COPRIME ARRAYS WITH ENHANCED DEGREES OF FREEDOM

Yıl 2018, Cilt: 19 Sayı: 2, 235 - 241, 30.06.2018

Ahmet M. Elbir

https://doi.org/10.18038/aubtda.330973

Öz

Coprime array geometries
provide robust performance for direction-of-arrival estimation problem with
more sources than sensor elements. In previous works it is shown that K source
directions can be resolved using only 2M + N -1 sensor elements where K is less
than or equal to MN. In this paper we introduce a new approach to enhance the
degrees of freedom (DOF) from MN to 2MN by using the same number of sensor
elements. The proposed method is based on computing the covariance matrix of
the observation data multiple times. Hence more DOF can be obtained. The
resulting cross terms corresponding to the coherent sources are modeled as an
interference in a sparse recovery algorithm which is solved effectively by an alternating
minimization procedure. The theoretical analysis of the proposed method is
provided and its superior performance is evaluated through numerical
simulations.

Anahtar Kelimeler

Coprime arrays, sparse recovery, interference mitigation, direction of arrival estimation

Kaynakça

• Tuncer T.E, Friedlander B, Classical and Modern Direction-of-Arrival Estimation. Academic Press, 2009.
• Schmidt R.O. Multiple emitter location and signal parameter estimation. Antennas and Propagation, IEEE Transactions on, 34(3):276–280, Mar 1986.
• Pillai S.U, Bar-Ness Y, Haber F, A new approach to array geometry for improved spatial spectrum estimation. Proceedings of the IEEE, 73(10):1522–1524, Oct 1985.
• Abramovich Y.I, Gray D.A, Gorokhov A.Y, Spencer N.K, Positive-definite toeplitz completion in doa estimation for nonuniform linear antenna arrays. i. fully augmentable arrays. IEEE Transactions on Signal Processing, 46(9):2458–2471, Sep 1998.
• Abramovich Y.I, Spencer N.K, Gorokhov A.Y, Positive-definite toeplitz completion in doa estimation for nonuniform linear antenna arrays. ii. partially augmentable arrays. IEEE Transactions on Signal Processing, 47(6):1502–1521, Jun 1999.
• Pal P, Vaidyanathan P.P, Nested arrays: A novel approach to array processing with enhanced degrees of freedom. IEEE Transactions on Signal Processing, 58(8):4167–4181, Aug 2010.
• Pal P, Vaidyanathan P.P, Coprime sampling and the music algorithm. In 2011 Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE), pages 289–294, Jan 2011.
• Khatri C.G, Radhakrishna Rao C, Solutions to some functional equations and their applications to characterization of probability distributions. Sankhyā: The Indian Journal of Statistics, Series A (1961-2002), 30(2):167–180, 1968.
• Yang Z, Zhang C, Xie L. Robustly stable signal recovery in compressed sensing with structured matrix perturbation. IEEE Transactions on Signal Processing, 60(9):4658–4671, Sept 2012.
• Eldar Y.C, Sampling Theory: Beyond Bandlimited Systems. Cambridge University Press, New York, NY, USA, 2014.