Wideband spectral estimation from compressed measurements exploiting spectral a priori information in Cognitive Radio systems

Vazquez-Vilar, Gonzalo; López-Valcarce, Roberto; Mosquera, Carlos; González–Prelcic, Nuria

doi:10.1109/icassp.2010.5496152

Cited by 14 publications

(12 citation statements)

References 8 publications

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“…We illustrate the effectiveness of the proposed multicoset sampling scheme in the context of the spectral estimation algorithm for multichannel wideband signals presented in [3] 3 . This algorithm reconstructs the power spectral density (psd) of the received signal from a set of compressed measurements, which are acquired by the TI-ADC scheme previously discussed.…”

Section: Experimental Results In a Cr Frameworkmentioning

confidence: 99%

“…Theorem 3 ensures that every subset of p ≤ 12 consecutive numbers of this sequence would yield maximum K-rank. For instance, (5, 10, 3) or its permutation (3,5,10) or its shifts, such as (0, 2, 7) , which is equivalent to its permutation (2, 7, 0) which is the end of that length-12 cycle.…”

Section: Examplesmentioning

confidence: 99%

“…At the same time, intensive work in the area of compressive sampling has yielded a number of algorithms and hardware systems to obtain compressed samples from frequency-domain sparse signals. Taking into account that CR systems need to analyze wide frequency bands, any scheme that could acquire the full wide band at a sampling rate lower than the corresponding Nyquist rate could provide samples to an spectrum analyzer based on compressed measurements [2,3] with the consequent reduction in resource usage.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Design of universal multicoset sampling patterns for compressed sensing of multiband sparse signals

Jiménez¹,

González–Prelcic

Vazquez-Vilar

et al. 2012

2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Many problems in digital communications involve wideband radio signals. As the most recent example, the impressive advances in Cognitive Radio systems make even more necessary the development of sampling schemes for wideband radio signals with spectral holes. This is equivalent to considering a sparse multiband signal in the framework of Compressive Sampling theory. Starting from previous results on multicoset sampling and recent advances in compressive sampling, we analyze the matrix involved in the corresponding reconstruction equation and define a new method for the design of universal multicoset codes, that is, codes guaranteeing perfect reconstruction of the sparse multiband signal.Index Terms-Multicoset sampling, compressive sampling, multiband sparse signal, TI-ADC, universal pattern.

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Section: Experimental Results In a Cr Frameworkmentioning

confidence: 99%

Section: Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Design of universal multicoset sampling patterns for compressed sensing of multiband sparse signals

Jiménez¹,

González–Prelcic

Vazquez-Vilar

et al. 2012

2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…2) Wideband Spectrum Sensing: If x = s σ s x s , where x s corresponds to a signal whose second-order statistics are known up to a scale, the parameters σ s capturing the power of each component can be estimated based on the observations provided by a C-ADC [30]- [33]. The covariance subspace is the span of the set of covariance matrices of the x s 's.…”

Section: ) Compressive Power Spectrum Estimationmentioning

confidence: 99%

Compression Limits for Random Vectors with Linearly Parameterized Second-Order Statistics

Romero

López-Valcarce

Leus

2015

IEEE Trans. Inform. Theory

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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 second-order 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 non-periodic 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. I. PRELIMINARIES Consider the problem of estimating the second-order statistics of a zero-mean random vector x ∈ C L from a set of K linear observations collected in the vector y ∈ C K given bywhereΦ ∈ C K×L is a known matrix and several realizations of y may be available. This matrix may be referred to as the compression matrix, measurement matrix or sampler, where compression is achieved by setting K < L (typically K L). The covariance matrix Σ = E xx H contains the second-order statistics of x and is assumed to be a linear combination of the Hermitian Toeplitz (HT) matrices in a given set This problem arises in inference operations over the secondorder statistics of a random vector with a Toeplitz covariance matrix. Operating on the compressed observations y entails multiple advantages due to their smaller dimension. In fact, many research efforts in the last decades have been pointed towards designing compression methods and reconstruction algorithms that allow for sampling rate reductions. While most efforts have been focused on reconstructing x, there were also important advances when only the second-order statistics of this vector are of interest. This paper is concerned with problems of the second kind.The compression ratio ρ = L/K measures how much x is compressed. The maximum compression ratio remains an open problem in many cases of interest; and most existing results rely on the usage of specific reconstruction algorithms (see Sec. I-D). This paper presents a general and unifying framework built on abstract criteria where the maximum compression ratio is defined and computed for most relevant settings. The proofs involved in this theory are constructive, resulting in several methods for designing optimal compression matrices. A. Covariance Matching FormulationThe prior information restricts the structure of Σ, thus determining how much x can be compressed. When no information at all is a...

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“…As discussed in [13] and [14], the canonical quickest search optimization problem in (8) can be solved equivalently by solving the following Bayesian formulation:…”

Section: Optimal Sampling Proceduresmentioning

confidence: 99%

Quickest spectrum sensing over correlated channels

Tajer

Heydari

2015

2015 IEEE International Conference on Communications (ICC)

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Quickest spectrum sensing seeks to optimize a balance between two opposing performance measures in spectrum sensing, one being the delay in identifying spectrum opportunities, and the other being the quality of the decision. The existing spectrum sensing approaches formed based on quickest detection theory rely on the assumption that the occupancy states of different spectrum bands over a wideband spectrum are statistically independent. This is an assumption that cannot be met in practice, especially in broadband communication schemes in which radio channels are dynamically grouped in bundles and allocated to different users based on the users' traffic needs. As a result of such channel grouping and allocation the occupancy states of the channels, especially the adjacent ones, are correlated. This paper, in contrast to the existing literature on quickest spectrum sensing, considers a wideband spectrum in which the occupancy states of different channels follow a pre-specified dependency kernel. The objective is to design the quickest spectrum sensing approach for identifying spectrum holes, which aims to minimize the average delay in identifying spectrum opportunities while assuring, in parallel, certain guarantees on the quality of the decision. The closedform expression of the optimal sensing scheme are delineated and are shown to have low computational complexity. IEEE ICC 2015 -Cognitive Radio and Networks Symposium 978-1-4673-6432-4/15/$31.00 ©2015 IEEE IEEE ICC 2015 -Cognitive Radio and Networks Symposium

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Wideband spectral estimation from compressed measurements exploiting spectral a priori information in Cognitive Radio systems

Cited by 14 publications

References 8 publications

Design of universal multicoset sampling patterns for compressed sensing of multiband sparse signals

Design of universal multicoset sampling patterns for compressed sensing of multiband sparse signals

Compression Limits for Random Vectors with Linearly Parameterized Second-Order Statistics

Quickest spectrum sensing over correlated channels

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