2,140 research outputs found
GLRT-Based Direction Detectors in Homogeneous Noise and Subspace Interference
In this paper, we derive and assess decision schemes to discriminate, resorting to an array of sensors, between the H0 hypothesis that data under test contain disturbance only (i.e., noise plus interference) and the H1 hypothesis that they also contain signal components along a direction which is a priori unknown but constrained to belong to a given subspace of the observables. The disturbance is modeled in terms of complex normal random vectors plus deterministic interference assumed to belong to a known subspace. We assume that a set of noise-only (secondary) data is available, which possess the same statistical characterization of noise in the cells under test. At the design stage, we resort to either the plain generalized-likelihood ratio test (GLRT) or the two-step GLRT-based design procedure. The performance analysis, conducted resorting to simulated data, shows that the one-step GLRT performs better than the detector relying on the two-step design procedure when the number of secondary data is comparable to the number of sensors; moreover, it outperforms a one-step GLRT-based subspace detector when the dimension of the signal subspace is sufficiently high
A Generalized Framework on Beamformer Design and CSI Acquisition for Single-Carrier Massive MIMO Systems in Millimeter Wave Channels
In this paper, we establish a general framework on the reduced dimensional
channel state information (CSI) estimation and pre-beamformer design for
frequency-selective massive multiple-input multiple-output MIMO systems
employing single-carrier (SC) modulation in time division duplex (TDD) mode by
exploiting the joint angle-delay domain channel sparsity in millimeter (mm)
wave frequencies. First, based on a generic subspace projection taking the
joint angle-delay power profile and user-grouping into account, the reduced
rank minimum mean square error (RR-MMSE) instantaneous CSI estimator is derived
for spatially correlated wideband MIMO channels. Second, the statistical
pre-beamformer design is considered for frequency-selective SC massive MIMO
channels. We examine the dimension reduction problem and subspace (beamspace)
construction on which the RR-MMSE estimation can be realized as accurately as
possible. Finally, a spatio-temporal domain correlator type reduced rank
channel estimator, as an approximation of the RR-MMSE estimate, is obtained by
carrying out least square (LS) estimation in a proper reduced dimensional
beamspace. It is observed that the proposed techniques show remarkable
robustness to the pilot interference (or contamination) with a significant
reduction in pilot overhead
Adaptive detection of a signal known only to lie on a line in a known subspace, when primary and secondary data are partially homogeneous
This paper deals with the problem of detecting a signal, known only to lie on a line in a subspace, in the presence
of unknown noise, using multiple snapshots in the primary data. To account for uncertainties about a signal's signature, we assume that the steering vector belongs to a known linear subspace. Furthermore, we consider the partially homogeneous case, for which the covariance matrix of the primary and the secondary data have the same structure but possibly different levels. This provides an extension to the framework considered by Bose and Steinhardt. The natural invariances of the detection problem are studied, which leads to the derivation of the maximal invariant. Then, a detector is proposed that proceeds in two steps. First, assuming that the noise covariance matrix is known, the generalized-likelihood ratio test (GLRT) is formulated. Then, the noise covariance matrix is replaced by its sample estimate based on the secondary data to yield the final detector. The latter is compared with a similar detector that assumes the steering vector to be known
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
Measuring gravitational waves from binary black hole coalescences: II. the waves' information and its extraction, with and without templates
We discuss the extraction of information from detected binary black hole
(BBH) coalescence gravitational waves, focusing on the merger phase that occurs
after the gradual inspiral and before the ringdown. Our results are: (1) If
numerical relativity simulations have not produced template merger waveforms
before BBH detections by LIGO/VIRGO, one can band-pass filter the merger waves.
For BBHs smaller than about 40 solar masses detected via their inspiral waves,
the band pass filtering signal to noise ratio indicates that the merger waves
should typically be just barely visible in the noise for initial and advanced
LIGO interferometers. (2) We derive an optimized (maximum likelihood) method
for extracting a best-fit merger waveform from the noisy detector output; one
"perpendicularly projects" this output onto a function space (specified using
wavelets) that incorporates our prior knowledge of the waveforms. An extension
of the method allows one to extract the BBH's two independent waveforms from
outputs of several interferometers. (3) If numerical relativists produce codes
for generating merger templates but running the codes is too expensive to allow
an extensive survey of the merger parameter space, then a coarse survey of this
parameter space, to determine the ranges of the several key parameters and to
explore several qualitative issues which we describe, would be useful for data
analysis purposes. (4) A complete set of templates could be used to test the
nonlinear dynamics of general relativity and to measure some of the binary
parameters. We estimate the number of bits of information obtainable from the
merger waves (about 10 to 60 for LIGO/VIRGO, up to 200 for LISA), estimate the
information loss due to template numerical errors or sparseness in the template
grid, and infer approximate requirements on template accuracy and spacing.Comment: 33 pages, Rextex 3.1 macros, no figures, submitted to Phys Rev
Code-timing synchronization in DS-CDMA systems using space-time diversity
The synchronization of a desired user transmitting a known training sequence in a direct-sequence (DS) asynchronous code-division multiple-access (CDMA) sys-tem is addressed. It is assumed that the receiver consists of an arbitrary antenna array and works in a near-far, frequency-nonselective, slowly fading channel. The estimator that we propose is derived by applying the maximum likelihood (ML) principle to a signal model in which the contribution of all the interfering compo-nents (e.g., multiple-access interference, external interference and noise) is modeled as a Gaussian term with an unknown and arbitrary space-time correlation matrix. The main contribution of this paper is the fact that the estimator makes eÆcient use of the structure of the signals in both the space and time domains. Its perfor-mance is compared with the Cramer-Rao Bound, and with the performance of other methods proposed recently that also employ an antenna array but only exploit the structure of the signals in one of the two domains, while using the other simply as a means of path diversity. It is shown that the use of the temporal and spatial structures is necessary to achieve synchronization in heavily loaded systems or in the presence of directional external interference.Peer ReviewedPostprint (published version
Blind adaptive constrained reduced-rank parameter estimation based on constant modulus design for CDMA interference suppression
This paper proposes a multistage decomposition for blind adaptive parameter estimation in the Krylov subspace with the code-constrained constant modulus (CCM) design criterion. Based on constrained optimization of the constant modulus cost function and utilizing the Lanczos algorithm and Arnoldi-like iterations, a multistage decomposition is developed for blind parameter estimation. A family of computationally efficient blind adaptive reduced-rank stochastic gradient (SG) and recursive least squares (RLS) type algorithms along with an automatic rank selection procedure are also devised and evaluated against existing methods. An analysis of the convergence properties of the method is carried out and convergence conditions for the reduced-rank adaptive algorithms are established. Simulation results consider the application of the proposed techniques to the suppression of multiaccess and intersymbol interference in DS-CDMA systems
Generalized robust shrinkage estimator and its application to STAP detection problem
Recently, in the context of covariance matrix estimation, in order to improve
as well as to regularize the performance of the Tyler's estimator [1] also
called the Fixed-Point Estimator (FPE) [2], a "shrinkage" fixed-point estimator
has been introduced in [3]. First, this work extends the results of [3,4] by
giving the general solution of the "shrinkage" fixed-point algorithm. Secondly,
by analyzing this solution, called the generalized robust shrinkage estimator,
we prove that this solution converges to a unique solution when the shrinkage
parameter (losing factor) tends to 0. This solution is exactly the FPE
with the trace of its inverse equal to the dimension of the problem. This
general result allows one to give another interpretation of the FPE and more
generally, on the Maximum Likelihood approach for covariance matrix estimation
when constraints are added. Then, some simulations illustrate our theoretical
results as well as the way to choose an optimal shrinkage factor. Finally, this
work is applied to a Space-Time Adaptive Processing (STAP) detection problem on
real STAP data
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