Type of Document Master's Thesis Author Kadanna Pally, Roshin Author's Email Address roshin@vt.edu URN etd-04272009-140049 Title Implementation of Instantaneous Frequency Estimation based on Time-Varying AR Modeling Degree Master of Science Department Electrical and Computer Engineering Advisory Committee

Advisor Name Title Beex, A. A. Louis Committee Chair Abbott, A. Lynn Committee Member Buehrer, Richard Michael Committee Member Keywords

- Narrowband Interference Mitigation
- Block Toeplitz Inversion
- Instantaneous Frequency Estimation
- Time-Varying Autoregressive Modeling
Date of Defense 2009-04-15 Availability unrestricted AbstractInstantaneous Frequency (IF) estimation based on time-varying autoregressive (TVAR) modeling has been shown to perform well in practical scenarios when the IF variation is rapid and/or non-linear and only short data records are available for modeling. A challenging aspect of implementing IF estimation based on TVAR modeling is the efficient computation of the time-varying coefficients by solving a set of linear equations referred to as the generalized covariance equations. Conventional approaches such as Gaussian elimination or direct matrix inversion are computationally inefficient for solving such a system of equations especially when the covariance matrix has a high order.

We implement two recursive algorithms for efficiently inverting the covariance matrix. First, we implement the Akaike algorithm which exploits the block-Toeplitz structure of the covariance matrix for its recursive inversion. In the second approach, we implement the Wax-Kailath algorithm that achieves a factor of 2 reduction over the Akaike algorithm in the number of recursions involved and the computational effort required to form the inverse matrix.

Although a TVAR model works well for IF estimation of frequency modulated (FM) components in white noise, when the model is applied to a signal containing a finitely correlated signal in addition to the white noise, estimation performance degrades; especially when the correlated signal is not weak relative to the FM components. We propose a decorrelating TVAR (DTVAR) model based IF estimation and a DTVAR model based linear prediction error filter for FM interference rejection in a finitely correlated environment. Simulations show notable performance gains for a DTVAR model over the TVAR model for moderate to high SIRs.

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