53 research outputs found
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
R-dimensional ESPRIT-type algorithms for strictly second-order non-circular sources and their performance analysis
High-resolution parameter estimation algorithms designed to exploit the prior
knowledge about incident signals from strictly second-order (SO) non-circular
(NC) sources allow for a lower estimation error and can resolve twice as many
sources. In this paper, we derive the R-D NC Standard ESPRIT and the R-D NC
Unitary ESPRIT algorithms that provide a significantly better performance
compared to their original versions for arbitrary source signals. They are
applicable to shift-invariant R-D antenna arrays and do not require a
centrosymmetric array structure. Moreover, we present a first-order asymptotic
performance analysis of the proposed algorithms, which is based on the error in
the signal subspace estimate arising from the noise perturbation. The derived
expressions for the resulting parameter estimation error are explicit in the
noise realizations and asymptotic in the effective signal-to-noise ratio (SNR),
i.e., the results become exact for either high SNRs or a large sample size. We
also provide mean squared error (MSE) expressions, where only the assumptions
of a zero mean and finite SO moments of the noise are required, but no
assumptions about its statistics are necessary. As a main result, we
analytically prove that the asymptotic performance of both R-D NC ESPRIT-type
algorithms is identical in the high effective SNR regime. Finally, a case study
shows that no improvement from strictly non-circular sources can be achieved in
the special case of a single source.Comment: accepted at IEEE Transactions on Signal Processing, 15 pages, 6
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Deterministic Cramer-Rao bound for strictly non-circular sources and analytical analysis of the achievable gains
Recently, several high-resolution parameter estimation algorithms have been
developed to exploit the structure of strictly second-order (SO) non-circular
(NC) signals. They achieve a higher estimation accuracy and can resolve up to
twice as many signal sources compared to the traditional methods for arbitrary
signals. In this paper, as a benchmark for these NC methods, we derive the
closed-form deterministic R-D NC Cramer-Rao bound (NC CRB) for the
multi-dimensional parameter estimation of strictly non-circular (rectilinear)
signal sources. Assuming a separable centro-symmetric R-D array, we show that
in some special cases, the deterministic R-D NC CRB reduces to the existing
deterministic R-D CRB for arbitrary signals. This suggests that no gain from
strictly non-circular sources (NC gain) can be achieved in these cases. For
more general scenarios, finding an analytical expression of the NC gain for an
arbitrary number of sources is very challenging. Thus, in this paper, we
simplify the derived NC CRB and the existing CRB for the special case of two
closely-spaced strictly non-circular sources captured by a uniform linear array
(ULA). Subsequently, we use these simplified CRB expressions to analytically
compute the maximum achievable asymptotic NC gain for the considered two source
case. The resulting expression only depends on the various physical parameters
and we find the conditions that provide the largest NC gain for two sources.
Our analysis is supported by extensive simulation results.Comment: submitted to IEEE Transactions on Signal Processing, 13 pages, 4
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Wavefield modeling and signal processing for sensor arrays of arbitrary geometry
Sensor arrays and related signal processing methods are key technologies in many areas of engineering including wireless communication systems, radar and sonar as well as in biomedical applications. Sensor arrays are a collection of sensors that are placed at distinct locations in order to sense physical phenomena or synthesize wavefields. Spatial processing from the multichannel output of the sensor array is a typical task. Such processing is useful in areas including wireless communications, radar, surveillance and indoor positioning.
In this dissertation, fundamental theory and practical methods of wavefield modeling for radio-frequency array processing applications are developed. Also, computationally-efficient high-resolution and optimal signal processing methods for sensor arrays of arbitrary geometry are proposed. Methods for taking into account array nonidealities are introduced as well. Numerical results illustrating the performance of the proposed methods are given using real-world antenna arrays.
Wavefield modeling and manifold separation for vector-fields such as completely polarized electromagnetic wavefields and polarization sensitive arrays are proposed. Wavefield modeling is used for writing the array output in terms of two independent parts, namely the sampling matrix depending on the employed array including nonidealities and the coefficient vector depending on the wavefield. The superexponentially decaying property of the sampling matrix for polarization sensitive arrays is established. Two estimators of the sampling matrix from calibration measurements are proposed and their statistical properties are established.
The array processing methods developed in this dissertation concentrate on polarimetric beamforming as well as on high-resolution and optimal azimuth, elevation and polarization parameter estimation. The proposed methods take into account array nonidealities such as mutual coupling, cross-polarization effects and mounting platform reflections. Computationally-efficient solutions based on polynomial rooting techniques and fast Fourier transform are achieved without restricting the proposed methods to regular array geometries. A novel expression for the Cramér-Rao bound in array processing that is tight for real-world arrays with nonidealities in the asymptotic regime is also proposed.
A relationship between spherical harmonics and 2-D Fourier basis, called equivalence matrix, is established. A novel fast spherical harmonic transform is proposed, and a one-to-one mapping between spherical harmonic and 2-D Fourier spectra is found. Improvements to the minimum number of samples on the sphere that are needed in order to avoid aliasing are also proposed
Reduced-Dimension Noncircular-Capon Algorithm for DOA Estimation of Noncircular Signals
The problem of the direction of arrival (DOA) estimation for the noncircular (NC) signals, which have been widely used in communications, is investigated. A reduced-dimension NC-Capon algorithm is proposed hereby for the DOA estimation of noncircular signals. The proposed algorithm, which only requires one-dimensional search, can avoid the high computational cost within the two-dimensional NC-Capon algorithm. The angle estimation performance of the proposed algorithm is much better than that of the conventional Capon algorithm and very close to that of the two-dimensional NC-Capon algorithm, which has a much higher complexity than the proposed algorithm. Furthermore, the proposed algorithm can be applied to arbitrary arrays and works well without estimating the noncircular phases. The simulation results verify the effectiveness and improvement of the proposed algorithm
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
A review of closed-form Cramér-Rao Bounds for DOA estimation in the presence of Gaussian noise under a unified framework
The Cramér-Rao Bound (CRB) for direction of arrival (DOA) estimation has been extensively studied over the past four decades, with a plethora of CRB expressions reported for various parametric models. In the literature, there are different methods to derive a closed-form CRB expression, but many derivations tend to involve intricate matrix manipulations which appear difficult to understand. Starting from the Slepian-Bangs formula and following the simplest derivation approach, this paper reviews a number of closed-form Gaussian CRB expressions for the DOA parameter under a unified framework, based on which all the specific CRB presentations can be derived concisely. The results cover three scenarios: narrowband complex circular signals, narrowband complex noncircular signals, and wideband signals. Three signal models are considered: the deterministic model, the stochastic Gaussian model, and the stochastic Gaussian model with the a priori knowledge that the sources are spatially uncorrelated. Moreover, three Gaussian noise models distinguished by the structure of the noise covariance matrix are concerned: spatially uncorrelated noise with unknown either identical or distinct variances at different sensors, and arbitrary unknown noise. In each scenario, a unified framework for the DOA-related block of the deterministic/stochastic CRB is developed, which encompasses one class of closed-form deterministic CRB expressions and two classes of stochastic ones under the three noise models. Comparisons among different CRBs across classes and scenarios are presented, yielding a series of equalities and inequalities which reflect the benchmark for the estimation efficiency under various situations. Furthermore, validity of all CRB expressions are examined, with some specific results for linear arrays provided, leading to several upper bounds on the number of resolvable Gaussian sources in the underdetermined case
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
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