31 research outputs found
Sparse Linear Antenna Arrays: A Review
Linear sparse antenna arrays have been widely studied in array processing literature. They belong to the general class of non-uniform linear arrays (NULAs). Sparse arrays need fewer sensor elements than uniform linear arrays (ULAs) to realize a given aperture. Alternately, for a given number of sensors, sparse arrays provide larger apertures and higher degrees of freedom than full arrays (ability to detect more source signals through direction-of-arrival (DOA) estimation). Another advantage of sparse arrays is that they are less affected by mutual coupling compared to ULAs. Different types of linear sparse arrays have been studied in the past. While minimum redundancy arrays (MRAs) and minimum hole arrays (MHAs) existed for more than five decades, other sparse arrays such as nested arrays, co-prime arrays and super-nested arrays have been introduced in the past decade. Subsequent to the introduction of co-prime and nested arrays in the past decade, many modifications, improvements and alternate sensor array configurations have been presented in the literature in the past five years (2015–2020). The use of sparse arrays in future communication systems is promising as they operate with little or no degradation in performance compared to ULAs. In this chapter, various linear sparse arrays have been compared with respect to parameters such as the aperture provided for a given number of sensors, ability to provide large hole-free co-arrays, higher degrees of freedom (DOFs), sharp angular resolutions and susceptibility to mutual coupling. The chapter concludes with a few recommendations and possible future research directions
Sparse Array Design via Fractal Geometries
Sparse sensor arrays have attracted considerable attention in various fields
such as radar, array processing, ultrasound imaging and communications. In the
context of correlation-based processing, such arrays enable to resolve more
uncorrelated sources than physical sensors. This property of sparse arrays
stems from the size of their difference coarrays, defined as the differences of
element locations. Thus, the design of sparse arrays with large difference
coarrays is of great interest. In addition, other array properties such as
symmetry, robustness and array economy are important in different applications.
Numerous studies have proposed diverse sparse geometries, focusing on certain
properties while lacking others. Incorporating multiple properties into the
design task leads to combinatorial problems which are generally NP-hard. For
small arrays these optimization problems can be solved by brute force, however,
in large scale they become intractable. In this paper, we propose a scalable
systematic way to design large sparse arrays considering multiple properties.
To that end, we introduce a fractal array design in which a generator array is
recursively expanded according to its difference coarray. Our main result
states that for an appropriate choice of the generator such fractal arrays
exhibit large difference coarrays. Furthermore, we show that the fractal arrays
inherit their properties from their generators. Thus, a small generator can be
optimized according to desired requirements and then expanded to create a
fractal array which meets the same criteria. This approach paves the way to
efficient design of large arrays of hundreds or thousands of elements with
specific properties.Comment: 16 pages, 9 figures, 1 Tabl
Antenna Systems
This book offers an up-to-date and comprehensive review of modern antenna systems and their applications in the fields of contemporary wireless systems. It constitutes a useful resource of new material, including stochastic versus ray tracing wireless channel modeling for 5G and V2X applications and implantable devices. Chapters discuss modern metalens antennas in microwaves, terahertz, and optical domain. Moreover, the book presents new material on antenna arrays for 5G massive MIMO beamforming. Finally, it discusses new methods, devices, and technologies to enhance the performance of antenna systems
Nested Arrays: A Novel Approach to Array Processing With Enhanced Degrees of Freedom
A new array geometry, which is capable of significantly
increasing the degrees of freedom of linear arrays, is
proposed. This structure is obtained by systematically nesting two
or more uniform linear arrays and can provide O(N^2) degrees
of freedom using only physical sensors when the second-order
statistics of the received data is used. The concept of nesting is
shown to be easily extensible to multiple stages and the structure
of the optimally nested array is found analytically. It is possible to
provide closed form expressions for the sensor locations and the
exact degrees of freedom obtainable from the proposed array as a
function of the total number of sensors. This cannot be done for
existing classes of arrays like minimum redundancy arrays which
have been used earlier for detecting more sources than the number
of physical sensors. In minimum-input–minimum-output (MIMO)
radar, the degrees of freedom are increased by constructing a
longer virtual array through active sensing. The method proposed
here, however, does not require active sensing and is capable of
providing increased degrees of freedom in a completely passive
setting. To utilize the degrees of freedom of the nested co-array, a
novel spatial smoothing based approach to DOA estimation is also
proposed, which does not require the inherent assumptions of the
traditional techniques based on fourth-order cumulants or quasi
stationary signals. As another potential application of the nested
array, a new approach to beamforming based on a nonlinear
preprocessing is also introduced, which can effectively utilize the
degrees of freedom offered by the nested arrays. The usefulness of
all the proposed methods is verified through extensive computer
simulations
Theory and Algorithms for Reliable Multimodal Data Analysis, Machine Learning, and Signal Processing
Modern engineering systems collect large volumes of data measurements across diverse sensing modalities. These measurements can naturally be arranged in higher-order arrays of scalars which are commonly referred to as tensors. Tucker decomposition (TD) is a standard method for tensor analysis with applications in diverse fields of science and engineering. Despite its success, TD exhibits severe sensitivity against outliers —i.e., heavily corrupted entries that appear sporadically in modern datasets. We study L1-norm TD (L1-TD), a reformulation of TD that promotes robustness. For 3-way tensors, we show, for the first time, that L1-TD admits an exact solution via combinatorial optimization and present algorithms for its solution. We propose two novel algorithmic frameworks for approximating the exact solution to L1-TD, for general N-way tensors. We propose a novel algorithm for dynamic L1-TD —i.e., efficient and joint analysis of streaming tensors. Principal-Component Analysis (PCA) (a special case of TD) is also outlier responsive. We consider Lp-quasinorm PCA (Lp-PCA) for
Statistical Performance Analysis of Sparse Linear Arrays
Direction-of-arrival (DOA) estimation remains an important topic in array signal processing. With uniform linear arrays (ULAs), traditional subspace-based methods can resolve only up to M-1 sources using M sensors. On the other hand, by exploiting their so-called difference coarray model, sparse linear arrays, such as co-prime and nested arrays, can resolve up to O(M^2) sources using only O(M) sensors. Various new sparse linear array geometries were proposed and many direction-finding algorithms were developed based on sparse linear arrays. However, the statistical performance of such arrays has not been analytically conducted. In this dissertation, we (i) study the asymptotic performance of the MUtiple SIgnal Classification (MUSIC) algorithm utilizing sparse linear arrays, (ii) derive and analyze performance bounds for sparse linear arrays, and (iii) investigate the robustness of sparse linear arrays in the presence of array imperfections. Based on our analytical results, we also propose robust direction-finding algorithms for use when data are missing.
We begin by analyzing the performance of two commonly used coarray-based MUSIC direction estimators. Because the coarray model is used, classical derivations no longer apply. By using an alternative eigenvector perturbation analysis approach, we derive a closed-form expression of the asymptotic mean-squared error (MSE) of both estimators. Our expression is computationally efficient compared with the alternative of Monte Carlo simulations. Using this expression, we show that when the source number exceeds the sensor number, the MSE remains strictly positive as the signal-to-noise ratio (SNR) approaches infinity. This finding theoretically explains the unusual saturation behavior of coarray-based MUSIC estimators that had been observed in previous studies.
We next derive and analyze the Cramér-Rao bound (CRB) for general sparse linear arrays under the assumption that the sources are uncorrelated. We show that, unlike the classical stochastic CRB, our CRB is applicable even if there are more sources than the number of sensors. We also show that, in such a case, this CRB remains strictly positive definite as the SNR approaches infinity. This unusual behavior imposes a strict lower bound on the variance of unbiased DOA estimators in the underdetermined case. We establish the connection between our CRB and the classical stochastic CRB and show that they are asymptotically equal when the sources are uncorrelated and the SNR is sufficiently high. We investigate the behavior of our CRB for co-prime and nested arrays with a large number of sensors, characterizing the trade-off between the number of spatial samples and the number of temporal samples. Our analytical results on the CRB will benefit future research on optimal sparse array designs.
We further analyze the performance of sparse linear arrays by considering sensor location errors. We first introduce the deterministic error model. Based on this model, we derive a closed-form expression of the asymptotic MSE of a commonly used coarray-based MUSIC estimator, the spatial-smoothing based MUSIC (SS-MUSIC). We show that deterministic sensor location errors introduce a constant estimation bias that cannot be mitigated by only increasing the SNR. Our analytical expression also provides a sensitivity measure against sensor location errors for sparse linear arrays. We next extend our derivations to the stochastic error model and analyze the Gaussian case. We also derive the CRB for joint estimation of DOA parameters and deterministic sensor location errors. We show that this CRB is applicable even if there are more sources than the number of sensors.
Lastly, we develop robust DOA estimators for cases with missing data. By exploiting the difference coarray structure, we introduce three algorithms to construct an augmented covariance matrix with enhanced degrees of freedom. By applying MUSIC to this augmented covariance matrix, we are able to resolve more sources than sensors. Our method utilizes information from all snapshots and shows improved estimation performance over traditional DOA estimators