Effect of Mutual Coupling on the Effect of Mutual Coupling on the Performance of Uniformly and Non-Performance of Uniformly and Non-

Uniformly spaced Adaptive Array AntennasUniformly spaced Adaptive Array Antennas

by:

Amin Al-Ka’bi, John Homer and M. Bialkowski

School of Information Technology & Electrical EngineeringThe University of Queensland, Australia

OutlineOutline

I. Abstract

II. Introduction

III. Signal Model

IV. Simulation Results

V. Experimental Results

VI. Conclusions

I. AbstractI. Abstract We present the effect of mutual coupling We present the effect of mutual coupling

on the performance of uniformly and non-on the performance of uniformly and non-uniformly spaced steered beam adaptive uniformly spaced steered beam adaptive dipole array antennas.dipole array antennas.

The behaviour of the adaptive array The behaviour of the adaptive array antennas in terms of the output Signal-to-antennas in terms of the output Signal-to-Interference-plus-Noise Ratio (SINR) and Interference-plus-Noise Ratio (SINR) and pointing accuracy is investigated .pointing accuracy is investigated .

II. IntroductionII. Introduction

It is desirable that the output SINR exceeds a It is desirable that the output SINR exceeds a certain threshold; hence the adaptive algorithm certain threshold; hence the adaptive algorithm aimed at SINR maximization is used to set the aimed at SINR maximization is used to set the

elements weights.elements weights. Maximizing SINR, referred to as optimal Maximizing SINR, referred to as optimal

combining in the mobile communications combining in the mobile communications literature, requires the knowledge of the literature, requires the knowledge of the Direction-Of-Arrival (DOA) of the desired signal, Direction-Of-Arrival (DOA) of the desired signal, where a DOA estimation algorithm is used to where a DOA estimation algorithm is used to

provide this information with certainprovide this information with certain inaccuracy inaccuracy known as pointing error.known as pointing error.

II. Introduction (cont.)II. Introduction (cont.) The paper is concerned with an analysis of The paper is concerned with an analysis of

performance of antenna arrays formed by wire performance of antenna arrays formed by wire dipoles, in which mutual coupling effects and dipoles, in which mutual coupling effects and elements’ radiation patterns are taken into elements’ radiation patterns are taken into account.account.

A method is presented to enhance the array’s A method is presented to enhance the array’s output Signal to Interference plus Noise Ratio output Signal to Interference plus Noise Ratio (SINR) in presence of pointing errors, and (SINR) in presence of pointing errors, and mutual coupling.mutual coupling.

It is shown that the array’s performance is It is shown that the array’s performance is significantly enhanced, by controlling the inter-significantly enhanced, by controlling the inter-element spacings.element spacings.

III. Signal ModelIII. Signal Model

Consider the array with N vertical dipoles separated by non-uniform distances along the y-axis

1 2 3 1, , ,..., Ny y y y

( )i tx

iw ( )o ts

The output signal from each element , which is assumed tobe a complex random process, is multiplied by a complex weight

and summed to produce the array output .

III. Signal Model (cont.)III. Signal Model (cont.)

I is the identity matrix, k is the feedback loop gain, and

The steady state weight vector is given by:-

01

21 ][]......,,[ wkIwwww TN

vectorsignaltheis(t)]x(t),....x(t),x[X

gainloopfeedback the isk matrix;identity the isI

arraytheofvectorsteeringtheis],....ww,[ww

matrixcovariancetheis}XE{XΦ

TN21

0N02010

T*

random

1

d I n

( )

S , S and S are the desired, interference and noise vectorsi

M

d i ni

X S S S

III. Signal Model (cont.)III. Signal Model (cont.)

)sin()(where

]1,,,....,[

max1

0121

i

jji

Tjjj

l

eeew N

Assuming that the desired narrowband signal comes from θmax:

The SINR is calculated from:

M

iIn

d

iPP

PSINR

1

log10

similarisPforexpressionThe

}]Re{2||[

||

iI

1 2

*1

1

2

1

22

elementperpowerreceivedS

ationautocorrelnormalizedtheis

wwwSP

wP

Td

N

n

N

mdmn

N

nnTdd

N

iin

nm

III. Signal Model (cont.)III. Signal Model (cont.)

AZ TZ

The mutual coupling can be included using the coupling matrix C, where

where is the element's impedance in isolation, is the impedance of the receiver at each element and is chosen as the complex conjugate of to obtain an impedance match for maximum power transfer, and Z is the mutual coupling impedance matrix given by:

1C ( )(Z I )A T T NZ Z Z

AZ

12 1

21 2

1 2

Z

A N

A N

N N A

Z Z Z

Z Z Z

Z Z Z

Note: for λ/2 dipole, AZ =73+j42.5 Ω,

III. Signal Model (cont.)III. Signal Model (cont.)

For the side-by-side configuration and dipole length , an element of the mutual impedance matrix is given by:-

/ 2l mnZ

1 2 1 2

30[0.5772 ln(2 ) (2 )] [30( (2 )],

30[2 ( ) ( ) ( )] [30(2 ( ) ( ) ( ))],

i imn

i o i i i o i i

l C l j S l m nZ

C u C u C u j S u S u S u m n

where 2 2 2 21 22 / , , ( ), ( ),o h h hu d u d l l u d l l

and is the horizontal distance between the two dipole antennas. hd

and are the cosine and sine integrals, respectively, and are defined as:

( )iC u ( )iS u

( ) (cos( ) / )u

iC u x x dx

and0

( ) (sin( ) / )u

iS u x x dx

III.III. Signal Model (cont.)Signal Model (cont.)

When mutual coupling is considered, the signal vector

The mutual coupling in the array can be compensated for by using the inverse coupling matrix . Therefore, the signal vector X can be rewritten as:

T1 2 3[ ( ), ( ), ( ),..., ( )]NX x t x t x t x t is expressed as:

1

C C CM

d i ni

X S S S

-1C

1 1 1

1

C C C C C CM

d i ni

X S S S

IV.IV. Simulation ResultsSimulation Results

Performance of three-element adaptive array with two interference signals and different DOA’s of the desired signal.

IV.IV. Simulation Results (Cont.)Simulation Results (Cont.)

Radiation patterns of the array with and without mutual coupling.

IV.IV. Simulation ResultsSimulation Results

The following four arrays, each including eight (0.45λ The following four arrays, each including eight (0.45λ long)-dipoles, are considered.long)-dipoles, are considered.

Arrangement (a) Arrangement (a) with spacing of 0.75λ, 0.5 λ, 0.35 λ, with spacing of 0.75λ, 0.5 λ, 0.35 λ, 0.3 λ, 0.35 λ, 0.5 λ, 0.75 λ (i.e. the elements in the 0.3 λ, 0.35 λ, 0.5 λ, 0.75 λ (i.e. the elements in the middle of the array are closer to each other than the middle of the array are closer to each other than the elements in the edges of the array). elements in the edges of the array).

Arrangement (b) Arrangement (b) with spacing of 0.9λ, 0.5 λ, 0.25 λ, 0.2 with spacing of 0.9λ, 0.5 λ, 0.25 λ, 0.2 λ, 0.25 λ, 0.5 λ, 0.9 λ (i.e. a similar spacing trend as λ, 0.25 λ, 0.5 λ, 0.9 λ (i.e. a similar spacing trend as arrangement (a) but with the elements in the middle of arrangement (a) but with the elements in the middle of the array even closer to each other). the array even closer to each other).

Arrangement (c)Arrangement (c) with spacings of 0.2 λ , 0.4 λ , 0.7 λ , with spacings of 0.2 λ , 0.4 λ , 0.7 λ , 0.9 λ , 0.7 λ , 0.4 λ , 0.2 λ (i.e. the elements in the 0.9 λ , 0.7 λ , 0.4 λ , 0.2 λ (i.e. the elements in the edges of the array are closer to each other than the edges of the array are closer to each other than the elements in the middle of the array).elements in the middle of the array).

Arrangement (d)Arrangement (d) with uniform spacing of λ/2. with uniform spacing of λ/2.

IV.IV. Simulation Results (Cont.)Simulation Results (Cont.)

Performance of 8-element adaptive array with different arrangements of the elements, without interference., and input SNR/element= 5dB. (a) Mutual coupling is ignored or compensated (b) With mutual coupling

IV.IV. Simulation Results (Cont.)Simulation Results (Cont.)

Performance of 8-element adaptive array with different arrangements of the elements. With 5 20dB-INR interference signals with DOA’s @ -40o, -50o, -70o ,-75o , and 60o . Input SNR/element=10dB.(a) Mutual coupling is ignored or compensated. (b) With mutual coupling.

IV.IV. Simulation Results (Cont.)Simulation Results (Cont.)

Normalized radiation patterns of 8-element adaptive array with different arrangements of the elements. With 5 20dB-INR interference signals with DOA’s @ -40o, -50o, -70o ,-75o , and 60o . Input SNR/element=10dB.(a) Mutual coupling is ignored or compensated. (b) With mutual coupling.

V. Experimental ResultsV. Experimental Results

An experiment is carried out to prove that the An experiment is carried out to prove that the array with non-uniform arrangement (b) (which array with non-uniform arrangement (b) (which provided the best performance in the simulation provided the best performance in the simulation results), has better performance than the λ /2-results), has better performance than the λ /2-uniformly spaced array. uniformly spaced array.

In this experiment, it is assumed that a desired In this experiment, it is assumed that a desired signal (with input SNR/element =10dB) and four signal (with input SNR/element =10dB) and four interference signals (with INR’s=20dB) are interference signals (with INR’s=20dB) are incident on the 8-element adaptive array with incident on the 8-element adaptive array with DOA’s of (0DOA’s of (0oo, and 65, and 65oo, 70, 70oo , -65 , -65oo , -70 , -70oo ). ).

V. Experimental ResultsV. Experimental Results Two array antennas formed by wire dipoles for Two array antennas formed by wire dipoles for

operation at 2.5GHz are developed. operation at 2.5GHz are developed.

In order to obtain the required complex weights, In order to obtain the required complex weights, the antenna elements are connected to varying-the antenna elements are connected to varying-length cables whose small sections are stripped length cables whose small sections are stripped of an outer conductor. Therefore, the complex of an outer conductor. Therefore, the complex weights (attenuation and phase shifting) weights (attenuation and phase shifting) required by the adaptation process of the required by the adaptation process of the adaptive array, are accomplished using fixed adaptive array, are accomplished using fixed attenuators and cables with different lengths. attenuators and cables with different lengths.

V. Experimental Results (Cont.)V. Experimental Results (Cont.)

Photograph of uniformly spaced 8-element dipole antenna array used in the experiment with spacings of λ/2.

V. Experimental Results (Cont.)V. Experimental Results (Cont.)

Photograph of non-uniformly spaced 8-element dipole antenna array used in the experiment with spacings of 0.9λ, 0.5λ, 0.25 λ, 0.2 λ, 0.25 λ, 0.5 λ, 0.9 λ.

V. Experimental ResultsV. Experimental Results

The phased signals are combined using an 8:1 The phased signals are combined using an 8:1 power combiner/divider. The dipoles length is power combiner/divider. The dipoles length is chosen to be 0.45 λ (=54mm) in order to minimize chosen to be 0.45 λ (=54mm) in order to minimize the return loss. The measurements of individual the return loss. The measurements of individual elements showed return loss not less than 13dB.elements showed return loss not less than 13dB.

In order to obtain the required complex weights, In order to obtain the required complex weights, the antenna elements are connected to varying-the antenna elements are connected to varying-length cables. Therefore, the complex weights length cables. Therefore, the complex weights (attenuation and phase shifting) required by the (attenuation and phase shifting) required by the adaptation process of the adaptive array, are adaptation process of the adaptive array, are accomplished using fixed attenuators and cables accomplished using fixed attenuators and cables with different lengths. with different lengths.

V. Experimental Results (Cont.)V. Experimental Results (Cont.)

Radiation patterns of uniformly and non-uniformly spaced 8-elementadaptive array antenna (shown in Fig. 5 & 6) with mutual coupling.(a) Simulation results (b) Experimental results.

V. Experimental Results (Cont.)V. Experimental Results (Cont.)

Performance of uniformly and non-uniformly spaced 8-element adaptive array antenna with mutual coupling.

VI. ConclusionsVI. Conclusions

We have presented theoretical and We have presented theoretical and experimental investigations into the experimental investigations into the performances of narrowband uniformly and performances of narrowband uniformly and non-uniformly spaced steered beam adaptive non-uniformly spaced steered beam adaptive dipole array antennas when they are subjected dipole array antennas when they are subjected to pointing errors.to pointing errors.

In the theoretical analysis mutual coupling In the theoretical analysis mutual coupling effects between array elements have been effects between array elements have been taken into consideration.taken into consideration.

VI. Conclusions VI. Conclusions

It has been shown that the array's tolerance to It has been shown that the array's tolerance to pointing errors can be enhanced by controlling pointing errors can be enhanced by controlling the inter-element spacing.the inter-element spacing.

It has been found that the array gives more It has been found that the array gives more tolerance to pointing errors by arranging the tolerance to pointing errors by arranging the elements of the array such that the elements in elements of the array such that the elements in the middle of the array are closer to each other the middle of the array are closer to each other than the elements in the edges.than the elements in the edges.

Thank youThank you