estimator of the eigenvectors of the true measurement covariance matrix, unless the AC protocol is carried out over an infinitely large number of iterations. Moreover, we show that when the number of AC iterations used in the d-PM converges to infinity, our expression and the conventional expression in [2, Theorem 9.2.2] become equivalent. The second contribution of this paper consists in the derivation of an analytical expression of the MSE in DOA estimation using the d-ESPRIT algorithm.The remainder of this paper is organized as follows. The measurement model is introduced in Section 2. In Section 3, we briefly revise the AC protocol [24] and the d-PM [14] and their main properties, used later in the analysis. Section 4 considers the performance analysis of the d-PM, nam...

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We consider decentralized direction-of-arrival (DoA) estimation for large partly calibrated arrays composed of multiple fully calibrated uniform linear subarrays. Due to the difficulty of maintaining coherence between signals received in widely separated subarrays, the practical case of non-coherent subarrays is investigated. Our novel approach for decentralized and non-coherent DoA estimation is based on finding the common roots (CRs) of multiple univariate polynomials corresponding to individual subarrays. We propose two algorithms using generalized Sylvester matrix to find the CRs and to estimate the DoAs. The proposed algorithms substantially reduce communication and computation costs compared to traditional centralized DoA estimation methods. Moreover, simulation results demonstrate that our algorithms outperform existing decentralized methods and can deal with possible DoA estimation ambiguities caused by subarray geometries.Index Terms-decentralized DoA estimation, generalized Sylvester matrix, root-MUSIC.