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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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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, “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.
POWER AND DIRECTION OF TRANSMISSION ESTIMATION FOR A DIRECTIVE SOURCE: IDENTIFIABILITY ANALYSIS AND ESTIMATION ALGORITHM
"... ABSTRACT Reliable spectrum cartography of directive sources depends on an accurate estimation of the direction of transmission (DoT) as well as the transmission power. Joint estimation of power and DoT of a directive source using ML estimation techniques is considered in this paper. We further anal ..."
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ABSTRACT Reliable spectrum cartography of directive sources depends on an accurate estimation of the direction of transmission (DoT) as well as the transmission power. Joint estimation of power and DoT of a directive source using ML estimation techniques is considered in this paper. We further analyze the parametric identifiability conditions of the problem, develop the estimation algorithm, and derive the CramerRaoBound (CRB).