2,215 research outputs found
Subspace Leakage Analysis and Improved DOA Estimation with Small Sample Size
Classical methods of DOA estimation such as the MUSIC algorithm are based on
estimating the signal and noise subspaces from the sample covariance matrix.
For a small number of samples, such methods are exposed to performance
breakdown, as the sample covariance matrix can largely deviate from the true
covariance matrix. In this paper, the problem of DOA estimation performance
breakdown is investigated. We consider the structure of the sample covariance
matrix and the dynamics of the root-MUSIC algorithm. The performance breakdown
in the threshold region is associated with the subspace leakage where some
portion of the true signal subspace resides in the estimated noise subspace. In
this paper, the subspace leakage is theoretically derived. We also propose a
two-step method which improves the performance by modifying the sample
covariance matrix such that the amount of the subspace leakage is reduced.
Furthermore, we introduce a phenomenon named as root-swap which occurs in the
root-MUSIC algorithm in the low sample size region and degrades the performance
of the DOA estimation. A new method is then proposed to alleviate this problem.
Numerical examples and simulation results are given for uncorrelated and
correlated sources to illustrate the improvement achieved by the proposed
methods. Moreover, the proposed algorithms are combined with the pseudo-noise
resampling method to further improve the performance.Comment: 37 pages, 10 figures, Submitted to the IEEE Transactions on Signal
Processing in July 201
Space Time MUSIC: Consistent Signal Subspace Estimation for Wide-band Sensor Arrays
Wide-band Direction of Arrival (DOA) estimation with sensor arrays is an
essential task in sonar, radar, acoustics, biomedical and multimedia
applications. Many state of the art wide-band DOA estimators coherently process
frequency binned array outputs by approximate Maximum Likelihood, Weighted
Subspace Fitting or focusing techniques. This paper shows that bin signals
obtained by filter-bank approaches do not obey the finite rank narrow-band
array model, because spectral leakage and the change of the array response with
frequency within the bin create \emph{ghost sources} dependent on the
particular realization of the source process. Therefore, existing DOA
estimators based on binning cannot claim consistency even with the perfect
knowledge of the array response. In this work, a more realistic array model
with a finite length of the sensor impulse responses is assumed, which still
has finite rank under a space-time formulation. It is shown that signal
subspaces at arbitrary frequencies can be consistently recovered under mild
conditions by applying MUSIC-type (ST-MUSIC) estimators to the dominant
eigenvectors of the wide-band space-time sensor cross-correlation matrix. A
novel Maximum Likelihood based ST-MUSIC subspace estimate is developed in order
to recover consistency. The number of sources active at each frequency are
estimated by Information Theoretic Criteria. The sample ST-MUSIC subspaces can
be fed to any subspace fitting DOA estimator at single or multiple frequencies.
Simulations confirm that the new technique clearly outperforms binning
approaches at sufficiently high signal to noise ratio, when model mismatches
exceed the noise floor.Comment: 15 pages, 10 figures. Accepted in a revised form by the IEEE Trans.
on Signal Processing on 12 February 1918. @IEEE201
Knowledge-Aided STAP Using Low Rank and Geometry Properties
This paper presents knowledge-aided space-time adaptive processing (KA-STAP)
algorithms that exploit the low-rank dominant clutter and the array geometry
properties (LRGP) for airborne radar applications. The core idea is to exploit
the fact that the clutter subspace is only determined by the space-time
steering vectors,
{red}{where the Gram-Schmidt orthogonalization approach is employed to
compute the clutter subspace. Specifically, for a side-looking uniformly spaced
linear array, the} algorithm firstly selects a group of linearly independent
space-time steering vectors using LRGP that can represent the clutter subspace.
By performing the Gram-Schmidt orthogonalization procedure, the orthogonal
bases of the clutter subspace are obtained, followed by two approaches to
compute the STAP filter weights. To overcome the performance degradation caused
by the non-ideal effects, a KA-STAP algorithm that combines the covariance
matrix taper (CMT) is proposed. For practical applications, a reduced-dimension
version of the proposed KA-STAP algorithm is also developed. The simulation
results illustrate the effectiveness of our proposed algorithms, and show that
the proposed algorithms converge rapidly and provide a SINR improvement over
existing methods when using a very small number of snapshots.Comment: 16 figures, 12 pages. IEEE Transactions on Aerospace and Electronic
Systems, 201
On convergence of the auxiliary-vector beamformer with rank-deficient covariance matrices
The auxiliary-vector beamformer is an algorithm that generates iteratively a sequence of beamformers which,
under the assumption of a positive definite covariance matrix R, converges to the minimum variance distortionless response beamformer, without resorting to any matrix inversion. In the case where R is rank-deficient, e.g., when R is substituted for the sample covariance matrix and the number of snapshots is less than the number of array elements, the behavior of the AV beamformer is not known theoretically. In this letter, we derive a new convergence result and show that the AV beamformer weights converge when R is rank-deficient, and that the limit belongs to the class of reduced-rank beamformers
Dephasing and leakage dynamics of noisy Majorana-based qubits: Topological versus Andreev
Topological quantum computation encodes quantum information nonlocally by nucleating non-Abelian anyons separated by distances L, typically spanning the qubit device size. This nonlocality renders topological qubits exponentially immune to dephasing from all sources of classical noise with operator support local on the scale of L. We perform detailed analytical and numerical analyses of a time-domain Ramsey-type protocol for noisy Majorana-based qubits that is designed to validate this coveted topological protection in near-term devices such as the so-called âtetronâ design. By assessing dependence of dephasing times on tunable parameters, e.g., magnetic field, our proposed protocol can clearly distinguish a bona fide Majorana qubit from one constructed from semilocal Andreev bound states, which can otherwise closely mimic the true topological scenario in local probes. In addition, we analyze leakage of the qubit out of its low-energy manifold due to classical-noise-induced generation of quasiparticle excitations; leakage limits the qubit lifetime when the bulk gap collapses, and hence our protocol further reveals the onset of a topological phase transition. This experiment requires measurement of two nearby Majorana modes for both initialization and readoutâachievable, for example, by tunnel coupling to a nearby quantum dotâbut no further Majorana manipulations, and thus constitutes an enticing prebraiding experiment. Along the way, we address conceptual subtleties encountered when discussing dephasing and leakage in the context of Majorana qubits
CS Decomposition Based Bayesian Subspace Estimation
In numerous applications, it is required to estimate the principal subspace of the data, possibly from a very limited number of samples. Additionally, it often occurs that some rough knowledge about this subspace is available and could be used to improve subspace estimation accuracy in this case. This is the problem we address herein and, in order to solve it, a Bayesian approach is proposed. The main idea consists of using the CS decomposition of the semi-orthogonal matrix whose columns span the subspace of interest. This parametrization is intuitively appealing and allows for non informative prior distributions of the matrices involved in the CS decomposition and very mild assumptions about the angles between the actual subspace and the prior subspace. The posterior distributions are derived and a Gibbs sampling scheme is presented to obtain the minimum mean-square distance estimator of the subspace of interest. Numerical simulations and an application to real hyperspectral data assess the validity and the performances of the estimator
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