Cramer–Rao Lower Bound for Constrained Complex Parameters

Jagannatham, Aditya K.; Rao, Bhaskar D.

doi:10.1109/lsp.2004.836948

Cited by 52 publications

(32 citation statements)

References 7 publications

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“…The constrained CRB can be derived by following the steps in [28] or [30]. If the unconstrained Fisher information matrix is singular, we have to use the constrained CRB from [30] which is briefly reviewed in Appendix D.…”

Section: Cramér-rao Bound For a Complex Parameter Vectormentioning

confidence: 99%

“…Due to the phase ambiguity in circular complex ICA, the Fisher information for the diagonal elements is 0 and hence their iCRB does not exist. However, we can constrain to be real and derive the constrained CRB [30] (see also Appendix D) for : As noted at the end of Section III.A, is decoupled from and and hence it is sufficient to consider the constrained CRB for alone. …”

Section: A All Sources Are Circular Complexmentioning

confidence: 99%

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Cramér-Rao Bound for Circular and Noncircular Complex Independent Component Analysis

Loesch

Yang

2013

IEEE Trans. Signal Process.

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Despite an increased interest in complex independent component analysis (ICA) during the last two decades, a closed form expression for the Cramér-Rao bound (CRB) for the demixing matrix is not known yet. In this paper, we fill this gap by deriving a closed-form expression for the CRB of the demixing matrix for instantaneous noncircular complex ICA. It contains the CRB for circular complex ICA and noncircular complex Gaussian ICA as two special cases. We also study the CRB numerically for the family of noncircular complex generalized Gaussian distributions and compare it to simulation results of two ICA estimators. Furthermore, we show how to extend the CRB to the case where the source signals are not temporally independent and identically distributed.Index Terms-Cramér-Rao bound, generalized Gaussian distribution, independent component analysis, noncircular complex.

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Section: Cramér-rao Bound For a Complex Parameter Vectormentioning

confidence: 99%

Section: A All Sources Are Circular Complexmentioning

confidence: 99%

Cramér-Rao Bound for Circular and Noncircular Complex Independent Component Analysis

Loesch

Yang

2013

IEEE Trans. Signal Process.

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“…Also in this case, it is trivial to verify that, when there is no mismatch, i.e. when B θ 0 = −A θ 0 , the bound in (39) is equal to the one derived [7] and [9].…”

Section: A5mentioning

confidence: 92%

“…with a non-vanishing pseudo-covariance), MS-unbiased, mismatched estimators. Our strategy to derived the complex MCRB follows the one adopted in [6] and [7] for the complex unconstrained and constrained CRB. Specifically, we will not derive any new covariance inequality directly in the complex field (as done e.g.…”

Section: Introductionmentioning

confidence: 99%

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Misspecified Cramér-rao bounds for complex unconstrained and constrained parameters

Fortunati

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Cramer–Rao bound based mean‐squared error and throughput analysis of superimposed pilots for semi‐blind multiple‐input multiple‐output wireless channel estimation

Jagannatham

Rao

2012

Int J Communication

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SUMMARYThis work presents a study of the mean‐squared error (MSE) and throughput performance of superimposed pilots (SP) for the estimation of a multiple‐input multiple‐output (MIMO) wireless channel. The Cramer–Rao bound (CRB) is derived for SP based estimation of the MIMO channel matrix. Employing the CRB analysis, it is proved that the asymptotic MSE bound is potentially 3 dB lower than the MSE performance of the existing SP mean based estimation (SPME) schemes. Motivated by this observation, a novel SP semi‐blind scheme is presented for MIMO channel estimation. This scheme asymptotically achieves the CRB and hence has a lower MSE of estimation when compared with SPME schemes. We also derive closed form expressions for the optimal source‐pilot power allocation in SP by maximizing the post‐processing signal‐to‐noise power ratio at the receiver. In the final part, a new result is presented for the worst‐case capacity of a communication channel with correlated information symbols and noise. This framework is employed to quantify the throughput performance of SP and also to demonstrate the bandwidth efficiency of SP compared with that of a conventional pilot based system. Copyright © 2012 John Wiley & Sons, Ltd.

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Cramer–Rao Lower Bound for Constrained Complex Parameters

Cited by 52 publications

References 7 publications

Cramér-Rao Bound for Circular and Noncircular Complex Independent Component Analysis

Cramér-Rao Bound for Circular and Noncircular Complex Independent Component Analysis

Misspecified Cramér-rao bounds for complex unconstrained and constrained parameters

Cramer–Rao bound based mean‐squared error and throughput analysis of superimposed pilots for semi‐blind multiple‐input multiple‐output wireless channel estimation

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