Michael Rübsamen

Direction-of-Arrival Estimation for Nonuniform Sensor Arrays: From Manifold Separation to Fourier Domain MUSIC Methods

In this paper, the problem of spectral search-free direction-of-arrival (DOA) estimation in arbitrary nonuniform sensor arrays is addressed. In the first part of the paper, we present a finite-sample performance analysis of the well-known manifold separation (MS) based root-MUSIC technique. Then, we propose a new class of search-free DOA estimation methods applicable to arrays of arbitrary geometry and establish their relationship to the MS approach. Our first technique is referred to as Fourier-domain (FD) root-MUSIC and is based on the fact that the spectral MUSIC function is periodic in angle. It uses the Fourier series to expand this function and reformulate the underlying DOA estimation problem as an equivalent polynomial rooting problem. Our second approach applies the zero-padded inverse Fourier transform to the FD root-MUSIC polynomial to avoid the polynomial rooting step and replace it with a simple line search. Our third technique refines the FD root-MUSIC approach by using weighted least-squares approximation to compute the polynomial coefficients. The proposed techniques are shown to offer substantially improved performance-to-complexity tradeoffs as compared to the MS technique.

One- and two-dimensional direction-of-arrival estimation: An overview of search-free techniques

One of major challenges in applying traditional subspace-based direction finding techniques to real-time practical problems is in that they normally require an exhaustive spectral search over the angular parameter(s). Therefore, methods avoiding such a computationally demanding spectral search step are of great interest. In this paper, an overview of one- and two-dimensional search-free direction-of-arrival (DOA) estimation methods is presented. Both cases of uniform and non-uniform sensor arrays are addressed.

Joint 2-D DOA Estimation and Phase Calibration for Uniform Rectangular Arrays

A precise model of the array response is required to maintain the performance of direction-of-arrival (DOA) estimation. When modeling errors are present or the sensor environment is time-varying, autocalibration becomes necessary. In this paper, the problem of phase autocalibration for uniform rectangular array (URA) geometries is considered. For the case with a single source, a simple and robust least-squares algorithm for joint 2-D DOA estimation and phase calibration is presented. When performing phase autocalibration with a URA, the phase and DOA parameters cannot be identified together without ambiguity. This problem is discussed and a suitable remedy is suggested. An approximate Cramér-Rao bound and analytical expressions for the mean squared error performance of the proposed estimator are presented. The proposed algorithm for phase autocalibration is extended for the case with multiple sources. The results are evaluated using a representative body of simulations.

Robust Adaptive Beamforming Using Multidimensional Covariance Fitting

Over the last decade, several set-based worst-case beamformers have been proposed. It has been shown that some of these beamformers can be formulated equivalently as one-dimensional (ID) covariance fitting problems. Based on this formulation, we show that these beamformers lead to inherently nonoptimum results in the presence of interferers. To mitigate the detrimental effect of interferers, we extend the ID covariance fitting approach to multidimensional (MD) covariance fitting, modeling the source steering vectors by means of uncertainty sets. The proposed MD covariance fitting approach leads to a nonconvex optimization problem. We develop a convex approximation of this problem, which can be solved, for example, by means of the logarithmic barrier method. The complexity required to compute the barrier function and its first- and second-order derivatives is derived. Simulation results show that the proposed beamformer based on MD covariance fitting achieves an improved performance as compared to the state-of-the-art narrowband beamformers in scenarios with large sample support.

Robust presteered broadband beamforming based on worst-case performance optimization

In this paper, two robust presteered broadband (PB) beamformers are developed using worst-case designs. The proposed techniques are shown to enjoy a reduced computational complexity and/or significant performance improvements as compared to the existing robust wideband beamforming techniques in scenarios with array response errors.

Maximally Robust Capon Beamformer

The standard Capon beamformer (SCB) achieves the maximum output signal-to-interference-plus-noise ratio in the error-free case. However, estimation errors of the signal steering vector and the array covariance matrix can result in severe performance deteriorations of the SCB, especially if the training data contains the desired signal component. A popular technique to improve the robustness against model errors is to compute the Capon beamformer with the maximum output power, considering an uncertainty set for the signal steering vector. However, maximizing the total beamformer output power may result in an insufficient suppression of interferers and noise. As an alternative approach to mitigate the detrimental effect of model errors, we propose to compute the Capon beamformer with the minimum sensitivity, considering the uncertainty set for the signal steering vector. The proposed maximally robust Capon beamformer (MRCB) is at least as robust as the maximum output power Capon beamformer with the same uncertainty set for the signal steering vector. We show that the MRCB can be implemented efficiently using Lagrange duality. Simulation results demonstrate that the MRCB outperforms state-of-the-art robust adaptive beamformers in many scenarios.

Root-music based direction-of-arrival estimation methods for arbitrary non-uniform arrays

Two computationally efficient high-resolution methods are proposed for direction-of-arrival (DOA) estimation in arbitrary nonuniform sensor arrays. Our first algorithm is based on the fact that the spectral MUSIC function is periodic in angle. Expanding this function using Fourier series, we reformulate the DOA estimation problem as an equivalent polynomial rooting problem. Our second approach applies the inverse Fourier transform to the so-obtained root-MUSIC polynomial to compute the null-spectrum without any polynomial rooting, using a simple line search. The proposed techniques are shown to offer substantially improved performance-to- complexity tradeoffs as compared to the existing root-MUSIC-type methods applicable to non-uniform arrays.

Sparse Array Design for Azimuthal Direction-of-Arrival Estimation

We propose a novel approach to the design of array geometries for azimuthal direction-of-arrival (DOA) estimation. The proposed array design is related to that of minimum redundancy arrays, but the array sensors are not required to lie on a uniform grid. Based on the proposed array geometry design, we develop a subspace-based DOA estimation technique, which allows to estimate the DOAs of more sources than sensors, using only second-order statistics of the received data. This DOA estimation technique is related to the covariance augmentation technique, but in contrast to the latter technique, it provides nonambiguous DOA estimates for the full 360° azimuth field-of-view.

Estimating the parameters of a moving target in MIMO radar with widely separated antennas

In this paper, we develop a new maximum likelihood (ML) moving target parameter estimation technique for multiple-input multiple-output (MIMO) radar. It is required for this technique that different receive antennas have the same time reference, but no synchronization of initial phases of the receive antennas is needed and, therefore, the estimation process is noncoherent. The target motion within a certain processing interval is modeled as a second-order polynomial whose coefficients are given by the initial location, velocity, and acceleration of the target. The proposed ML estimator is able to jointly process the data collected from multiple consecutive radar pulses. It is shown that the considered ML problem simplifies to the classic “overdetermined” nonlinear least-squares problem. The proposed ML estimator requires multi-dimensional search over the unknown location, velocity, and acceleration parameters. The performance of the proposed estimator is validated by simulation results.

ISI Mitigation Capability of MLSE Direct-Detection Receivers

We explain why maximum-likelihood sequence estimation (MLSE) receivers for direct-detection optical communication systems do not achieve the single-pulse performance of threshold receivers, in which there is no intersymbol interference (ISI). For this purpose, we propose a simple and intuitive model to approximate the performance of MLSE receivers under the assumption of moderate ISI. A performance analysis of this model shows that an MLSE receiver does not reach the performance of an ISI-free threshold receiver. By simulations we evaluate the range over which the model accurately approximates the MLSE receiver.