On MMSE Crossing Properties and Implications in Parallel Vector Gaussian Channels

Bustin, Ronit; Payaró, Miquel; Palomar, Daniel P.; Shamai, Shlomo

doi:10.1109/tit.2012.2225405

Cited by 32 publications

(47 citation statements)

References 23 publications

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“…Also building on the work of [1], the functional properties of MMSE and mutual information were studied in detail in [9]. The MMSE crossing property developed in [4] was generalized to parallel vector Gaussian channels in [10]. Pointwise relations between estimation-theoretic and information-theoretic random quantities were derived in [11] to shed new light on their expectation counterparts.…”

Section: Introductionmentioning

confidence: 99%

Mismatched estimation and relative entropy in vector Gaussian channels

Chen

Lafferty

2013

2013 IEEE International Symposium on Information Theory

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We derive a novel relation between mismatched estimation and relative entropy (KL divergence) in vector Gaussian channels under the mean squared estimation criterion. This relation includes as special cases several previous results connecting estimation theory and information theory. A direct proof is provided, together with a verification using Gaussian inputs. An interesting relationship between the KL divergence and Fisher divergence is derived as a direct consequence of our work. The relations established here are potentially useful for inference in graphical models and the design of information systems.

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Section: Introductionmentioning

confidence: 99%

Mismatched estimation and relative entropy in vector Gaussian channels

Chen

Lafferty

2013

2013 IEEE International Symposium on Information Theory

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“…Upper bounds on the MMSE are useful, thanks to the I-MMSE relationship, as tools to derive information theoretic converse results, and have been used in [23,30,33,34] to name a few. The key MMSE upper bound that will be used in conjunction with the I-MMSE to derive information theoretic converses is the single crossing point property (SCPP).…”

Section: Single Crossing Point Propertymentioning

confidence: 99%

“…The key MMSE upper bound that will be used in conjunction with the I-MMSE to derive information theoretic converses is the single crossing point property (SCPP). [30,33]) Let X 2 ≤ 1. Then for any fixed snr 0 there exists a unique α ∈ [0, 1] such that…”

Section: Single Crossing Point Propertymentioning

confidence: 99%

“…Even though the statement of Proposition 4 seems quite simple it turns out that it is sufficient to show a special case of the EPI [33]: where Z ∼ N (0, R Z ). Interestingly, the I-MMSE appears to be a very powerful tool in deriving EPI type inequalities; the interested reader is referred to [35][36][37][38].…”

Section: Proposition 4 (Scppmentioning

confidence: 99%

“…A matrix version of the SCPP could facilitate a new proof of the converse of the MIMO BC by following the steps of Section 6.1. The reader is referred to [33] where the SCPP type bounds have been extended to several classes of MIMO Gaussian channels.…”

Section: Concluding Remarks and Future Directionsmentioning

confidence: 99%

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A View of Information-Estimation Relations in Gaussian Networks

Dytso

Bustin

Poor

et al. 2017

Entropy

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Abstract:Relations between estimation and information measures have received considerable attention from the information theory community. One of the most notable such relationships is the I-MMSE identity of Guo, Shamai and Verdú that connects the mutual information and the minimum mean square error (MMSE). This paper reviews several applications of the I-MMSE relationship to information theoretic problems arising in connection with multi-user channel coding. The goal of this paper is to review the different techniques used on such problems, as well as to emphasize the added-value obtained from the information-estimation point of view.

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Channel estimation using variational Bayesian learning for multi‐user mmWave MIMO systems

et al. 2020

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This paper presents a novel variational Bayesian learning‐based channel estimation scheme for hybrid pre‐coding‐employed wideband multiuser millimetre wave multiple‐input multiple‐output communication systems. We first propose a frequency variational Bayesian algorithm, which leverages common sparsity of different sub‐carriers in the frequency domain. The algorithm shares all the information of the support sets from the measurement matrices, significantly improving channel estimation accuracy. To enhance robustness of the frequency variational Bayesian algorithm, we develop a hierarchical Gaussian prior channel model, which employs an identify‐and‐reject strategy to deal with random outliers imposed by hardware impairments. A support selection frequency variational Bayesian channel estimation algorithm is also proposed, which adaptively selects support sets from the measurement matrices. As a result, the overall computational complexity can be reduced. Validated by the Bayesian Cramér‐Rao bound, simulation results show that, both frequency variational Bayesian and support selection‐frequency variational Bayesian algorithms can achieve higher channel estimation accuracy than existing methods. Furthermore, compared with frequency variational Bayesian, support selection‐frequency variational Bayesian requires significantly lower computational complexity, and hence, it is more practical for channel estimation applications.

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On MMSE Crossing Properties and Implications in Parallel Vector Gaussian Channels

Cited by 32 publications

References 23 publications

Mismatched estimation and relative entropy in vector Gaussian channels

Mismatched estimation and relative entropy in vector Gaussian channels

A View of Information-Estimation Relations in Gaussian Networks

Channel estimation using variational Bayesian learning for multi‐user mmWave MIMO systems

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