Rate Distortion Function of Gaussian Asymptotically WSS Vector Processes

Gutiérrez-Gutiérrez, Jesús; Zárraga-Rodríguez, Marta; Crespo, Pedro M.; Insausti, Xabier

doi:10.3390/e20090719

Cited by 5 publications

(4 citation statements)

References 19 publications

(44 reference statements)

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“…To show that Theorem 4 can be here applied, we only need to prove that {A n } ∼ {E x 1:n x * 1:n }. From Equation (13) we obtain E (x 1:n x * 1:n ) 2 = T n (G)T n (Λ)(T n (G)) * 2 ≤ T n (G) 2 T n (Λ) 2 (T n (G)) * 2 = Λ 2 T n (G) 2 2 for all n ∈ N. Hence, as { T n (G) 2 } is bounded (see, e.g., ([5], Theorem 4.3) or ( [9], Corollary 4.2)), { E x 1:n x * 1:n 2 } is also bounded and {E x 1:n x * 1:n } ∼ {E x 1:n x * 1:n }. Since { − T n (Υ) 2 } = { T n (Υ) 2 } is bounded, {−T n (Υ)} ∼ {−T n (Υ)}, and consequently, applying ( [5], Lemma 3.1) yields {E 1:n * 1:n − T n (Υ)} ∼ {0 nN×nN }.…”

Section: Definitionmentioning

confidence: 99%

Applications of the Periodogram Method for Perturbed Block Toeplitz Matrices in Statistical Signal Processing

2020

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In this paper, we combine the periodogram method for perturbed block Toeplitz matrices with the Cholesky decomposition to give a parameter estimation method for any perturbed vector autoregressive (VAR) or vector moving average (VMA) process, when we only know a perturbed version of the sequence of correlation matrices of the process. In order to combine the periodogram method for perturbed block Toeplitz matrices with the Cholesky decomposition, we first need to generalize a known result on the Cholesky decomposition of Toeplitz matrices to perturbed block Toeplitz matrices.

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Section: Definitionmentioning

confidence: 99%

Applications of the Periodogram Method for Perturbed Block Toeplitz Matrices in Statistical Signal Processing

2020

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“…Observe that the integral formula in Equation ( 13 ) provides the value of the RDF of the Gaussian AWSS vector source whenever

. An integral formula of such an RDF for any

can be found in ([ 15 ] (Theorem 1)). It should be mentioned that ([ 15 ] (Theorem 1)) generalized the integral formulas previously given in the literature for the RDF of certain Gaussian AWSS sources, namely, WSS scalar sources [ 9 ], AR AWSS scalar sources [ 16 ], and AR AWSS vector sources of finite order [ 17 ].…”

Section: Optimality Of the Proposed Coding Strategy For Gaussian Amentioning

confidence: 99%

“…Step 2: We prove the first equality in Equation ( 18 ). Applying ([ 15 ] (Theorem 3)), we obtain that

is AWSS. From Theorem 4, we only need to show that

.…”

Section: Relevant Awss Vector Sourcesmentioning

confidence: 99%

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A Low-Complexity and Asymptotically Optimal Coding Strategy for Gaussian Vector Sources

Zárraga-Rodríguez

Gutiérrez-Gutiérrez

Insausti

2019

Entropy

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In this paper, we present a low-complexity coding strategy to encode (compress) finite-length data blocks of Gaussian vector sources. We show that for large enough data blocks of a Gaussian asymptotically wide sense stationary (AWSS) vector source, the rate of the coding strategy tends to the lowest possible rate. Besides being a low-complexity strategy it does not require the knowledge of the correlation matrix of such data blocks. We also show that this coding strategy is appropriate to encode the most relevant Gaussian vector sources, namely, wide sense stationary (WSS), moving average (MA), autoregressive (AR), and ARMA vector sources.

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Asymptotic Task-Based Quantization With Application to Massive MIMO

Shlezinger

Eldar

Rodrigues

2019

IEEE Trans. Signal Process.

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Multiple-input multiple-output (MIMO) systems are required to communicate reliably at high spectral bands using a large number of antennas, while operating under strict power and cost constraints.In order to meet these constraints, future MIMO receivers are expected to operate with low resolution quantizers, namely, utilize a limited number of bits for representing their observed measurements, inherently distorting the digital representation of the acquired signals. The fact that MIMO receivers use their measurements for some task, such as symbol detection and channel estimation, other than recovering the underlying analog signal, indicates that the distortion induced by bit-constrained quantization can be reduced by designing the acquisition scheme in light of the system task, i.e., by task-based quantization.In this work we survey the theory and design approaches to task-based quantization, presenting modelaware designs as well as data-driven implementations. Then, we show how one can implement a task-based bit-constrained MIMO receiver, presenting approaches ranging from conventional hybrid receiver architectures to structures exploiting the dynamic nature of metasurface antennas. This survey narrows the gap between theoretical task-based quantization and its implementation in practice, providing concrete algorithmic and hardware design principles for realizing task-based MIMO receivers. N. Shlezinger and Y. C. Eldar are with the Faculty of Math and CS, the number of BS antennas grow arbitrarily large [1], [2]. An additional method to increase the network throughput is to explore the millimeter wave (mmWave) frequency range [3], thus overcoming the spectral congestion of traditional wireless bands. Such mmWave communications is particularly suitable for massive MIMO systems: The short wavelengths of mmWave signals allows packing a large number of antenna elements at a small physical size, and the massive number of elements facilitates directed beamforming which is essential at mmWave bands. While the theoretical gains of massive MIMO systems, particularly when combined with mmWave transmission, are clear, implementing such systems in practice under strict cost and power constraints is a challenging task. A major source of this increased cost are the analog-todigital convertor (ADC) components, which allow the analog signals observed by each antenna element to be processed in digital. The power consumption of an ADC is directly related to the signal bandwidth and the number of bits used for digital representation [4], [5]. Consequently, in massive MIMO systems, where the number of antennas and ADCs operating at high frequency bands is large, limiting the number of bits, thus operating under quantization constraints, is crucial to keep cost and power consumption feasible [3].Focusing on uplink communications, i.e., when the BS acts as the receiver, quantization constraints imply that the BS cannot process the channel output directly but rather only an inaccurate distorted digital representation of it. The distor...

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Rate Distortion Function of Gaussian Asymptotically WSS Vector Processes

Cited by 5 publications

References 19 publications

Applications of the Periodogram Method for Perturbed Block Toeplitz Matrices in Statistical Signal Processing

Applications of the Periodogram Method for Perturbed Block Toeplitz Matrices in Statistical Signal Processing

A Low-Complexity and Asymptotically Optimal Coding Strategy for Gaussian Vector Sources

Asymptotic Task-Based Quantization With Application to Massive MIMO

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