A polynomial rooting approach for synchronization in multipath channels using antenna arrays

The estimation of the delay of a known training signal received by an antenna array in a multipath channel is addressed. The effect of the co-channel interference is taken into account by including a term with unknown spatial correlation. The channel is modeled as an unstructured FIR filter. The exact maximum likelihood (ML) solution for this problem is derived, but it does not have a simple dependence on the delay. An approximate estimator that is asymptotically equivalent to the exact one is presented. Using an appropriate reparameterization, it is shown that the delay estimate is obtained by rooting a low-order polynomial, which may be of interest in applications where fast feedforward synchronization is needed.Peer ReviewedPostprint (published version

Detection in distributed sensor networks

This thesis describes detection and communication algorithms for distributed sensor networks.In the first part of the thesis, we investigate a new architecture for distributed binary hypothesis detection by employing a Collision Resolution Algorithm (CRA), where all local sensors share a common channel to communicate with the decision fusion center. This architecture is important in the design of sensor fields, where a large number of distributed sensors share a single "emergency" channel.In the second part of the thesis, we discuss an industrial application of such a distributed detection system, namely, the LonWorks control network. We concentrate on the predictive p-persistent CSMA protocol implemented in the MAC layer of LonWorks protocol, which was proposed by the Echelon Corporation in the 1980s. In order to model this algorithm, we expand the CRA model developed in the first part to analyze variable-length messages. Predictions of the model are compared to an OPNET simulator of LonWorks, and to resultsfrom a physical network.Finally, we propose a direction-of-arrival (DOA) algorithm for sensor networks. It employs an improved polynomial rooting method using unitary transformations.Ph.D., Electrical Engineering -- Drexel University, 200

Efficient Beamspace Eigen-Based Direction of Arrival Estimation schemes

The Multiple SIgnal Classification (MUSIC) algorithm developed in the late 70\u27s was the first vector subspace approach used to accurately determine the arrival angles of signal wavefronts impinging upon an array of sensors. As facilitated by the geometry associated with the common uniform linear array of sensors, a root-based formulation was developed to replace the computationally intensive spectral search process and was found to offer an enhanced resolution capability in the presence of two closely-spaced signals. Operation in beamspace, where sectors of space are individually probed via a pre-processor operating on the sensor data, was found to offer both a performance benefit and a reduced computationa1 complexi ty resulting from the reduced data dimension associated with beamspace processing. Little progress, however, has been made in the development of a computationally efficient Root-MUSIC algorithm in a beamspace setting. Two approaches of efficiently arriving at a Root-MUSIC formulation in beamspace are developed and analyzed in this Thesis. In the first approach, a structura1 constraint is placed on the beamforming vectors that can be exploited to yield a reduced order polynomial whose roots provide information on the signal arrival angles. The second approach is considerably more general, and hence, applicable to any vector subspace angle estimation algorithm. In this approach, classical multirate digital signal processing is applied to effectively reduce the dimension of the vectors that span the signal subspace, leading to an efficient beamspace Root-MUSIC (or ESPRIT) algorithm. An auxiliaay, yet important, observation is shown to allow a real-valued eigenanalysis of the beamspace sample covariance matrix to provide a computational savings as well as a performance benefit, particularly in the case of correlated signal scenes. A rigorous theoretical analysis, based upon derived large-sample statistics of the signal subspace eigenvectors, is included to provide insight into the operation of the two algorithmic methodologies employing the real-valued processing enhancement. Numerous simulations are presented to validate the theoretical angle bias and variance expressions as well as to assess the merit of the two beamspace approaches

Efficient Two-Dimensional Direction Finding via Auxiliary-Variable Manifold Separation Technique for Arbitrary Array Structure

A polynomial rooting direction of arrival (DOA) algorithm for multiple plane waves incident on an arbitrary array structure that combines the multipolynomial resultants and matrix computations is proposed in this paper. Firstly, a new auxiliary-variable manifold separation technique (AV-MST) is used to model the steering vector of arbitrary array structure as the product of a sampling matrix (dependent only on the array structure) and two Vandermonde-structured wavefield coefficient vectors (dependent on the wavefield). Then the propagator operator is calculated and used to form a system of bivariate polynomial equations. Finally, the automatically paired azimuth and elevation estimates are derived by polynomial rooting. The presented algorithm employs the concept of auxiliary-variable manifold separation technique which requires no sector by sector array interpolation and thus does not suffer from any mapping errors. In addition, the new algorithm does not need any eigenvalue decomposition of the covariance matrix and exhausted search over the two-dimensional parameter space. Moreover, the algorithm gives automatically paired estimates, thus avoiding the complex pairing procedure. Therefore, the proposed algorithm shows low computational complexity and high robustness performance. Simulation results are shown to validate the effectiveness of the proposed method

Efficient Two-Dimensional Direction-of-Arrival Estimation for a Mixture of Circular and Noncircular Sources

In this paper, the two-dimensional (2-D) direction-of-arrival (DOA) estimation problem for a mixture of circular and noncircular sources is considered. In particular, we focus on a 2-D array structure consisting of two parallel uniform linear arrays and build a general array model with mixed circular and noncircular sources. The received array data and its conjugate counterparts are combined together to form a new data vector, based on which a series of 2-D DOA estimators is derived. Compared with existing methods, the proposed one has three main advantages. First, it can give a more accurate estimation in situations, where the number of sources is within the traditional limit of high-resolution methods. Second, it can still work effectively when the number of mixed signals is larger than that of the array elements. Finally, the paired 2-D DOAs of the proposed method can be obtained automatically without the complicated 2-D spectrum peak search and, therefore, has a much lower computational complexity

Sensor array signal processing : two decades later

Caption title.Includes bibliographical references (p. 55-65).Supported by Army Research Office. DAAL03-92-G-115 Supported by the Air Force Office of Scientific Research. F49620-92-J-2002 Supported by the National Science Foundation. MIP-9015281 Supported by the ONR. N00014-91-J-1967 Supported by the AFOSR. F49620-93-1-0102Hamid Krim, Mats Viberg

New Approaches for Two-Dimensional DOA Estimation of Coherent and Noncircular Signals with Acoustic Vector-sensor Array

This thesis is mainly concerned with the two-dimensional direction of arrival (2D-DOA) estimation using acoustic vector-sensor array for coherent signals and noncircular signals. As for coherent signals, the thesis proposes two algorithms, namely, a 2D-DOA estimation algorithm with acoustic vector-sensor array using a single snapshot, and an improved 2D-DOA estimation algorithm of coherent signals. In the first algorithm, only a single snapshot is employed to estimate the 2D-DOA, and the second is an improved algorithm based on the method of Palanisamy et al. Compared to the existing algorithm, the proposed algorithm has the following advantages: (1) lower computational complexity, (2) better estimation performance, and (3) acquiring automatically-paired 2D-DOA estimates. As for noncircular signals, we propose real-valued space PM and ESPRIT algorithms for 2D-DOA estimation using arbitrarily spaced acoustic vector-sensor array. By exploiting the noncircularity of incoming signals to increase the amount of effective data, the proposed algorithms can provide a better 2D-DOA estimation performance with fewer snapshots, which means a relatively lower sample rate can be used in practical implementations. Compared with the traditional PM and ESPRIT, the proposed algorithms provide better estimation performance while having similar computational complexity. Furthermore, the proposed algorithms are suitable for arbitrary arrays and yield paired azimuth and elevation angle estimates without requiring extra computationally expensive pairing operations

3-D Beamspace ML Based Bearing Estimator Incorporating Frequency Diversity and Interference Cancellation

The problem of low-angle radar tracking utilizing an array of antennas is considered. In the low-angle environment, echoes return from a low flying target via a specular path as well as a direct path. The problem is compounded by the fact that the two signals arrive within a beamwidth of each other and are usually fully correlated, or coherent. In addition, the SNR at each antenna element is typically low and only a small number of data samples, or snapshots, is available for processing due to the rapid movement of the target. Theoretical studies indicates that the Maximum Likelihood (ML) method is the only reliable estimation procedure in this type of scenario. However, the classical ML estimator involves a multi-dimensional search over a multi-modal surface and is consequently computationally burdensome. In order to facilitate real time processing, we here propose the idea of beamspace domain processing in which the element space snapshot vectors are first operated on by a reduced Butler matrix composed of three orthogonal beamforming weight vectors facilitating a simple, closed-form Beamspace Domain ML (BDML) estimator for the direct and specular path angles. The computational simplicity of the method arises from the fact that the respective beams associated with the three columns of the reduced Butler matrix have all but three nulls in common. The performance of the BDML estimator is enhanced by incorporating the estimation of the complex reflection coefficient and the bisector angle, respectively, for the symmetric and nonsymmetric multipath cases. To minimize the probability of track breaking, the use of frequency diversity is incorporated. The concept of coherent signal subspace processing is invoked as a means for retaining the computational simplicity of single frequency operation. With proper selection of the auxiliary frequencies, it is shown that perfect focusing may be achieved without iterating. In order to combat the effects of strong interfering sources, a novel scheme is presented for adaptively forming the three beams which retains the feature of common nulls