 Research Article
 Open Access
Fast Signal Recovery in the Presence of Mutual Coupling Based on New 2D Direct Data Domain Approach
 Ali Azarbar^{1}Email author,
 G. R. Dadashzadeh^{2} and
 H. R. Bakhshi^{2}
https://doi.org/10.1155/2011/607679
© Ali Azarbar et al. 2011
 Received: 17 August 2010
 Accepted: 18 January 2011
 Published: 7 February 2011
Abstract
The performance of adaptive algorithms, including direct data domain least square, can be significantly degraded in the presence of mutual coupling among array elements. In this paper, a new adaptive algorithm was proposed for the fast recovery of the signal with one snapshot of receiving signals in the presence of mutual coupling, based on the twodimensional direct data domain least squares (2D D^{3}LS) for uniform rectangular array (URA). In this method, inverse mutual coupling matrix was not computed. Thus, the computation was reduced and the signal recovery was very fast. Taking mutual coupling into account, a method was derived for estimation of the coupling coefficient which can accurately estimate the coupling coefficient without any auxiliary sensors. Numerical simulations show that recovery of the desired signal is accurate in the presence of mutual coupling.
Keywords
 Coupling Coefficient
 Adaptive Algorithm
 Antenna Element
 Mutual Coupling
 Uniform Linear Array
1. Introduction
Adaptive antenna arrays are strongly affected by the existence of mutual coupling (MC) effect between antenna elements; thus, if the effects of MC are ignored, the system performance will not be accurate [1, 2]. Research into compensation for the MC has been mainly based on the idea of using open circuit voltages, firstly proposed by Gupta and Ksienski [2]. While this method has calculated the mutual impedance, the presence of other antenna elements has been ignored and a very simplified current distribution has been assumed for each antenna elements. Many efforts have been made to compensate for the MC effect for uniform linear array (ULA) and uniform circular array (UCA) [2–9]. In [3], an adaptive algorithm was used to compensate for the MC effect in a ULA. In [7], the authors introduced a minimum norm technique MC compensation method, which is based on the technique in [2] for general arrays with arbitrary elements and more accurate. In [9], a new method was proposed to compensate for the MC effect which relied on the calculation of a new definition of mutual impedance. however, the authors did not deal with 2D DOA estimation problem.
On the other hand, many algorithms of the 1D DOA estimation have been extended to solve the 2D cases [10, 11]; however, a few have considered the effect of mutual coupling or any other array errors [12]. Besides, most of these proposed adaptive algorithms are based on the covariance matrix of the interference. However, these statistical algorithms suffer from two major drawbacks. First, they require independent identicallydistributed secondary data in order to estimate the covariance matrix of the interference. Unfortunately, the statistics of the interference may fluctuate rapidly over a short distance, limiting the availability of homogeneous secondary data. The resulting errors in the covariance matrix reduce the ability to suppress the interference. The second drawback is that the estimation of the covariance matrix requires the storage and processing of the secondary data. This is computationally intensive, requiring many calculations in realtime. Recently, direct data domain algorithms have been proposed to overcome these drawbacks of statistical techniques [13–16]. The approach is to adaptively minimize the interference power while maintaining the array gain in the direction of the signal. The sample support problem is eliminated by avoiding the estimation of a covariance matrix which leads to enormous savings in the required realtime computations. The performance of this algorithm is affected by the MC effect, too [17] and must be compensated.
Unfortunately, the MC matrix tends to change with time due to environmental factors, so full elimination of its effect and prediction of its variability are impossible. Therefore, calibration procedures based upon signal processing algorithms are needed to estimate and compensate for the effect of the MC. The most likely way is to carry out some measurements for calibration. However, this procedure has the drawbacks of being timeconsuming and very expensive [18]. Some other researches suggested selfcalibration adaptive algorithms for damping the MC effect [19–21].
In this paper, a new adaptive algorithm was proposed for the fast recovery of the signal with one snapshot of receiving signals in the presence of mutual coupling, based on 2D D^{3}LS algorithm for URA. Then, utilizing the 2D D^{3}LS algorithm properties, a novel technique for the coupling coefficients estimation, without using any auxiliary sensors is presented.
This paper is organized as follows. Section 2, conventional 2D D^{3}LS algorithm is reviewed. In Section 3, a fast adaptive algorithm of direct data domain including mutual coupling effect is presented. In Section 4, a new technique is presented for compensation of the MC effect. In Section 5, numerical simulations illustrate these proposed techniques which can accurately recover the desired signal in the presence of MC.
2. 2D Direct Data Domain Algorithm
3. 2D Fast Signal Recovery Algorithm in the Presence of Mutual Coupling
where denotes, rows from the vector. is computationally intensive and requires many calculations in the realtime because evaluation of the inverse requires an process (here denotes "on the order of"). Therefore, (14) can be replaced with (16) and the number of processes would be an .
4. Mutual Coupling Compensation
where is the estimation of and is with replacement of , , with , , .
5. Numerical Examples
Parameters for the desired signal and interferer.
Magnitude  Phase 

 

Signal  1–10 V/m  0  75°  45° 
Jammer1  1000 V/m  0  43°  −77° 
Later on, the performance of the proposed method is illustrated by the various simulations. The amplitude of the desired signal accuracy is measured by the root meansquared error (RMSE), and is the number of Monte Carlo runs.
6. Conclusion
In this paper, the problems of 2D D^{3}LS algorithms were studied for recovering of the signal in the presence of mutual coupling and driving a new formulation to recover the signal in the presence of MC. Without using the moment of method and impedance matrix calculation, coupling coefficients can be automatically estimated and without computing the inverse matrix, the desired signal can be recovered. Because we did not use the inverse MC matrix, the amount of computation would be reduced. Moreover, simulation results were confirmed when SNR was high and the RMSE of the method was very close to the ideal D^{3}LS in the absence of MC.
Appendix
(a) Absence of the Mutual Coupling
If the one row from each column is multiplied by and subtracted from the next row and then the result of each column is multiplied by and subtracted from the next column, in the absence of mutual coupling, this will cancel out all the signals and only noise and interferer will be left
(b) Presence of the Mutual Coupling
Declarations
Acknowledgment
The authors want to acknowledge the Iran Telecommunication Research Centre (ITRC) for their kindly supports.
Authors’ Affiliations
References
 Nishimura T, Bui HP, Nishimoto H, Ogawa Y, Ohgane T: Channel characteristics and performance of MIMO ESDM systems in an indoor timevarying fading environment. Eurasip Journal on Wireless Communications and Networking 2010, 2010:14.Google Scholar
 Gupta IJ, Ksienski AA: Effect of mutual coupling on the performance of adaptive array. IEEE Transactions on Antennas and Propagation 1983, 31(5):785791. 10.1109/TAP.1983.1143128View ArticleGoogle Scholar
 Friedlander B, Weiss AJ: Direction finding in the presence of mutual coupling. IEEE Transactions on Antennas and Propagation 1991, 39: 273284. 10.1109/8.76322View ArticleGoogle Scholar
 Friel EM, Pasala KM: Effects of mutual coupling on the performance of STAP antenna arrays. IEEE Transactions on Aerospace and Electronic Systems 2000, 36(2):518527. 10.1109/7.845236View ArticleGoogle Scholar
 Lui HS, Hui HT: Mutual coupling compensation for directionofarrival estimations using the receivingmutualimpedance method. International Journal of Antennas and Propagation 2010, 2010:7.Google Scholar
 Svantesson T: Modeling and estimation of mutual coupling in a uniform linear array of dipoles. Dept. Signals and Systems, Chalmers Univ. of Tech., Sweden; 1999.View ArticleGoogle Scholar
 Lau CKE, Adve RS, Sarkar TK: Minimum norm mutual coupling compensation with applications in direction of arrival estimation. IEEE Transactions on Antennas and Propagation 2004, 52(8):20342041. 10.1109/TAP.2004.832511View ArticleGoogle Scholar
 Huang Z, Balanis CA, Britcher CR: Mutual coupling compensation in UCAs: simulations and experiment. IEEE Transactions on Antennas and Propagation 2006, 54(11):30823086.View ArticleGoogle Scholar
 Zhang TT, Lu YL, Hui HT: Compensation for the mutual coupling effect in uniform circular arrays for 2D DOA estimations employing the maximum likelihood technique. IEEE Transactions on Aerospace and Electronic Systems 2008, 44(3):12151221.View ArticleGoogle Scholar
 Zoltowski MD, Haardt M, Mathews CP: Closedform 2D angle estimation with rectangular arrays in element space or beamspace via unitary ESPRIT. IEEE Transactions on Signal Processing 1996, 44(2):316328. 10.1109/78.485927View ArticleGoogle Scholar
 Liu J, Liu X: Joint 2D DOA tracking for multiple moving targets using adaptive frequency estimation. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '07), 2007 2: 11131116.Google Scholar
 Ye Z, Liu C: 2D DOA estimation in the presence of mutual coupling. IEEE Transactions on Antennas and Propagation 2008, 56(10):31503158.MathSciNetView ArticleGoogle Scholar
 Sarkar TK, Sangruji N: Adaptive nulling system for a narrowband signal with a lookdirection constraint utilizing the conjugate gradient method. IEEE Transactions on Antennas and Propagation 1989, 37(7):940944. 10.1109/8.29389View ArticleGoogle Scholar
 Sarkar TK, Wang H, Park S, Adve R, Koh J, Kim K, Zhang Y, Wicks MC, Brown RD: A deterministic leastsquares approach to spacetime adaptive processing (STAP). IEEE Transactions on Antennas and Propagation 2001, 49(1):91103. 10.1109/8.910535MATHView ArticleGoogle Scholar
 Sarkar T, Wicks M, Palma M, Bonneau R: Smart Antennas. Wiley, New York, NY, USA; 2003.View ArticleGoogle Scholar
 Wang LL, Fang DAG: Modified 2D direct data domain algorithm in adaptive antenna arrays. Proceedings of AsiaPacific Microwave Conference (APMC '05), December 2005Google Scholar
 Adve RS, Sarkar TK: Compensation for the effects of mutual coupling on direct data domain adaptive algorithms. IEEE Transactions on Antennas and Propagation 2000, 48(1):8694. 10.1109/8.827389View ArticleGoogle Scholar
 Wang B, Wang Y, Guo Y: Mutual coupling calibration with instrumental sensors. Electronics Letters 2004, 40(7):406408. 10.1049/el:20040287View ArticleGoogle Scholar
 Horiki Y, Newman EH: A selfcalibration technique for a DOA array with nearzone scatterers. IEEE Transactions on Antennas and Propagation 2006, 54(4):11621166. 10.1109/TAP.2006.872672View ArticleGoogle Scholar
 Sellone F, Serra A: A novel online mutual coupling compensation algorithm for uniform and linear arrays. IEEE Transactions on Signal Processing 2007, 55(2):560573.MathSciNetView ArticleGoogle Scholar
 Ye Z, Liu C: On the resiliency of MUSIC direction finding against antenna sensor coupling. IEEE Transactions on Antennas and Propagation 2008, 56(2):371380.MathSciNetView ArticleGoogle Scholar
Copyright
This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.