- Research Article
- Open Access
Asymptotic Bounds for Frequency Estimation in the Presence of Multiplicative Noise
EURASIP Journal on Advances in Signal Processing volume 2007, Article number: 017090 (2006)
We discuss the asymptotic Cramer-Rao bound (CRB) for frequency estimation in the presence of multiplicative noise. To improve numerical stability, covariance matrix tapering is employed when the covariance matrix of the signal is singular at high SNR. It is shown that the periodogram-based CRB is a special case of frequency domain evaluation of the CRB, employing the covariance matrix tapering technique. Using the proposed technique, large sample frequency domain CRB is evaluated for Jake's model. The dependency of the large sample CRB on the Doppler frequency, signal-to-noise ratio, and data length is investigated in the paper. Finally, an asymptotic closed form CRB for frequency estimation in the presence of multiplicative and additive colored noise is derived. Numerical results show that the asymptotic CRB obtained in frequency domain is accurate, although its evaluation is computationally simple.
Besson O, Vincent F, Stoica P, Gershman AB: Approximate maximum likelihood estimators for array processing in multiplicative noise environments. IEEE Transactions on Signal Processing 2000,48(9):2506–2518. 10.1109/78.863054
Ringelstein J, Gershman AB, Böhme JF: Direction finding in random inhomogeneous media in the presence of multiplicative noise. IEEE Signal Processing Letters 2000,7(10):269–272. 10.1109/97.870675
Gini F, Luise M, Reggiannini R: Cramer-Rao bounds in the parametric estimation of fading radiotransmission channels. IEEE Transactions on Communications 1998,46(10):1390–1398. 10.1109/26.725316
Kay SM: Fundamentals of Statistical Signal Processing: Estimation Theory. PTR Prentice Hall, Englewood Cliffs, NJ, USA; 1993.
Ghogho M, Swami A, Durrani TS: Frequency estimation in the presence of Doppler spread: performance analysis. IEEE Transactions on Signal Processing 2001,49(4):777–789. 10.1109/78.912922
Baddour KE, Beaulieu NC: Autoregressive models for fading channel simulation. Proceedings of IEEE Global Telecommunicatins Conference (GLOBECOM '01), November 2001, San Antonio, Tex, USA 2: 1187–1192.
Rugini L, Banelli P, Cacopardi S: Regularized MMSE multiuser detection using covariance matrix tapering. Proceedings of IEEE International Conference on Communications (ICC '03), May 2003, Anchorage, Alaska, USA 4: 2460–2464.
Stoica P, Marzetta TL: Parameter estimation problems with singular information matrices. IEEE Transactions on Signal Processing 2001,49(1):87–90. 10.1109/78.890346
Guerci JR: Theory and application of covariance matrix tapers for robust adaptive beamforming. IEEE Transactions on Signal Processing 1999,47(4):977–985. 10.1109/78.752596
Frehlich R: Cramer-Rao bound for Gaussian random process and applications to radar processing of atmospheric signals. IEEE Transactions on Geoscience and Remote Sensing 1993,31(6):1123–1131. 10.1109/36.317450
Abeysekera SS: Performance of pulse-pair method of Doppler estimation. IEEE Transactions on Aerospace and Electronic Systems 1998,34(2):520–531. 10.1109/7.670333
Proakis JG: Digital Communications. McGraw-Hill, Singapore; 1995.
Rife DC, Boorstyn RR: Single-tone parameter estimation from discrete-time observations. IEEE Transactions on Information Theory 1974,20(5):591–598. 10.1109/TIT.1974.1055282
Hajek BE: On the strong information singularity of certain stationary processes. IEEE Transactions on Information Theory 1979,25(5):605–609. 10.1109/TIT.1979.1056088
Zeira A, Nehorai A: Frequency domain Cramer-Rao bound for Gaussian processes. IEEE Transactions on Acoustics, Speech, and Signal Processing 1990,38(6):1063–1066. 10.1109/29.56071
Swingler DN: Approximate bounds on frequency estimates for short cisoids in colored noise. IEEE Transactions on Signal Processing 1998,46(5):1456–1458. 10.1109/78.668810
About this article
Cite this article
Wang, Z., Abeysekera, S.S. Asymptotic Bounds for Frequency Estimation in the Presence of Multiplicative Noise. EURASIP J. Adv. Signal Process. 2007, 017090 (2006). https://doi.org/10.1155/2007/17090
- Information Technology
- Covariance Matrix
- Frequency Domain
- Closed Form
- Sample Frequency