Cramer-Rao Bounds for Compressive Frequency Estimation

Xushan CHEN; Xiongwei ZHANG; Jibin YANG; Meng SUN; Weiwei YANG

doi:10.1587/transfun.E98.A.874

Cramer-Rao Bounds for Compressive Frequency Estimation

Xushan CHEN, Xiongwei ZHANG, Jibin YANG, Meng SUN, Weiwei YANG

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Compressive sensing (CS) exploits the sparsity or compressibility of signals to recover themselves from a small set of nonadaptive, linear measurements. The number of measurements is much smaller than Nyquist-rate, thus signal recovery is achieved at relatively expense. Thus, many signal processing problems which do not require exact signal recovery have attracted considerable attention recently. In this paper, we establish a framework for parameter estimation of a signal corrupted by additive colored Gaussian noise (ACGN) based on compressive measurements. We also derive the Cramer-Rao lower bound (CRB) for the frequency estimation problems in compressive domain and prove some useful properties of the CRB under different compressive measurements. Finally, we show that the theoretical conclusions are along with experimental results.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E98-A No.3 pp.874-877

Publication Date: 2015/03/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E98.A.874

Type of Manuscript: LETTER

Category: Digital Signal Processing

Authors

Xushan CHEN
  PLA University of Science and Technology (PLAUST)
Xiongwei ZHANG
  PLA University of Science and Technology (PLAUST)
Jibin YANG
  PLA University of Science and Technology (PLAUST)
Meng SUN
  PLA University of Science and Technology (PLAUST)
Weiwei YANG
  PLAUST

Keyword

Cramer-Rao bound, compressive sensing, parameter estimation, additive colored Gaussian noise

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Xushan CHEN, Xiongwei ZHANG, Jibin YANG, Meng SUN, Weiwei YANG, "Cramer-Rao Bounds for Compressive Frequency Estimation" in IEICE TRANSACTIONS on Fundamentals, vol. E98-A, no. 3, pp. 874-877, March 2015, doi: 10.1587/transfun.E98.A.874.
Abstract: Compressive sensing (CS) exploits the sparsity or compressibility of signals to recover themselves from a small set of nonadaptive, linear measurements. The number of measurements is much smaller than Nyquist-rate, thus signal recovery is achieved at relatively expense. Thus, many signal processing problems which do not require exact signal recovery have attracted considerable attention recently. In this paper, we establish a framework for parameter estimation of a signal corrupted by additive colored Gaussian noise (ACGN) based on compressive measurements. We also derive the Cramer-Rao lower bound (CRB) for the frequency estimation problems in compressive domain and prove some useful properties of the CRB under different compressive measurements. Finally, we show that the theoretical conclusions are along with experimental results.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E98.A.874/_p

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@ARTICLE{e98-a_3_874,
author={Xushan CHEN, Xiongwei ZHANG, Jibin YANG, Meng SUN, Weiwei YANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Cramer-Rao Bounds for Compressive Frequency Estimation},
year={2015},
volume={E98-A},
number={3},
pages={874-877},
abstract={Compressive sensing (CS) exploits the sparsity or compressibility of signals to recover themselves from a small set of nonadaptive, linear measurements. The number of measurements is much smaller than Nyquist-rate, thus signal recovery is achieved at relatively expense. Thus, many signal processing problems which do not require exact signal recovery have attracted considerable attention recently. In this paper, we establish a framework for parameter estimation of a signal corrupted by additive colored Gaussian noise (ACGN) based on compressive measurements. We also derive the Cramer-Rao lower bound (CRB) for the frequency estimation problems in compressive domain and prove some useful properties of the CRB under different compressive measurements. Finally, we show that the theoretical conclusions are along with experimental results.},
keywords={},
doi={10.1587/transfun.E98.A.874},
ISSN={1745-1337},
month={March},}

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TY - JOUR
TI - Cramer-Rao Bounds for Compressive Frequency Estimation
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 874
EP - 877
AU - Xushan CHEN
AU - Xiongwei ZHANG
AU - Jibin YANG
AU - Meng SUN
AU - Weiwei YANG
PY - 2015
DO - 10.1587/transfun.E98.A.874
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E98-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2015
AB - Compressive sensing (CS) exploits the sparsity or compressibility of signals to recover themselves from a small set of nonadaptive, linear measurements. The number of measurements is much smaller than Nyquist-rate, thus signal recovery is achieved at relatively expense. Thus, many signal processing problems which do not require exact signal recovery have attracted considerable attention recently. In this paper, we establish a framework for parameter estimation of a signal corrupted by additive colored Gaussian noise (ACGN) based on compressive measurements. We also derive the Cramer-Rao lower bound (CRB) for the frequency estimation problems in compressive domain and prove some useful properties of the CRB under different compressive measurements. Finally, we show that the theoretical conclusions are along with experimental results.
ER -