Correlation Coefficient Expression by S-parameters for Two Omni-Directional MIMO Antennas Xuan Wang, Hieu Duy Nguyen, and Hon Tat Hui Dept. Electrical and Computer Engineering National University of Singapore Singapore
[email protected] Abstract—This paper derives a new expression of the correlation coefficient for two omni-directional antennas in terms of the easyto-measure S-parameters. The omni-directional antennas can be monopole or dipole antennas and they are aimed for use in MIMO communication systems whose capacity performance is significantly affected by signal correlation. With this new expression, it can greatly reduce the computational complexity of antenna correlation calculations since the embedded radiation patterns of the antennas are no longer necessary. Numerical calculations demonstrate the accuracy and efficiency of the new formula.
II.
TWO OMNI-DIRECTIONAL ANTENNA ARRAYS
A. Equvalent Circuit Consider a two-Omni-directional antenna array in the free space and separated by a distance d, as shown in Fig. 1. Vs1 ,
Vs 2 are voltage sources and Z g represents their internal impedance.
Keywords—Correlation coefficient, omni-directional antennas, S-parameters, MIMO systems, mutual coupling, mutual impedance.
I.
INTRODUCTION
By providing a spatial dimension in addition to time, frequency, and code dimensions, the multiple-input-multipleoutput (MIMO) technique has received a lot of attention as a method to greatly increase the system capacity. Many recent researches have focused on installing small and simple antenna arrays in space-limited terminals. Omni-directional antennas, such as monopoles and dipoles, are found to be very suitable for MIMO applications, especially in small MIMO devices. Spatial correlation coefficient is an important factor in antenna analysis and design for MIMO application. Its behavior directly affects the capacity of a MIMO system. In order to calculate the correlation coefficient, radiation patterns are required, as well as a complicated integration operation over the whole space. Because of this difficulty, people have used new method to compute the correlation coefficient, e.g. by S-parameters or Z-parameters, [1][2]. As we know, in numerical simulation, S-parameters can be calculated with an antenna array once the antenna array model is constructed. In experiments, S-parameters could be measured directly and easily. In this paper, we derive a new expression for the crosscorrelation coefficient, using the S-parameters. To verify the accuracy of the new expression, correlation coefficients are calculated from the antenna radiation patterns for both the monopole and dipole antennas and compared with the results calculated from the new formula.
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Fig. 1.
The two-monopole array (a) and the two-dipole array (b).
The conventional Z-parameters of a two-port network are defined as,
V1 = Z11 I1 + Z12 I 2
(1)
V2 = Z 21 I1 + Z 22 I 2
(2)
where V1 , V2 are the voltages at the feeding points of antennas #1, #2, and I1 , I 2 are the feeding port currents of the antennas.
AP-S/URSI 2011
Fig. 2 illustrates the Thevenin equivalent circuit [3] of the antenna feeding network and the antenna array. All the impedances and sources are included.
Substituting (3) and (4) into (6) and (7), we get the relation between the embedded radiation patterns and the antenna impedances as (8) and (9) below. V Z12 π F1 ( , φi ) = s1 (1 − e jkd cos φi ) D Z11 + Z g 2
(8)
V Z12 π F2 ( , φi ) = s 2 (e jkd cos φi − ) D Z11 + Z g 2
(9)
C. Cross-Correlation Coefficient The definition of the correlation coefficient in terms of the embedded radiation patterns of the antennas is: Fig. 2.
The Thevenin equivant circuit.
For the antenna array composed of two identical antennas, the network is a symmetric and reciprocal one, where Z11 = Z 22 Z12 = Z 21 , .
ρ12 =
From the equivalent circuit diagram in Fig. 2, currents I1 , I 2 can be denoted as (3) and (4) below, when the two antennas are excited by excitation voltages Vs1 and Vs 2 .
Z12 1 Vs 2 ) (Vs1 − D Z11 + Z g
(3)
Z 21 1 I 2 = (Vs 2 − Vs1 ) D Z 22 + Z g
(4)
D = ( Z11 + Z g ) − Z122 / ( Z11 + Z g )
(5)
I1 =
=
* ° ª N § π · ºª N §π · º ½° E ® « ¦ F1 ¨ , φi ¸ Gi » « ¦ F2 ¨ , φi ¸ Gi » ¾ 2 ¹ ¼ ¬ i =1 © 2 ¹ ¼ ° ¯° ¬ i =1 © ¿
° N § π · E ® ¦ F1 ¨ , φi ¸ Gi 2 © ¹ = i 1 °¯
N
¦
2
§π · N §π · F1 ¨ , φi ¸
