**5. References**


Robust Beamforming and DOA Estimation 141

[38] Liu Congfeng, Liao Guisheng, Robust capon beamformer under norm constraint, Signal

[39] Dolph C L. A current distribution for broadside arrays which optimizes the relationship between beam width and sidelobe level. Proc IRE, June.1946, Vol.34, pp:335–348. [40] Zhou P, Ingram M. Pattern synthesis for arbitrary arrays using an adaptive array

[41] Wang F, Balakrishnan V, Zhou P Y, et al. Optimal array pattern synthesis using

[42] Guo Q, Liao G., Wu Y, et al. Pattern synthesis method for arbitrary arrays based on LCMV criterion. Electronics Letters. May.2003, Vol.39, No.23, pp:1628-1630. [43] Xie Yao, Jian Li, Zheng Xiayu, et al. Optimal array pattern synthesis via matrix

[44] Kurup D G., Himdi M, Rydberg A. Synthesis of uniform amplitude unequally spaced

[45] Boeringer D W, Werner D H. Particle swarm optimization versus genetic algorithms for

[46] Liu Xiaojun, Liu Congfeng, Liao Guisheng, Improved pattern synthesis method with

[47] Barabell A.J, Improving the resolution performance of eigenstructure-based direction-

[48] Kumaresan R. and Tufts D.W., Estimating the angles of arrival of multiple plane

[49] Bao B and Hari.K, Performance analysis of root-MUSIC, IEEE Trans, 1989, ASSP-

[50] Li F and Vaccaro.R.J,Analytical performance prediction of subspace-based algorithms

[51] Xu X.L and Buckley K.M, Reduced dimension beamspace broad-band localization,

[52] Ta sung Lee, Fast implementation of root-form eigen-based methods for detecting closely spaced sources IEE Proceedings-F Vol.139.No.4,August 1992. [53] Marius P, Alex B.G and Martin H, Unitary root-MUSIC with a real-valued

[54] Liu Congfeng, Liao Guisheng, Fast algorithm for root-MUSIC with real-valued

for DOA estimation: SVD and Signal Processing II Algorithms,Analysis and

preprocessor design and evaluation.Proc.IEEE Forth Workshop on Spectrum

eigendecomposition: a theoretical and experimental performacce study, IEEE

eigendecomposition, Radar-2006: 2006 CIE International Conference on Radar

Piscataway, NJ 08855-1331, United States, Vol.2, pp: 885-888.

Antennas And Propagation. Sep.2003, Vol.51, No.9, pp:2210-2217.

method. IEEE Transactions on Antennas And Propagation. May.1999, Vol.47, No.5,

semidefinite programming. IEEE Transactions on Signal Processing, May.2003,

weighting, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing – Proceedings, Apr 15-20 2007, Honolulu, HI, United States, IEEE Inc.,

antenna arrays using the differential evolution algorithm, IEEE Transactions on

phased array synthesis, IEEE Transactions on Antennas And Propagation.

linearly constraint minimum variance criterion, 2010 IEEE Internation Conference on Wireless Communications, Networking and Information Security (WCNIS2010),

Processing, May.2010, Vol.90, Issue.5, pp: 1573-1581.

pp:862-869.

Vol.51, No.5, pp:1172-1183.

Mar.2004, Vol.52, No.3, pp:771-779.

2010.6,25-27, Vol.2, Beijing China。

37,pp.1939-1949.

wave,IEEE Trans,1983,AES-19,pp.134-138.

Applications (Elsevier,New York,1991)

Estimation and Modeling, 1988,pp22-26.

2006.10 ShangHai China.

finding algorithms.Proc,ICASSP 83,1983,pp.336-339.

Transactions on SP,Vol.48,No.5,May 2000,pp:1306-1314.


140 Fourier Transform Applications

[19] Sergiy A. Vorobyov, A. B. Gershman, Zhi-Quan Luo. Robust adaptive beamforming

problem. IEEE Trans. Signal Processing. Vol.51, No.2, pp: 313-324, Feb.2003. [20] Jian Li, Petre Stotica, Zhisong Wang.On robust capon beamformer and diagonal loading. IEEE Trans. Signal Processing. Vol.51, No.7, pp: 1702-1715, Jul.2003. [21] S. Shahram, A. B. Gershman, Zhiquan Luo, et al. Robust adaptive beamforming for

[22] Jian Li, Petre Stotica, Zhisong Wang, Doubly constrained robust capon beamformer. IEEE Trans. Signal Processing. Vol.52, No.9, pp: 2407-2423, Sep.2004. [23] G.L. Robert, P.B. Stephen. Robust minimum variance beamforming. IEEE Trans. Signal

[24] Ayman Elnashar, Said M. Elnoubi, Hamdi A. El-Mikati. Further study on robust

[25] C.Y.Chen, P.P.Vaidyanathan. Quadratically constrained beamforming robust against

[26] R. A. Monzingo, T. W. Miller. Introduction to adaptive arrays. New York: Wiley, 1980. [27] Z. Tian, K. L. Bell, H. L. Van Trees. A recursive least squares implementation for LCMP

[28] L. C. Godara. Error analysis of the optimal antenna array processors. IEEE Trans.

[29] K. L. Bell, Y. Ephraim, H. L. Van Trees, A Bayesian approach to robust adaptive beamforming. IEEE Trans. Signal Processing, Vol.48, pp: 386-398, Feb.2000. [30] L. Chang, C. C. Yeh. Performance of DMI and eigenspace-based beamformers. IEEE

[31] Cheng-Chou Lee, Ju-Hong Lee. Eigenspace-based adaptive array beamforming with

[32] J. Riba, J. Goldberg, G. Vazquez. Robust beamforming for interference rejection in

[33] J. R. Guerci. Theory and application of covariance matrix tapers for robust adaptive beamforming. IEEE Trans. Signal Processing, Vol.47, pp: 997-985, Apr.1999. [34] J. R. Guerci, J.S.Bergin. Principal components,covariance matrix tapers,and the subspace leakage problem. IEEE Trans. Aerosp. Electron. Syst, Vol.38, pp: 152-162, Jan.2002.

[35] F. Vincent, O. Besson. Steering vector errors and diagonal loading, IEE Proceedings.-

[36] O. Besson, F. Vincent. Performance analysis of beamformers using generalized loading

[37] Almir Mutapcic, Seung-Jean Kim, Stephen Boyd. Beamforming with uncertain weights.

IEEE Signal Processing Letter, Vol.14, No.5, pp: 348-351, May.2007.

of the covariance matrix in the presence of random steering vector errors. IEEE

Radar Sonar Navig., Vol.151, No.6, pp: 337-343, Dec.2004.

Trans. Signal Processing, Vol.53, pp: 452-459, Feb.2005.

robust capabilities. IEEE Trans. Antennas Propagation, Vol.45, pp: 1711-1716,

mobile communications. IEEE Trans. Signal Processing, Vol.45, pp: 271-275,

Processing, Vol.53, No.5, pp: 1684-1696, May.2005.

Propagation, Vol.AP-54, No.12, pp: 3647-3658, Dec.2006.

Aerosp. Electron. Syst., Vol. AES-22, pp: 395-409, Jul.1986.

Trans. Antennas Propagation, Vol.40, pp: 1336-1347, Nov.1992.

2269, Sep.2003.

4139-4150, Aug.2007.

Dec.1997.

Jan.1997.

No.6, pp: 1365-1376, Jun.2001.

using worst-case performance optimization: a solution to the signal mismatch

general-rank signal models. IEEE Trans. Signal Processing, Vol.51, No.9, pp: 2257-

adaptive beamforming with optimum diagonal loading. IEEE Trans. Antennas

direction-of- arrival mismatch. IEEE Trans. Signal Processing, Vol.55, No.8, pp:

beamforming under quadratic constraint. IEEE Trans. Signal Processing, Vol.49,


2010.6,25-27, Vol.2, Beijing China。


**1. Introduction**

2005; Zaitsev et al., 2003).

The solar corona has a very complex and highly dynamic structure. It consists of a large number of constantly evolving, loops and filaments, which interact with each other and are closely associated with the local magnetic field. The non-stationary character of solar plasma-magnetic structures manifests itself in various forms of the coronal magnetic loops dynamics as rising motions, oscillations, meandering, twisting (Aschwanden et al., 1999; Schrijver et al., 1999), as well as in formation, sudden activation and eruption of filaments and prominences. Energetic phenomena, related to these types of magnetic activity, range from tiny transient brightenings (micro-flares) and jets to large, active-region-sized flares and coronal mass ejections (CMEs). They are naturally accompanied by different kinds of electromagnetic (EM) emission, covering a wide frequency band from radio waves to gamma-rays. Radiation, produced within a given plasma environment, carries an information on physical and dynamic conditions in a radiating source. This causes an exceptional importance of the EM radiation, as a diagnostic tool, for understanding the nature and physics of various solar dynamic phenomena. As a relatively new, in that context, direction of study in the traditional branch of the solar microwave radio astronomy appears the analysis of the slow, long-periodic (e.g., > 1 s) fluctuations of the radiation intensity (Khodachenko et al.,

**Analysis of Long-Periodic Fluctuations of Solar** 

**Microwave Radiation, as a Way for Diagnostics** 

Maxim L. Khodachenko1, Albert G. Kislyakov2 and Eugeny I. Shkelev2

**of Coronal Magnetic Loops Dynamics** 

*1Space Research Institute, Austrian Academy of Sciences, Graz,* 

*2Lobachevsky State University, Nizhny Novgorod,* 

*1Austria 2Russia* 

**5**

Microwave radiation from the magnetic loops in solar active regions (e.g., during solar flares) is usually interpreted as a gyro-synchrotron radiation, produced by fast electrons on harmonics of the gyro-frequency *ν<sup>B</sup>* in the magnetic field *B* of the loop. In the case of a power-law distribution of electrons in energy as *<sup>f</sup>*(E) <sup>∝</sup> <sup>E</sup>−*δ*, the intensity of gyro-synchrotron

where *θ* is the angle between magnetic field and the direction of electromagnetic wave propagation. For the observed typical values of the electron energy spectrum index 2 ≤ *δ* ≤ 7 this implies the proportionality of intensity to a moderately high power of the background

*I<sup>ν</sup>* ∝ *B*−0.22+0.9*δ*(sin *θ*) <sup>−</sup>0.43+0.65*δ*, (1)

radiation *I<sup>ν</sup>* from an optically thin loop (Dulk, 1985; Dulk & Marsh, 1982) is

