Complex exponential signal angle estimation based on angle invariant combiner

Authors: Stanković Veljko

Keywords: signal processing; direction of arrival estimation; frequency estimation; array processing

Abstract:

Abstract: In order to achieve estimation performance limits, we often need to use computationally demanding estimation algorithms and/or signal information of higher order such as cumulants. Our goal is to reduce the computational complexity of angle estimation, and to achieve the Cramer-Rao estimation bound, and the maximum-likelihood signal-to-noise ratio threshold by using iterative estimation where the most computationally demanding processing is done as much as possible in the initialisation step, while in each iteration we require less complex processing. This is achieved by using the angle invariant combinations of signal autocorrelation samples for estimation.

References:

[1] H.L. VAN TREES, Optimum Array Processing, Wiley Interscience, New York, NY, USA, 2002 [2] S. KAY, Mean Likelihood Frequency Estimation, IEEE Trans. on Sig. Proc., Vol. 48, (7), (2000), p. 1937-1946 [3] H.C. SO AND F.K.W. CHAN, A Generalized Weighted Linear Predictor Frequency Estimation Approach for a Complex Sinusoid, IEEE Trans. on Sig. Proc., Vol. 54, (4), (2006), p. 1304-1312 [4] C. QIAN ET AL., Enhanced PUMA for direction-of-arrival estimation and its performance analysis, IEEE Trans. on Sig. Proc., Vol. 64, (16), (2016), p. 4127-4137 [5] P. STOICA AND A. NEHORAI, MUSIC, Maximum Likelihood, and Cramer-Rao Bound, IEEE Trans. on Acoustics, Speech and Sig. Proc., Vol. 37, (5), (1989), p. 720-741 [6] P. STOICA ET AL., Maximum Likelihood Estimation of the Parameters of Multiple Sinusoids from Noisy Measurements, IEEE Trans. on Acoustics, Speech and Signal Proc., Vol. 37, (3), (1989), p. 378-392 [7] J. STEINWANDT ET AL., Generalized least squares for ESPRIT-type direction of arrival estimation, IEEE Sig. Proc. Letters, Vol. 24, (11), (2017), p. 1681-1685 [8] P. PORAT AND B. FRIEDLANDER, Direction finding algorithms based on high-order statistics, IEEE Trans. on Sig. Proc., Vol. 39, (9), (1991), p. 2016-2024 [9] W.K. LAI AND P.C. CHING, A higher-order cumulant based DOA estimation algorithm, European Signal Processing Conference, EUSIPCO, Trieste, Italy, 1996. [10] X. JIANG, Fundamental frequency estimation by higher order spectrum, International conference on Acoustics, Speech, and Signal Processing, (ICASSP), 2000. [11] K.W.K. LUI, H.C. SO, Two-stage autocorrelation approach for accurate single sinusoidal frequency estimation, Signal Processing (Elsevier), Vol. 88, (7), (2008), p.1852-1857 [12] Y. CAO ET AL., Aclosed-form expanded autocorrelation method for frequency estimation of a sinusoid, Signal Processing (Elsevier), Vol. 92, (4), (2012), p. 885-892 [13] C. CANDAN, Analysis and further improvement of fine resolution frequency estimation method from three DFT samples, IEEE Sig. Proc. Letters, 20, (9), (2013), p. 913-916 [14] S. KAY,AFastandAccurateSingleFrequencyEstimator, IEEETrans.onAcoustics, Speech and Signal Proc., Vol. 37, (12), (1989), p. 1987-1990 [15] W.F. TRENCH, Numerical solution of the eigenvalue problem for Hermitian Toeplitz matrices, SIAM J. Matrix Anal. Appl., Vol. 10, (2), (1989), p. 135-156