Asymptotically Equivalent Sequences of Matrices and Hermitian Block Toeplitz Matrices With Continuous Symbols: Applications to MIMO Systems

Gutiérrez-Gutiérrez, Jesús; Crespo, Pedro M.

doi:10.1109/tit.2008.2006401

Cited by 62 publications

(34 citation statements)

References 20 publications

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“…Furthermore, in this case, from [3] (Theorem 4.4.2) (it was previously given in [4] (p. 5674) but without a proof) and [5] (Corollary VI.1.6), we obtain min ω∈ [0,2π] …”

Section: Definitionmentioning

confidence: 52%

On the Complexity Reduction of Coding WSS Vector Processes by Using a Sequence of Block Circulant Matrices

Gutiérrez-Gutiérrez

Zárraga-Rodríguez

Insausti

et al. 2017

Entropy

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“…Furthermore, in this case, from [3] (Theorem 4.4.2) (it was previously given in [4] (p. 5674) but without a proof) and [5] (Corollary VI.1.6), we obtain min ω∈ [0,2π] …”

Section: Definitionmentioning

confidence: 52%

On the Complexity Reduction of Coding WSS Vector Processes by Using a Sequence of Block Circulant Matrices

Gutiérrez-Gutiérrez

Zárraga-Rodríguez

Insausti

et al. 2017

Entropy

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“…where (a) follows from [27,Eq. (8.71)] asF a n is invertible, and (b) follows from the extension of Szego's theorem to block-Toeplitz matrices [49,Thm. 5].…”

Section: Proof Of Propositionmentioning

confidence: 99%

“…), for any input distribution satisfying 1 n E X [i] 2 ≤ P and for any n. Lastly, we note that in the limit as n → ∞, it follows from the extension of Szego's theorem to block-Toeplitz matrices [37, Appendix A.2],[49, Thm. 5] that dω, therefore, since 2 t is continuous w.r.t.…”

mentioning

confidence: 99%

On the Capacity of MIMO Broadband Power Line Communications Channels

Shlezinger

Shaked

Dabora

2018

IEEE Trans. Commun.

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Communications over power lines in the frequency range above 2 MHz, commonly referred to as broadband (BB) power line communications (PLC), has been the focus of increasing research attention and standardization efforts in recent years. BB-PLC channels are characterized by a dominant colored non-Gaussian additive noise, as well as by periodic variations of the channel impulse response and the noise statistics. In this work we study the fundamental rate limits for BB-PLC channels by bounding their capacity while accounting for the unique properties of these channels. We obtain explicit expressions for the derived bounds for several BB-PLC noise models, and illustrate the resulting fundamental limits in a numerical analysis.Index terms-Power line communications, MIMO systems, channel capacity. noise. We emphasize that all the works mentioned above, i.e., [7], [10], [26], derived expressions assuming Gaussian noise, while major works have concluded that the noise is non-Gaussian, see, e.g., [4], [8], [9]. We also note the work [28], which derived an approximate expression for the achievable rates when using Gaussian inputs and when using inputs with discrete amplitudes, for memoryless channels with additive GM noise, which were used for modelling communications in the presence of co-channel interference. Finally, we note that the capacity of PLC channels in the narrowband frequency range (0−500 kHz), modeled as additive noise channels in which the CIR is modeled as an LPTV filter and the noise is a cyclostationary Gaussian process, was derived in [29]. To the best of our knowledge, the fundamental limits for BB-PLC channels, accounting for their unique characteristics, including the non-Gaussianity and the temporal correlation of the noise, as well as the periodic variations of the CIR and of the noise statistics, have not been characterized to date. In this work we aim to address this gap. Main Contributions:In this work we study the fundamental rate limits of discrete-time (DT) BB-PLC channels. We consider a general channel model accounting for a wide range of the characteristics of BB-PLC channels, in which the CIR is modeled as an LPTV filter, and the additive noise is modeled as a temporally correlated non-Gaussian cyclostationary process 1 . Accordingly, we characterize an upper bound and two lower bounds on the capacity of these channels. We note that when the noise is not a Gaussian process, obtaining a closed-form expression for the capacity is generally a very difficult task, even for stationary and memoryless channels, and the common approach is to characterize upper and lower bounds on the capacity, see, e.g., [30, Ch. 7.4]. To facilitate the derivation, we first derive bounds on the capacity of a general LTI MIMO channel with additive non-Gaussian stationary noise. Then, we prove that the capacity of BB-PLC channels can be obtained from the capacity of non-Gaussian LTI MIMO channels by properly setting the parameters of the model, and finally we apply the bounds on the capacity of the latter model to ob...

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“…Since X, Y , and Z are stochastically degraded, we can assume without loss of generality that X − Y − Z form a Markov chain, and use (40) and (45) to obtain (47). In this case (45) is supremized as Q X approaches the equiprobable distribution on {0, 1}.…”

Section: Example 1 (Symmetric Bernoulli Source) Suppose X Y and Z Amentioning

confidence: 99%

Key Capacity for Product Sources With Application to Stationary Gaussian Processes

Liu

Cuff

Verdú

2016

IEEE Trans. Inform. Theory

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Abstract-We show that for product sources, rate splitting is optimal for secret key agreement using limited one-way communication between two terminals. This yields an alternative information-theoretic-converse-style proof of the tensorization property of a strong data processing inequality originally studied by Erkip and Cover and amended recently by Anantharam et al. We derive a water-filling solution of the communication-ratekey-rate tradeoff for a wide class of discrete memoryless vector Gaussian sources which subsumes the case without an eavesdropper. Moreover, we derive an explicit formula for the maximum secret key per bit of communication for all discrete memoryless vector Gaussian sources using a tensorization property and a variation on the enhanced channel technique of Weingarten et al. Finally, a one-shot information spectrum achievability bound for key generation is proved from which we characterize the communication-rate-key-rate tradeoff for stationary Gaussian processes.

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Asymptotically Equivalent Sequences of Matrices and Hermitian Block Toeplitz Matrices With Continuous Symbols: Applications to MIMO Systems

Cited by 62 publications

References 20 publications

On the Complexity Reduction of Coding WSS Vector Processes by Using a Sequence of Block Circulant Matrices

On the Complexity Reduction of Coding WSS Vector Processes by Using a Sequence of Block Circulant Matrices

On the Capacity of MIMO Broadband Power Line Communications Channels

Key Capacity for Product Sources With Application to Stationary Gaussian Processes

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