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11
Compression limits for random vectors with linearly parameterized secondorder statistics,” arXiv:1311.0737 [math.ST
, 2013
"... Abstract — The class of complex random vectors whose covariance matrix is linearly parameterized by a basis of Hermitian Toeplitz (HT) matrices is considered, and the maximum compression ratios that preserve all secondorder information are derived—the statistics of the uncompressed vector must be ..."
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Cited by 3 (3 self)
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Abstract — The class of complex random vectors whose covariance matrix is linearly parameterized by a basis of Hermitian Toeplitz (HT) matrices is considered, and the maximum compression ratios that preserve all secondorder information are derived—the statistics of the uncompressed vector must be recoverable from a set of linearly compressed observations. This kind of vectors arises naturally when sampling widesense stationary random processes and features a number of applications in signal and array processing. Explicit guidelines to design optimal and nearly optimal schemes operating both in a periodic and nonperiodic fashion are provided by considering two of the most common linear compression schemes, which we classify as dense or sparse. It is seen that the maximum compression ratios depend on the structure of the HT subspace containing the covariance matrix of the uncompressed observations. Compression patterns attaining these maximum ratios are found for the case without structure as well as for the cases with circulant or banded structure. Universal samplers are also proposed to compress unknown HT subspaces. Index Terms — Compressive covariance sensing, covariance matching, compression matrix design.
Giannakis, “Spectrum cartography using quantized observations
 IEEE Int. Conf. Acoust., Speech, Signal Process. (Accepted
, 2015
"... This work proposes a spectrum cartography algorithm used for learning the power spectrum distribution over a wide frequency band across a given geographic area. Motivated by lowcomplexity sensing hardware and stringent communication constraints, compressed and quantized measurements are consider ..."
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This work proposes a spectrum cartography algorithm used for learning the power spectrum distribution over a wide frequency band across a given geographic area. Motivated by lowcomplexity sensing hardware and stringent communication constraints, compressed and quantized measurements are considered. Setting out from a nonparametric regression framework, it is shown that a sensible approach leads to a support vector machine formulation. The simulated tests verify that accurate spectrum maps can be constructed using a simple sensing architecture with significant savings in the feedback. 1.
Giannakis, “Online spectrum cartography via quantized measurements
, 2015
"... Abstract—An online spectrum cartography algorithm is proposed to reconstruct power spectral density (PSD) maps in space and frequency based on compressed and quantized sensor measurements. The emerging interpolation task is formulated as a nonparametric regression problem in a reproducing kernel Hi ..."
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Abstract—An online spectrum cartography algorithm is proposed to reconstruct power spectral density (PSD) maps in space and frequency based on compressed and quantized sensor measurements. The emerging interpolation task is formulated as a nonparametric regression problem in a reproducing kernel Hilbert space (RKHS) of vectorvalued functions, and solved using a stochastic gradient descent iteration. Numerical tests verify the map estimation performance of the proposed technique. I.
Parametric frugal sensing of power spectra for moving average models
 IEEE Trans. Signal Process
, 2015
"... Abstract—Wideband spectrum sensing is a fundamental component of cognitive radio and other applications. A novel frugal sensing schemewas recently proposed as ameans of crowdsourcing the task of spectrum sensing. Using a network of scattered lowend sensors transmitting randomly filtered power meas ..."
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Abstract—Wideband spectrum sensing is a fundamental component of cognitive radio and other applications. A novel frugal sensing schemewas recently proposed as ameans of crowdsourcing the task of spectrum sensing. Using a network of scattered lowend sensors transmitting randomly filtered power measurement bits to a fusion center, a nonparametric approach to spectral estimation was adopted to estimate the ambient power spectrum. Here, a parametric spectral estimation approach is considered within the context of frugal sensing. Assuming a MovingAverage (MA) representation for the signal of interest, the problem of estimating admissible MA parameters, and thus the MA power spectrum, from single bit quantized data is formulated. This turns out being a nonconvex quadratically constrained quadratic program (QCQP), which is NP–Hard in general. Approximate solutions can be obtained via semidefinite relaxation (SDR) followed by randomization; but this rarely produces a feasible solution for this particular kind of QCQP. A new Sequential Parametric Convex Approximation (SPCA) method is proposed for this purpose, which can be initialized from an infeasible starting point, and yet still produce a feasible point for the QCQP, when one exists, with high probability. Simulations not only reveal the superior performance of the parametric techniques over the globally optimum solutions obtained from the nonparametric formulation, but also the better performance of the SPCA algorithm over the SDR technique. Index Terms—Cognitive radio, distributed spectrum sensing, parametric spectral analysis, movingaverage processes, quantization, quadratically constrained quadratic programming (QCQP), semidefinite programming (SDP) relaxation. I.
Compressive Modeling of Stationary Autoregressive Processes
"... AbstractCompressive covariance sampling (CCS) methods that estimate the correlation function from compressive measurements have achieved great compression rates lately. In stationary autoregressive (AR) processes, the power spectrum is fully determined by the AR parameters, and vice versa. Therefo ..."
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AbstractCompressive covariance sampling (CCS) methods that estimate the correlation function from compressive measurements have achieved great compression rates lately. In stationary autoregressive (AR) processes, the power spectrum is fully determined by the AR parameters, and vice versa. Therefore, compressive estimation of AR parameters amounts to CCS for such signals. However, previous CCS methods typically do not fully exploit the structure of AR power spectra. On the other hand, traditional AR parameter estimation methods cannot be used when only a compressed version of the AR signal is observed. We propose a Bayesian algorithm for estimating AR parameters from compressed observations, using a MetropolisHastings sampler. Simulation results confirm the promising performance of the proposed method.
Compressive Angular and Frequency Periodogram Reconstruction for Multiband Signals
"... Abstract—In this paper, we present a duality between two problems: the reconstruction of the angular periodogram from spatialdomain signals received at different time indices and that of the frequency periodogram from timedomain signals received at different wireless sensors. We assume the existen ..."
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Abstract—In this paper, we present a duality between two problems: the reconstruction of the angular periodogram from spatialdomain signals received at different time indices and that of the frequency periodogram from timedomain signals received at different wireless sensors. We assume the existence of a multiband structure in either the angular or frequency domain representation of the received spatial or timedomain signal, respectively, where different bands are assumed to be uncorrelated. The two problems lead to a similar circulant structure in the socalled coset correlation matrix, which allows for a strong compression and a leastsquares (LS) reconstruction approach. The LS reconstruction of the periodogram is possible under the full column rank condition of the system matrix, which is achievable by designing the spatial or temporal sampling patterns based on a circular sparse ruler. I.
Compressive Periodogram Reconstruction Using Uniform Binning
, 2014
"... Abstract—In this paper, two problems that show great similarities are examined. The first problem is the reconstruction of the angulardomain periodogram from spatialdomain signals received at different time indices. The second one is the reconstruction of the frequencydomain periodogram from ti ..."
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Abstract—In this paper, two problems that show great similarities are examined. The first problem is the reconstruction of the angulardomain periodogram from spatialdomain signals received at different time indices. The second one is the reconstruction of the frequencydomain periodogram from timedomain signals received at different wireless sensors. We split the entire angular or frequency band into uniform bins. The bin size is set such that the received spectra at two frequencies or angles, whose distance is equal to or larger than the size of a bin, are uncorrelated. These problems in the two different domains lead to a similar circulant structure in the socalled coset correlation matrix. This circulant structure allows for a strong compression and a simple leastsquares reconstruction method. The latter is possible under the full column rank condition of the system matrix, which can be achieved by designing the spatial or temporal sampling patterns based on a circular sparse ruler. We analyze the statistical performance of the compressively reconstructed periodogram, including bias and variance. We further consider the case when the bins are so small that the received spectra at two frequencies or angles, with a spacing between them larger than the size of the bin, can still be correlated. In this case, the resulting coset correlation matrix is generally not circulant and thus a special approach is required. Index Terms—Averaged periodogram, circulant matrix, circular sparse ruler, compression, coset correlation matrix, multicoset sampling, nonuniform linear array, periodogram. I.
I. PRELIMINARIES AND BACKGROUND
"... Abstract—The class of complex random vectors whose covariance matrix is linearly parameterized by a basis of Hermitian Toeplitz (HT) matrices is considered, and the maximum compression ratios that preserve all secondorder information are derived the statistics of the uncompressed vector must be ..."
Abstract
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Abstract—The class of complex random vectors whose covariance matrix is linearly parameterized by a basis of Hermitian Toeplitz (HT) matrices is considered, and the maximum compression ratios that preserve all secondorder information are derived the statistics of the uncompressed vector must be recoverable from a set of linearly compressed observations. This kind of vectors typically arises when sampling widesense stationary random processes and features a number of applications in signal and array processing. Explicit guidelines to design optimal and nearly optimal schemes operating both in a periodic and nonperiodic fashion are provided by considering two of the most common linear compression schemes: nonuniform sampling and random sampling. It is seen that the maximum compression ratios depend on the structure of the HT subspace where the covariance matrix of the uncompressed observations is known to be contained. Compression patterns attaining these maximum ratios are found for the case without structure as well as for the cases with circulant or banded structure.