On the Hybrid Cramér Rao Bound and Its Application to Dynamical Phase Estimation

Bay, S.; Geller, Benoît; Renaux, Alexandre; Barbot, Jean–Pierre; Brossier, Jean-Marc

doi:10.1109/lsp.2008.921461

Cited by 48 publications

(50 citation statements)

References 4 publications

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“…), we obtain matrix : (25) For both the DA and NDA scenarios (see (9) and (10) We now invert the HIM. Starting with and just similarly to Appendix I of [15], we find:…”

Section: B Analytical Expressions Of Hcrbsmentioning

confidence: 90%

Bayesian and hybrid Cramer-Rao bounds for QAM dynamical phase estimation

Yang

Geller

Wei

2009

2009 IEEE International Conference on Acoustics, Speech and Signal Processing

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Abstract-In this paper, we study Bayesian and hybrid Cramer-Rao bounds for the dynamical phase estimation of QAM modulated signals. We present the analytical expressions for the various CRBs. This avoids the calculation of any matrix inversion and thus greatly reduces the computation complexity. Through simulations, we also illustrate the behaviors of the BCRB and of the HCRB with the signal-to-noise ratio.

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“…), we obtain matrix : (25) For both the DA and NDA scenarios (see (9) and (10) We now invert the HIM. Starting with and just similarly to Appendix I of [15], we find:…”

Section: B Analytical Expressions Of Hcrbsmentioning

confidence: 90%

Bayesian and hybrid Cramer-Rao bounds for QAM dynamical phase estimation

Yang

Geller

Wei

2009

2009 IEEE International Conference on Acoustics, Speech and Signal Processing

Self Cite

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“…The HCRB is a lower bound on the joint estimation of random and deterministic parameters and unlike the CRB is not a function of the random parameters [31], [32]. In this context, the derived HCRB does not depend on the particular channels.…”

Section: A Hybrid Cramér-rao Lower Boundsmentioning

confidence: 99%

Optimal Training Sequences for Joint Timing Synchronization and Channel Estimation in Distributed Communication Networks

Nasir

Mehrpouyan

Durrani

et al. 2013

IEEE Trans. Commun.

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Abstract-For distributed multi-user and multi-relay cooperative networks, the received signal may be affected by multiple timing offsets (MTOs) and multiple channels that need to be jointly estimated for successful decoding at the receiver. This paper addresses the design of optimal training sequences for efficient estimation of MTOs and multiple channel parameters. A new hybrid Cramér-Rao lower bound (HCRB) for joint estimation of MTOs and channels is derived. Subsequently, by minimizing the derived HCRB as a function of training sequences, three training sequence design guidelines are derived and according to these guidelines, two training sequences are proposed. In order to show that the proposed design guidelines also improve estimation accuracy, the conditional Cramér-Rao lower bound (ECRB), which is a tighter lower bound on the estimation accuracy compared to the HCRB, is also derived. Numerical results show that the proposed training sequence design guidelines not only lower the HCRB, but they also lower the ECRB and the mean-square error of the proposed maximum a posteriori estimator. Moreover, extensive simulations demonstrate that application of the proposed training sequences significantly lowers the bit-error rate performance of multi-relay cooperative networks when compared to training sequences that violate these design guidelines.

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“…One can cite, for example, the Gaussian generalized linear model [9], array shape calibration [1], time-delay estimation in radar signal [4], phase estimation in binary phase-shift keying transmission in a nondata-aided context [10], phase estimation of QAM modulated signals [11], cisoid frequency estimation [12], joint estimation of the pair dynamic carrier phase/Doppler shift and the time-delay in a digital receiver [13], parameters estimation in long-code DS/CDMA systems [14], bearing estimation for deformed towed arrays in the fluid mechanics context [15]. It is therefore the aim of this paper to provide an extension of the deterministic CCRB [16] to the hybrid parameter context yielding the Constrained HCRB (CHCRB).…”

Section: Introductionmentioning

confidence: 99%

A constrained hybrid Cramér-Rao bound for parameter estimation

Ren

Kernec

Galy

et al. 2015

2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. Numerous works have shown the versatility of deterministic constrained Cramér-Rao bound for estimation performance analysis and design of a system of measurement. However in many systems both random and non-random parameters may occur simultaneously. In this communication, we propose a constrained hybrid lower bound which take into account of equality constraint on deterministic parameters. The usefulness of the proposed bound is illustrated with an application to radar Doppler estimation

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On the Hybrid Cramér Rao Bound and Its Application to Dynamical Phase Estimation

Cited by 48 publications

References 4 publications

Bayesian and hybrid Cramer-Rao bounds for QAM dynamical phase estimation

Bayesian and hybrid Cramer-Rao bounds for QAM dynamical phase estimation

Optimal Training Sequences for Joint Timing Synchronization and Channel Estimation in Distributed Communication Networks

A constrained hybrid Cramér-Rao bound for parameter estimation

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On the Hybrid Cramér Rao Bound and Its Application to Dynamical Phase Estimation

Cited by 48 publications

References 4 publications

Bayesian and hybrid Cramer-Rao bounds for QAM dynamical phase estimation

Bayesian and hybrid Cramer-Rao bounds for QAM dynamical phase estimation

Optimal Training Sequences for Joint Timing Synchronization and Channel Estimation in Distributed Communication Networks

A constrained hybrid Cram&#x00E9;r-Rao bound for parameter estimation

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A constrained hybrid Cramér-Rao bound for parameter estimation