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Plane Wave Synthesis with Irregular Chamber Planar

Antenna Arrays for Compact OTA Measurements

Mohammad Poordaraee1, and A. Alayón Glazunov1,2

1 Dept. of Electrical Engineering, University of Twente, Netherlands, m.poordaraee@utwente.nl , a.alayonglazunov@utwente.nl

2 Dept. of Electrical Engineering, Chalmers University of Technology, Sweden, andres.glazunov@chalmers.se

Abstract—Over-The-Air (OTA) testing techniques shall

meet cost- and time-efficiency as well as measurement accuracy

constraints stemming from the characterization of massive

multi-element array antennas in 5G systems. The Random-LOS

(Line-of-Sight) OTA measurement setup aims at emulating a

plane wave field in the test zone of the measurement chamber.

The test zone is in the near-field of the chamber antenna used to

emulate the far-field from a base station. In this paper, the

thinned array antenna concept is applied to synthesize the plane

wave field within the test zone. The thinning is performed by

means of the Genetic Algorithm. Two planar array antenna

configurations are considered for emulating a plane wave for 2D

and 3D test zones at 2.7 GHz. The optimized thinned array

achieves a 55% reduction of the number of antenna elements. In

addition, amplitude and phase fluctuations in the test zone have

been considerably reduced in comparison to other similar array

antennas, in this way, improving the measurement accuracy in

Random-LOS OTA measurement setups.

Index Terms—Over-The-Air, Planar Array, Chamber

Antenna, 5G systems .

I. INTRODUCTION

In 5G communication systems, Massive MIMO (Multiple-

Input Multiple-Output) array antennas are deployed at the

Base Station (BS). Possibly, also some models of User

Equipment (UE) such as laptops, pads and smart phones will

use array antennas. In this context, the challenging task comes

for Over-The-Air (OTA) performance evaluation of wireless

“devices” of very large size such as sub-6 GHz Massive

MIMO BSs and also vehicles of various sizes supporting

many different communication standards and deployed in

different propagation environments. Consequently, OTA

testing setups providing a sufficiently large test zone for

performance verification of devices mounted on a car or a

large BS are in high demand [1].

According to the Kildal hypothesis [2], a wireless device

is expected to have good performance in a realistic

propagation environment, in the statistical sense, if it can

achieve good performance both in the Rich Isotropic

Multipath (RIMP) environment and the Random Line-Of-

Sight (Random-LOS) environment [3]. In this paper we focus

on an OTA setup emulating a Random-LOS propagation

scenario, where a linearly polarized plane wave is synthesized

in anechoic or semi-anechoic chambers [1-3].

Synthesizing the Random-LOS environment for OTA

characterization of large antenna systems poses some practical

challenges. First, given the overall large size of the Device

Fig.1. Figure captions will be corrected. Overall configuration of 2D and 3D

test zones. Center of cartesian coordinate system is aligned with the origin of

the array plane.

Under Test (DUT), large measurement chambers are then

required. Second, also massive chamber arrays are required to

test the massive DUTs. All this massiveness may lead to

costly solutions that need to be avoided. Therefore, the main

goal of this paper is to devise compact OTA measurement

setups.

Various plane wave synthesis methods in the near-field of

a planar array for reduced anechoic chamber size have been

proposed, e.g., in [3-6]. The synthetized plane wave emulates

the far-field of a base station [2]. In such a way, an antenna

system can be evaluated in a more compact test zone than in

traditional antenna measurement setups. The same OTA test

setup may be employed for traditional antenna measurements,

e.g., as in a Compact Antenna Test Range (CATR) [7], giving

a great flexibility for testing various propagation scenarios and

applications within the same OTA setup.

As shown in the references given above, employing planar

arrays may reduce the anechoic chamber size but at the

expense of a large number of elements that rapidly grow with

the test zone size making it expensive to implement in

practice. One way to overcome this problem is to use a

reflector antenna [8], [9]. Another way, which is presented in

this paper, is to exclude some of the elements of the planar

array using a thinning optimization procedure resulting in an

irregular planar array. In this work, we were able to show that

a reduction of up to 55% of array elements can be achieved

with the aid of the Genetic Algorithm. Cost can therefore be

reduced while also improving the quality of the test zone as

compared to a fully populated chamber planar array antenna.

However, the reflector antenna solution is still a much cost-

effective solution for Random-LOS OTA setups of very large

DUTs.

II. FOM FOR FIELD UNIFORMITY CHARACTERIZATION

The non-uniformity of the wave field within the test zone

can be systematically evaluated by computing two relevant

Figures of Merit (FoM). The following dispersion

characteristics suggested in [3] are considered here as well.

The power spread is evaluated in dB by the standard deviation

formula [10]

dB

1

5log 1

+

=

−

, (1)

where is the standard deviation of the normalized power

computed as

VAR MEAN

P

P

=

, (2)

where P is in linear units and VAR{P} and MEAN {P} are

the standard deviation and the mean of P, respectively. Since

only the vertical polarization is considered, the power

received by a probe antenna in the test zone is defined as

P=|∑ 𝐸𝑧|2, where Ez is the complex amplitude of the

impinging wave stemming from one antenna element of the

chamber array.

The second FoM is the phase spread computed along a line

parallel to the array plane (see Fig.1) defined as the maximum

phase deviation from the mean

max max MEAN

= −

, (3)

where

is the argument of the plane wave field complex

amplitude Ez.

The analysis presented in this paper is based on the

evaluation of the relative receive power variation in the test

zone

norm / MEANP P P=

and the corresponding relative

phase variation

norm MEAN

=−

.

III. OPTIMIZATION COST FUNCTION

The optimization cost function seeks to minimize the

standard deviation of the normalized power given by (2) based

on the Genetic Algorithm (GA). The standard deviation of the

power in dB, i.e., dB (1), within the desired test zone and the

maximum phase deviation from the mean ∆∅𝑚𝑎𝑥 (3) along the

parallel line are the outputs of the optimization process. The

inter-element distance d (see Fig.1), and a binary decision

variable defining the population of each “node” in the array

antenna, i.e., that a certain antenna element position in the

array layout are the inputs of the optimization fitness function.

The GA implementation in Matlab is used in the

computations.

(a) (b)

Fig. 2. The simulated (a) power and (b) phase within a 5 m 5 m area for 8 ×

23 array.

(a) (b)

Fig. 3. The simulated (a) power and (b) phase within a 5 m 5 m area for 23

× 23 array.

The dB and ∆∅𝑚𝑎𝑥 are then minimized by applying the

GA algorithm for the obtained chamber irregular planar arrays

in the Random LOS setup. A schematic representation of the

OTA setup with a planar array as the chamber array and the

considered test zones are shown in Fig. 1. For instance, a DUT

mounted on a car may be placed on a turntable at a distance D

from chamber array in a shielded anechoic chamber.

Measurements for this case are assumed to take place on a 2D

test zone as shown in Fig. 1. On the other hand, a 3D test zone

is required for performance evaluation of a BS array antenna.

In this case, the array under test with overall width of 2R and

height h may be placed on a rotating platform at a distance of

D from chamber antenna. Consequently, as shown in Fig. 1, a

cylindrical test zone is required for performance evaluation of

the DUT due to the rotation of the DUT around the vertical

(cylinder) axis.

We specialize our analysis to two chamber array

configurations. In the first one, we consider the optimization

of an 8 × 23 planar array with the objective to synthesize a

plane wave within a 2 Dimensional (2D) circular test zone. As

shown in Fig. 1, the 2D test zone is situated on the horizontal

plane perpendicular to the chamber array plane with both

centers aligned. The considered radius of the 2D circular zone

is R = 0.5 m and its center is in distance of D = 3.7 m from

antenna array. In the second configuration a 23 × 23 planar

array is optimized with the objective to synthesize a plane

wave within the 3D cylindrical test zone with height h. In both

of the considered arrays the inter-element distance d is

uniform.

Fig. 4. Array configuration for emulating plane wave within test zone. Colored

squares are active elements while other elements are removed as a result of

the application of the GA.

(a) (b)

Fig. 5. Simulated power and phase spread within the 2D circular test zone.

Fig. 6. Power and phase spread along parallel line.

Table I. Comparison of optimized irregular array and 8 × 23 regular array of

equal aperture size.

FoM

This paper

Ref. [3]

dB

[dB]

Parallel line

0.28

1.02

Circular curve

0.74

0.77

Circular zone

0.28

0.86

max

[]

Parallel line

9.5

13

Number of elements

82

8 × 23=184

The considered thinning procedure minimizes the standard

deviation of the receive power within the 2D circular zone for

the 8 × 23 array. For the 23 × 23 array, the standard deviation

is minimized within the 3D cylindrical zone.

Fig. 7. Array configuration for emulating plane wave within test zone.

Colored squares are active elements while other elements are removed as a

result of the application of the GA.

(a) (b)

Fig. 8. Simulated power and phase spread within the 2D circular test zone.

Fig. 9. Power and phase spread along parallel line.

Table II. Comparison of optimized irregular array and 23 × 23 regular array

of equal aperture size.

FoM

Thinned array

Full array

dB

[dB]

Parallel line

0.51

1.08

Circular curve

1.05

1.83

Circular zone

0.53

1.08

Cylindrical zone

0.52

1.39

max

[]

Parallel line

14

19

Number of elements

291

23 × 23=529

As a result of the optimization procedure, some elements

are removed from the array at the same time as the value of d

is adjusted. During the optimization procedure the amplitudes

and phases of the antenna elements are fixed and equal to each

other. The inter-element distance is limited to λ/2 ≤ d ≤ λ to

prevent grating lobes and reduce mutual coupling effects,

where λ is the free space wavelength at the considered

operating frequency for the chamber array f = 2.7 GHz.

IV. SIMULATION RESULTS

Fig. 2(a) and (b) show the received power P and phase

as explained above over a 5 m × 5 m area (y-x plane) in front

of the optimized array for 2D zone which contains origins of

the array plane and test zone. Outlined is the 2D circular zone

over which the optimization has been performed.

Corresponding simulations corresponding to the 23 × 23

optimized array for 3D cylindrical zone are shown in Fig. 3.

A. Design of planar array layout for 2D test zone

A uniform planar array antenna with 8 × 23 array elements

is considered here for 2D test zone optimization. The main

ideas behind the chamber array characterization for a Random

LOS OTA setup design are explained in [1], [3] and [8]. A

schematic representation of the array is shown in Fig.1. As a

result of the layout optimization, the optimum array inter-

element spacing is determined as d = 0.7 = 7.7 cm. The

optimized array layout is shown in Fig. 4, where the colored

and white squares show the positions where antenna elements

remained populated, and the positions where they were

removed as a result of the optimization, respectively. As

explained above, no weighting of phases or amplitudes of the

array elements is performed during the optimization for both

optimized array layouts.

Fig. 5(a) and (b) show the receive power P and phase

for the optimized array for the 2D circular test zone defined in

Fig.1. Corresponding results along the parallel line are shown

in Fig. 6. It is worthwhile to note that power spread and phase

spread within the 2D circular test zone are sufficiently low to

conclude that the synthesized field in the test zone is

approximately a plane wave. A summary of the standard

deviation of the power and maximum phase deviation are

presented in the Table I and compared with the chamber array

presented in [3].

From the comparison presented in Table I, it can be

concluded that the GA optimization resulted in 55% and 51%

reduction of the number of antenna elements and antenna

aperture, respectively, and at the same time a considerable

improvement of the accuracy of the synthesized plane wave in

the 2D test zone was achieved.

B. Design of planar array layout for 3D test zone.

In this section, results for uniform planar array antenna

with 23 × 23 array elements are provided for 3D test zone

optimization. Inter-element distance is d = 0.59λ = 6.55 cm

for the optimized configuration. Fig. 7 shows the final

configuration of the thinned chamber planar array. The

colored and white squares show the positions were antenna

elements remained populated, and the ones that removed as a

result of the optimization, respectively.

Fig. 8(a) and (b) show the receive power P and phase

as

explained above within the 2D circular test zone defined in

Fig.1. Corresponding results along the parallel line are shown

in Fig. 9. Further metrics of the plane wave in the cylindrical

3D test zone are presented in the Table II, where results for

the fully populated chamber array are also provided for

comparison. For example, it can be seen that the power

standard deviation 𝜎𝑑𝐵 within the cylindrical test zone is 0.52

dB for the optimized irregular array, whereas for the fully

populated 23 × 23 planar array antenna it is 1.39 dB.

V. CONCLUSIONS

In this paper we investigate the effects of irregular arrays

on the accuracy of plane wave synthesis in the near-field of

the arrays at 2.7 GHz. Two array layouts are considered. In

the first one, the optimization is performed within a 2D

circular test zone, while in the second the optimization is done

within a 3D cylindrical test zone. In both cases, the standard

deviation of power within the desired test zones and the

maximum phase deviation from the mean along the parallel

line are minimized. The optimum value of the inter-element

distance and as well as the population of each “node” of the

array have been obtained by means of the Genetic Algorithm

optimization. Optimization seeks to minimize both the

standard deviation of the received power and the maximum

phase variation within the test zone.

As a result of the optimization it is shown that for the array

targeting the 2D test zone 55% and 51% reduction of number

of antenna elements and antenna aperture can be achieved,

respectively. On the other hand, the array targeting the 3D test

zone, a 45% reduction was achieved for number of array

elements. The optimized planar array improved the standard

deviation from 0.86 dB to 0.28 dB in a circular test zone for

the optimization targeting 2D test zone. For optimization

targeting the 3D test zone, the reduction was from 1.39 dB to

0.53 dB within the 3D cylindrical zone.

Our results show that optimized irregular arrays have less

elements and antenna aperture than the fully populated

uniform planar arrays, which can result in more cost-effective

OTA chamber antennas.

ACKNOWLEDGMENT

This work was supported by the European Union’s H2020:

ITN program for the “mmWave communications in the Built

Environments - WaveComBE” project under the grant no.

766231.

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