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The number of wireless electronic gadgets used in mobile communication, vehicle collision avoidance system, compact radars, etc. is extremely increasing at a rapid rate. Thus, the characteristics of the antennas involved in these gadgets are to be designed very stringently so as to avoid interferences & coupling and to improve compatibility, susceptibility, etc. Compact smart antenna with improved performance is highly essential to meet this challenging scenario. Mutual coupling between various elements of an array is one of the main factors which can be considered for improvement of performance of the antenna. Influence of mutual coupling on performance of the antenna is considered in this paper and various techniques to minimize this effect are presented. Effect of mutual coupling on radiation characteristics of the antenna can be compensated employing various methods like Conventional Mutual Impedance (CMI), Receiving Mutual Impedance (RMI). Analysis is presented as comparison between the two methods for different number of elements in the array. Analysis is also presented for different geometries of the array like circular and elliptical for improved performance. The results show performance improvement in the proposed array for parameters like SNR and Speed of convergence.

Wide spread application of wireless communication technology in daily life demands efficient and reliable signal transmission. Increased directivity, user capacity, battery life and source separation can be achieved by smart antenna to cope-up the demands. Smart antenna is popularly used in radar systems, wireless communications and in vehicle collision avoidance applications [

A systematic arrangement of group of radiating elements is called an array. Size of the array and aperture proportionally increases with gain of the antenna [

Linear array is simple in structure and is limited to estimation of the elevation angle (one dimensional) of incoming signal only. In addition, the linear array can only estimate the range of azimuth angle limited by 180˚ (−90˚ < θ < 90˚) [

The entire transmitted signal is equal to the sum and reradiated signal from the elements. Similarly, induced current on the antenna element reradiates electromagnetic field which would be received by the other neighboring elements in the array. Such mutual coupling effect is usually considered as a defect which degrades the performance of the array. Two types of coupling compensation methods: Conventional Mutual Impedance (CMI) and Receiving Mutual Impedance (RMI) methods are popular.

For an antenna array with N elements, receiving an incoming signal, being a plane wave source, the received terminal voltage at the k_{th} antenna element V_{k} can be expressed as

U_{k} = received voltage of k_{th} antenna element by the plane wave source alone

W_{k} = coupled voltage of the scattered fields from the other antenna elements in the array

The coupled voltage W_{k} in (1) can be written as [

where Z_{k} is the receiving mutual impedance between the k_{th} and the i_{th} antenna elements and I_{i} is the terminal current at the i_{th} antenna element given by:

with Z_{L} being the terminal load impedance of the antenna elements. Putting (2) and (3) into (1), we have:

The relationship between the uncoupled voltages U_{k} and the received voltages (i.e., coupled voltages) V_{k} can be written in a matrix equation as:

A circuit theory approach for reducing or compensating mutual coupling effect is discussed in this work. This method is called conventional mutual impedance method (CMI) [

The relation between the terminal voltage and current can be given by

Z_{L} being impedance, relation between voltage and current is given by

The relationship between the open-circuit voltages and terminal voltages can be written as

Another circuit theory approach for reducing or compensating mutual coupling effect is receiving mutual impedance method (RMI) [

The receiving mutual impedance between two antennas is the ratio of the coupled voltage across antenna1’s terminal load Z_{L}_{1} (due to the receiving current distribution on antenna 2) to the terminal current through antenna 2’sterminal load Z_{L}_{2} when the array is excited by an external plane wave source.

i.e. Receiving mutual impedance with a receiving current on antenna 2 = coupled voltages across antenna 1’s terminal load/receiving current through antenna 2’s terminal load.

The definition of the receiving mutual impedance requires specifying a plane wave to excite the two antennas as shown in _{1} and V_{2} are the received voltages across the terminal loads of antennas 1 and 2, respectively. The corresponding currents through the two antennas are I_{1} and I_{2}. In equation (1), U_{1} is the received voltage across the terminal load of antennas 1 when antenna 1 is excited by the external plane wave source alone (with antenna 2 removed from the array). U_{1} is also called the isolation voltage on antenna 1.

Two different geometries of the array are considered for comparison in this paper viz., Circular and Elliptical (Oval).

In circular array it is assumed that N equally spaced isotropic elements are placed on X-Y plane along a circular ring. Let the radius be “a”. Circular array can able to scan 360˚ azimuthally. The geometry of N-element circular

array antenna is shown in

where,

I_{n} = amplitude of excitation

α_{n} = phase of the n th element

θ = elevation angle from z axis.

Circumference = 2πr

Area = πr^{2}

The radius of the array increases the directivity of uniform circular array and tends to a value N [

The geometry of the elliptical antenna array with origin as center is shown in

The array factor is given by equation (10) [

I_{n}=amplitude of excitation

α_{n}=phase of the n th element

θ=elevation angle from z axis.

ø_{n}=Azimuth angle measured from x axis for n-th element.

a, b=semi major and minor axises respectively.

e=eccentricity of elliptical array and is 0.5

θ_{0} = 90˚, ø_{0} = 0˚.

N=no of elements is 8 or 10.

Comparisons of area of circular and elliptical arrays are given below in

The objective is to analyze the response of elliptical antenna array with modified LMS (Least Mean Square) algorithm which optimizes the weight factor for DOA (Direction of Arrival) estimation. Mutual coupling is minimized by the CMI method in this case.

Example 1: Eight (Dipole) Element Array using CMI

In this example, an 8-element array using CMI is optimized with uniform spacing between the elements. It is assumed that the angle of signal and interference be 90˚ and 180˚ respectively.

Circumference (cm) | Circular and oval array area. | |||||
---|---|---|---|---|---|---|

Circular array radius r (cm) | Circular array area A (cm) | Oval array major radius a (cm) | Oval array minor radius b (cm) | Area (cm^{2}) | ||

1.00 1.50 2.00 3.00 4.00 | 0.16 0.24 0.32 0.48 0.64 | 0.08 0.18 0.32 0.72 1.27 | 0.20 0.30 0.40 0.62 0.84 | 0.10 0.15 0.21 0.31 0.42 | 0.07 0.15 0.27 0.60 1.07 | |

It can be evident from

Example 2: Ten (Dipole) Element Array using CMI

In this example, a 10-element array using CMI is optimized with uniform spacing between the elements. It is assumed that the angle of signal and interference be 90˚ and 180˚ respectively.

In

In CMI compensation both 8 & 10 element arrays of circular and elliptical arrays are compared. Elliptical arrays show better in pattern generation, SNR and convergence speed. Advantage of elliptical antenna compared to circular antenna is its low area for same number of elements.

In this RMI Method, the source and noise are assumed to be 90˚ and 180˚ of azimuth directions respectively. A modified LMS algorithm is used to optimize the weight factor for DOA estimation.

Example 3: Eight (Dipole) Element Array using RMI

In this example, an 8-element Circular array is optimized with uniform spacing between the elements.

The best amplitude value determined by the optimized technique is shown in

It can be evident that from

Example 4: Ten (Dipole) Element Array using RMI

In this example, a 10-element array with uniform spacing between the elements is optimized using RMI. As per the

RMI Method, the elliptical antenna has better SNR below 20 iterations. Hence convergence is faster in elliptical antenna. For the iterations below 10, circular array has minimum of −12 db SNR.

Example 5: Sixteen (Dipole) Element Array using RMI

In this example, an 16-element Circular & Elliptical arrays are optimized with uniform spacing between the elements. Simulations are shown in

In RMI compensation along with 8 & 10 element arrays of circular and elliptical arrays, 16-element arrays are also compared. Elliptical arrays shows better in pattern generation, SNR. Convergence speed is more improved. Geometrical advantage of compact size for elliptical antenna with same number of elements as in circular antenna is sustained.

More over RMI sanctions receiving current distribution on an antenna compared to CMI mode of compensation. It is additional advantage to recommend the RMI in elliptical arrays so that DOA estimation depends on Direction of receiving signal strength.

Example 6: Sixteen (Dipole) Element Array with non linear spacing using RMI

Lobes between 180˚ - 240˚ & 300˚ - 330˚ are smoothening and shaped compared to circular array in elliptical antenna.

However, below 180˚ of angle uniform spaced array is seems to be performing better.

The simulations categorically show that CMI compensation method applied to elliptical array with 8 & 10 elements has better response in pattern generation, convergence speed and SNR compared with circular array. Compactness of elliptical antenna compared to circular antenna for the same number of elements is additional geometrical advantage.

Using RMI compensation method, a comparison is made for 8, 10 and 16 element array in circular as well as elliptical array. Elliptical arrays show better performance in pattern generation, SNR. Convergence speed is better compared to CMI method of compensation. Moreover, receiving current distribution on an antenna for RMI

method is better compared to CMI mode of compensation. It is additional advantage to recommend the RMI in elliptical arrays because DOA estimation depends on Direction of receiving signal strength.

Also, the simulation of non uniform spaced elements array in either circular or elliptical patterns confirms that below 180 degrees of angle, uniform spaced array performance is better. Hence, it can be concluded that elliptical array of uniform spaced elements with RMI compensation method of mutual coupling has the best performance in a smart antenna.

Aluru Venkata Lakshmi NarayanaRao,Nunna BalaAnkaiah,Dharma RajCheruku, (2016) Antenna Performance Improvement in Elliptical Array Using RMI Method of Mutual Coupling Compensation. Journal of Electromagnetic Analysis and Applications,08,8-21. doi: 10.4236/jemaa.2016.81002