The influence of random element displacement on DOA estimates obtained with (Khatri-Rao-)root-MUSIC

Although a wide range of direction of arrival (DOA) estimation algorithms has been described for a diverse range of array configurations, no specific stochastic analysis framework has been established to assess the probability density function of the error on DOA estimates due to random errors in the array geometry. Therefore, we propose a stochastic collocation method that relies on a generalized polynomial chaos expansion to connect the statistical distribution of random position errors to the resulting distribution of the DOA estimates. We apply this technique to the conventional root-MUSIC and the Khatri-Rao-root-MUSIC methods. According to Monte-Carlo simulations, this novel approach yields a speedup by a factor of more than 100 in terms of CPU-time for a one-dimensional case and by a factor of 56 for a two-dimensional case

Statistical Nested Sensor Array Signal Processing

Source number detection and direction-of-arrival (DOA) estimation are two major applications of sensor arrays. Both applications are often confined to the use of uniform linear arrays (ULAs), which is expensive and difficult to yield wide aperture. Besides, a ULA with N scalar sensors can resolve at most N − 1 sources. On the other hand, a systematic approach was recently proposed to achieve O(N 2 ) degrees of freedom (DOFs) using O(N) sensors based on a nested array, which is obtained by combining two or more ULAs with successively increased spacing. This dissertation will focus on a fundamental study of statistical signal processing of nested arrays. Five important topics are discussed, extending the existing nested-array strategies to more practical scenarios. Novel signal models and algorithms are proposed. First, based on the linear nested array, we consider the problem for wideband Gaussian sources. To employ the nested array to the wideband case, we propose effective strategies to apply nested-array processing to each frequency component, and combine all the spectral information of various frequencies to conduct the detection and estimation. We then consider the practical scenario with distributed sources, which considers the spreading phenomenon of sources. Next, we investigate the self-calibration problem for perturbed nested arrays, for which existing works require certain modeling assumptions, for example, an exactly known array geometry, including the sensor gain and phase. We propose corresponding robust algorithms to estimate both the model errors and the DOAs. The partial Toeplitz structure of the covariance matrix is employed to estimate the gain errors, and the sparse total least squares is used to deal with the phase error issue. We further propose a new class of nested vector-sensor arrays which is capable of significantly increasing the DOFs. This is not a simple extension of the nested scalar-sensor array. Both the signal model and the signal processing strategies are developed in the multidimensional sense. Based on the analytical results, we consider two main applications: electromagnetic (EM) vector sensors and acoustic vector sensors. Last but not least, in order to make full use of the available limited valuable data, we propose a novel strategy, which is inspired by the jackknifing resampling method. Exploiting numerous iterations of subsets of the whole data set, this strategy greatly improves the results of the existing source number detection and DOA estimation methods

Sparse Array Architectures for Wireless Communication and Radar Applications

This thesis focuses on sparse array architectures for the next generation of wireless communication, known as fifth-generation (5G), and automotive radar direction-of-arrival (DOA) estimation. For both applications, array spatial resolution plays a critical role to better distinguish multiple users/sources. Two novel base station antenna (BSA) configurations and a new sparse MIMO radar, which both outperform their conventional counterparts, are proposed.\ua0We first develop a multi-user (MU) multiple-input multiple-output (MIMO) simulation platform which incorporates both antenna and channel effects based on standard network theory. The combined transmitter-channel-receiver is modeled by cascading Z-matrices to interrelate the port voltages/currents to one another in the linear network model. The herein formulated channel matrix includes physical antenna and channel effects and thus enables us to compute the actual port powers. This is in contrast with the assumptions of isotropic radiators without mutual coupling effects which are commonly being used in the Wireless Community.\ua0Since it is observed in our model that the sum-rate of a MU-MIMO system can be adversely affected by antenna gain pattern variations, a novel BSA configuration is proposed by combining field-of-view (FOV) sectorization, array panelization and array sparsification. A multi-panel BSA, equipped with sparse arrays in each panel, is presented with the aim of reducing the implementation complexities and maintaining or even improving the sum-rate.\ua0We also propose a capacity-driven array synthesis in the presence of mutual coupling for a MU-MIMO system. We show that the appearance of\ua0grating lobes is degrading the system capacity and cannot be disregarded in a MU communication, where space division\ua0multiple access (SDMA) is applied. With the aid of sparsity and aperiodicity, the adverse effects of grating lobes and mutual coupling\ua0are suppressed and capacity is enhanced. This is performed by proposing a two-phase optimization. In Phase I, the problem\ua0is relaxed to a convex optimization by ignoring the mutual coupling and weakening the constraints. The solution of Phase I\ua0is used as the initial guess for the genetic algorithm (GA) in phase II, where the mutual coupling is taken into account. The\ua0proposed hybrid algorithm outperforms the conventional GA with random initialization.\ua0A novel sparse MIMO radar is presented for high-resolution single snapshot DOA estimation. Both transmit and receive arrays are divided into two uniform arrays with increased inter-element spacings to generate two uniform sparse virtual arrays. Since virtual arrays are uniform, conventional spatial smoothing can be applied for temporal correlation suppression among sources. Afterwards, the spatially smoothed virtual arrays satisfy the co-primality concept to avoid DOA ambiguities. Physical antenna effects are incorporated in the received signal model and their effects on the DOA estimation performance are investigated

2-D DOA Estimation for L-Shaped Array With Array Aperture and Snapshots Extension Techniques

A two-dimensional (2-D) direction of arrival estimation method for L-shaped array with automatic pairing is proposed. It exploits the conjugate symmetry property of the array manifold matrix to increase the effective array aperture and the number of virtual snapshots simultaneously, and then applies the principle of MUSIC to construct an angle cost function and transforms the conventional 2-D search into 1-D via a Rayleigh quotient, which can greatly reduce the computation complexity. Finally, the azimuth and elevation angles are estimated without pair matching. Simulation results show that the proposed method has a better performance and can resolve more sources than some existing computationally efficient methods

Three more Decades in Array Signal Processing Research: An Optimization and Structure Exploitation Perspective

The signal processing community currently witnesses the emergence of sensor array processing and Direction-of-Arrival (DoA) estimation in various modern applications, such as automotive radar, mobile user and millimeter wave indoor localization, drone surveillance, as well as in new paradigms, such as joint sensing and communication in future wireless systems. This trend is further enhanced by technology leaps and availability of powerful and affordable multi-antenna hardware platforms. The history of advances in super resolution DoA estimation techniques is long, starting from the early parametric multi-source methods such as the computationally expensive maximum likelihood (ML) techniques to the early subspace-based techniques such as Pisarenko and MUSIC. Inspired by the seminal review paper Two Decades of Array Signal Processing Research: The Parametric Approach by Krim and Viberg published in the IEEE Signal Processing Magazine, we are looking back at another three decades in Array Signal Processing Research under the classical narrowband array processing model based on second order statistics. We revisit major trends in the field and retell the story of array signal processing from a modern optimization and structure exploitation perspective. In our overview, through prominent examples, we illustrate how different DoA estimation methods can be cast as optimization problems with side constraints originating from prior knowledge regarding the structure of the measurement system. Due to space limitations, our review of the DoA estimation research in the past three decades is by no means complete. For didactic reasons, we mainly focus on developments in the field that easily relate the traditional multi-source estimation criteria and choose simple illustrative examples.Comment: 16 pages, 8 figures. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl