Wassim Suleiman

Performance Analysis of the Decentralized Eigendecomposition and ESPRIT Algorithm

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.

Decentralized direction finding using Lanczos method

The problem of Direction of Arrival (DoA) estimation using partly calibrated arrays composed of multiple identically oriented subarrays is considered. The subarrays are assumed to possess the shift invariance property which is exploited to achieve decentralized search free DoA estimation based on the ESPRIT method. In our previous work, the decentralized power method and the Averaging Consensus (AC) algorithm were used in the subspace estimation. To reduce the communicational cost without compromising the performance, our new algorithm uses the decentralized Lanczos method in combination with the AC algorithm to estimate the signal subspace. We further address the problem of Spurious Eigenvalues (SEVs) that usually arises in the Lanczos method. We propose a scheme to avoid the occurrence of SEVs while keeping the communicational cost low. Simulation results demonstrate that the proposed scheme is able to achieve similar performance as the decentralized power method with substantially reduced communicational cost. Furthermore, our method is able to estimate more DoAs than each subarray can autonomously identify.

Search-free decentralized direction-of-arrival estimation using common roots for non-coherent partly calibrated arrays

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 subar-rays 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.

Gridless compressed sensing under shift-invariant sampling

Parameter estimation has applications in many fields of signal processing, such as spectral analysis or direction-of-arrival estimation. Subspace-based methods like root-MUSIC and ESPRIT provide high parameter resolution at low computational complexity by exploiting specific sampling structure, namely uniform linear sampling and shift-invariant sampling, respectively. On the other hand, compressed sensing has been shown to outperform subspace-based methods in difficult scenarios such as low number of measurement vectors, high noise power or correlated signals. While it is well known that uniform sampling admits gridless compressed sensing methods, e.g., based on atomic norm minimization, no such approaches are known for shift-invariant sampling. In this paper we present a novel approach for gridless compressed sensing under shift-invariant sampling. We show by numerical experiments that the proposed method outperforms ESPRIT in difficult scenarios.

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.

Decentralized cooperative DOA tracking using non-Hermitian generalized eigendecomposition

The problem of direction-of-arrival (DOA) estimation using partly calibrated arrays composed of multiple identically oriented subarrays is considered. The subarrays are assumed to possess the shift-invariance property which is exploited to develop a distributed search-free DOA estimation algorithm that is based on the generalized eigendecomposition (GED) of a pair of covariance matrices. We propose a fully decentralized adaptive algorithm which tracks the generalized eigenvalues (GEVs) of a non-Hermitian pair of covariance matrices, from which the DOAs are estimated. Moreover, to enforce the amplitude property of the nominal source GEDs, we propose a suitable measurement weighting scheme. We demonstrate the estimation performance of our algorithm with simulations and confirm that our algorithm is able to identify more sources than each subarray individually can.

Decentralized cooperative detection based on averaging consensus

In this paper, decentralized spectrum sensing in a network of multiple cooperative cognitive nodes is considered. Based on the averaging consensus protocol, we propose a decentralized implementation of the energy detector, which is conventionally applied for spectrum sensing in a centralized fashion. The exact (non-asymptotic) null distribution of the decentralized energy detector test statistic is derived and used to compute the test threshold. The communication overhead of our proposed detector is low compared to the existing decentralized spectrum sensing algorithms. Moreover, we extend the energy detector to the problem of detecting the number of sources impinging onto a network of sensors. Simulation results demonstrate that using a moderate number of averaging consensus iterations, the extended energy detector is able to detect the correct number of sources with high probability.

Performance analysis of eigenvalue based distributed spectrum sensing.

In this paper, we consider the performance analysis of the distributed eigenvalue estimation technique based on the decentralized power method (d-PM) and the averaging consensus (AC) protocol. An analytical asymptotic expression of the second order statistics of the eigenvalues obtained from the d-PM is presented. This expression is essential for assessing the performance of estimators which are based on the d-PM. We show that the d-PM is not a consistent estimator of the eigenvalues of the true covariance matrix unless the AC protocol is carried out for a infinitely large number of iterations. However, for a moderately large number of samples a finite number of AC iterations is sufficient to achieve a performance which is comparable to that of the centralized eigendecomposition.

Decentralized direction-of-arrival estimation for arbitrary array geometries

Direction-of-arrival (DOA) estimation in partly calibrated array composed of multiple fully calibrated subarrays is considered. The location of the sensors in the subarrays are assumed to be arbitrary, i.e., no specific subarray geometry is assumed. Using array interpolation, we extend the previously proposed decentralized ESPRIT algorithm (d-ESPRIT), originally designed for shift-invariance array geometries, to arbitrary array geometries. In our proposed algorithm, the array interpolation is carried out locally at the subarrays, thus, communication between the subarrays is required for DOA estimation but not for interpolation. Simulation results demonstrate that our proposed algorithm achieves better performance than the conventional ESPRIT algorithm in perturbed shift-invariance arrays.