# Comparison of Synthesis Strategies for a Dual-Polarized Reflectarray

Authors: Loic Marnat; Renaud Loison; Raphaël Gillard; Daniele Bresciani; Hervé Legay
Journal: International Journal of Antennas and Propagation
 (2012)

---

## Abstract

This paper presents and compares four optimization
strategies for printed reflectarrays. They are applied to synthesize
a dual-polarized reflectarray using two kinds of slot-loaded
patches. They provide objective criteria to deal with the numerous
geometrical parameters available to tune the phase. The
study relies on the comparative measurements of four different
prototypes for the same22λ0×22λ0 reflectarray (with λ0 the
wavelength at f0=14.25 GHz).


---

## Body

## 1. Introduction

A reflectarray antenna combines advantages of reflectors and phased array antennas. Indeed, neither lossy feeding network nor heavy and cumbersome profile are involved. A reflectarray antenna is composed of a primary feed lighting elementary cells that delay the impinging wave and permit to shape the radiated field. In most cases, the reflected phase is controlled by the geometry or orientation of the radiating elements [1, 2], stubs or delay lines [3], or the use of reconfigurable material [4]. To achieve the phase law all over the reflectarray surface, the unit cell must be able to cover the whole 360° phase range. In [3], a reflectarray has been synthesized with a multiple layer structure allowing a true time delay compensation. A large bandwidth has then been achieved 20 (%). Single-layer reflectarrays are usually more limited in term of bandwidth. The required 360° phase range is more difficult to obtain without a strong resonance which introduces more losses. On the other hand, single substrate layer is cost effective and easy to manufacture.In this paper, the used radiating element is a patch loaded with slots (Figure1), having dual polarization capabilities [5]. It is an extension of the single-polarized patch structure introduced in [6, 7]. Furthermore, a reconfigurable cell can be obtained by controlling slots with PIN diodes or MEMS [8, 9]. The considered cell design is defined with six parameters for each polarization. As a consequence, a large number of cell designs are available to produce a given phase shift. This amount of solutions is advantageous for an accurate reflectarray synthesis and it also increases its complexity.Patch loaded by (a) centered crossed slots or (b) emerging slots(h=4mm,εr≃1).
(a)
(b)The aim of this paper is to present and validate an original reflectarray layout synthesis. This synthesis technique is based on specific cell selection strategies. Three strategies are proposed and compared. In the first part of the paper, the used elementary cell is described and its RF characteristics are studied. The proposed synthesis process is presented in the second part. In the third one, it is applied to a specific space telecommunication antenna configuration. Finally, the measurement of the resulting reflectarray are presented.


## 2. Elementary Cell

### 2.1. Description

Figure1 presents the proposed dual-polarized cells. Two cell configurations are considered. Figures 1(a) and 1(b) depicts the centered slots configuration (defined by a microstrip square patch loaded with a Jerusalem cross slot) and the emerging slots configuration (defined by two pairs of orthogonal slots located at the edges of the microstrip square patch), respectively. For each polarization, the phase reflected by the cell is tuned by varying six geometrical parameters characterizing the cell design in each direction: the patch size (Lx and Ly), the slot length (Bx and By) and width (Wx and Wy), the stub length (Sx and Sy) and width (WSx and WSy), and the slot configuration (centered crossed and emerging).


### 2.2. Analysis of the Reflected Phase

The phase response of the cell is simulated for a linearly polarized incident plane wave under normal incidence with a self-developed 2.5D electromagnetic simulator. It has been specifically developed for planar self-similar structures and validated through different simulation comparisons and measurements [10]. Floquet hypotheses are used in order to take mutual coupling effects into account while keeping a reasonable simulation time. In these conditions, the cell is assumed to be extracted from an infinite periodic array. A y polarized incident field is applied and the phase computed is the one of the direct reflection coefficient: ∠Γyy. In the following, this achieved phase is noted ϕach.Figure2 presents the phase shift for the centered slots configuration (Figure 1(a)) versus the slots lengths for different patch dimensions. In this section, a symmetrical cell is considered which means the x and y cell parameters are equal. The size of the array lattice is set to 0.5λ0 at f0=14.25GHz (m=10.526mm). The substrate is a 4mm thick composite panel whose equivalent dielectric constant is approximated by 1.Figure 2
Phase shift versus slots lengths for different patch sizes (Lx) at f0=14.25GHz in normal incidence, and Wx=0.9mm.Two areas can be identified in Figure2. The first one corresponds to short slots (Bx smaller than 4mm) with a phase shift which is mainly controlled by the size of the patch. In the second one, where Bx is greater than 4mm, the slot length becomes the most effective tuning parameter. The addition of stubs (here, only for Lx=8.5mm and Bx=7.5mm) permits to extend the phase range up to 414.1°. Note that the phase range could be increased further by using thinner slots (up to 548.5°  for 0.1mm slot widths).The same results are presented in Figure3 for the emerging slots configuration (Figure 1(b)). It appears that the slot lengths are more influent for this cell configuration. Indeed, they directly affect the currents which are mainly concentrated on patch edges. These different behaviors motivate the use of the two complementary configurations. As will be seen later on, this provides an additional flexibility to the optimization process.Figure 3
Phase shift versus slot lengths for different patch sizes (Lx) at f0=14.25GHz under normal incidence, and Wx=0.9mm.It can be highlighted that the considered cells are patches on air substrate which gives low loss elements. Nevertheless, the losses of the centered crossed slots configuration are higher when stubs are used due to the resonance of the cell which is shifted close to the operating frequency.


### 2.3. Dual-Polarization Capabilities

In this section, the dual polarization capabilities of the cell are investigated. As previously, the cell is excited by ay polarized electric field. The phase of the reflected wave is thus controlled by the x oriented main slot (Bx) and y oriented stubs (Sx) referred to as the excited slots. The orthogonal slots defined by By and Sy should not affect the reflected wave and are referred to as the parasitic slots. The evolution of the phase of the direct reflection coefficient is plotted in Figure 4 as a function of the lengths of the excited slots at the central frequency. Different lengths of parasitic slots are considered for the two cell configurations.Figure 4
Effect of the parasitic slots (By+Sy) on the phase of the direct reflection coefficient for the centered (+) and the emerging (□) slots configurations at f0=14.25GHz under normal incidence, and Wx=0.9mm.This figure shows that the reflected phase can be tuned by varying the excited slots while the effect of the parasitic slots is negligible. As a consequence, both orthogonal linear polarizations can be controlled independently.


### 2.4. Cell Diversity

One key issue in the reflectarray layout synthesis is to select the appropriate design for each cell in order to comply with the desired antenna performance. One cell design is defined by six geometrical parameters for each polarization. Consequently, a large number of cell designs can be obtained, with several ones that produce the same phase shift. This diversity gives flexibility to the synthesis process but increases its complexity.As an illustration, we consider the situation where each geometrical parameter has been sampled so that 1074 different cell designs are obtained. The resulting phase distribution, corresponding to the number of cell designs producing a given phase shift under normal incidence, is plotted in Figure5.Figure 5
Number of cell designs producing a given range of phase shift (20° by 20°) under normal incidence at14.25GHz for a uniform sampling of the geometrical parameter.This figure shows the multiplicity of cell designs available to reach a given phase shift. However, it can be noted that this distribution is not uniform. For instance, a  “pinched zone” can be observed from 40 to 100° where only few cell designs are available. This restricts the possible choices in this phase range for the optimization process. Nevertheless, the phase distribution is different for each incident angle. At the end, for a given reflectarray, many layouts can be generated satisfying the phase law at the central frequency. For instance, in [5], up to 6.45×103187 distinctive layouts could theoretically be generated for the studied antenna.In these conditions, cell selection strategies must be implemented in order to optimize the reflectarray layout.


## 2.1. Description

Figure1 presents the proposed dual-polarized cells. Two cell configurations are considered. Figures 1(a) and 1(b) depicts the centered slots configuration (defined by a microstrip square patch loaded with a Jerusalem cross slot) and the emerging slots configuration (defined by two pairs of orthogonal slots located at the edges of the microstrip square patch), respectively. For each polarization, the phase reflected by the cell is tuned by varying six geometrical parameters characterizing the cell design in each direction: the patch size (Lx and Ly), the slot length (Bx and By) and width (Wx and Wy), the stub length (Sx and Sy) and width (WSx and WSy), and the slot configuration (centered crossed and emerging).


## 2.2. Analysis of the Reflected Phase

The phase response of the cell is simulated for a linearly polarized incident plane wave under normal incidence with a self-developed 2.5D electromagnetic simulator. It has been specifically developed for planar self-similar structures and validated through different simulation comparisons and measurements [10]. Floquet hypotheses are used in order to take mutual coupling effects into account while keeping a reasonable simulation time. In these conditions, the cell is assumed to be extracted from an infinite periodic array. A y polarized incident field is applied and the phase computed is the one of the direct reflection coefficient: ∠Γyy. In the following, this achieved phase is noted ϕach.Figure2 presents the phase shift for the centered slots configuration (Figure 1(a)) versus the slots lengths for different patch dimensions. In this section, a symmetrical cell is considered which means the x and y cell parameters are equal. The size of the array lattice is set to 0.5λ0 at f0=14.25GHz (m=10.526mm). The substrate is a 4mm thick composite panel whose equivalent dielectric constant is approximated by 1.Figure 2
Phase shift versus slots lengths for different patch sizes (Lx) at f0=14.25GHz in normal incidence, and Wx=0.9mm.Two areas can be identified in Figure2. The first one corresponds to short slots (Bx smaller than 4mm) with a phase shift which is mainly controlled by the size of the patch. In the second one, where Bx is greater than 4mm, the slot length becomes the most effective tuning parameter. The addition of stubs (here, only for Lx=8.5mm and Bx=7.5mm) permits to extend the phase range up to 414.1°. Note that the phase range could be increased further by using thinner slots (up to 548.5°  for 0.1mm slot widths).The same results are presented in Figure3 for the emerging slots configuration (Figure 1(b)). It appears that the slot lengths are more influent for this cell configuration. Indeed, they directly affect the currents which are mainly concentrated on patch edges. These different behaviors motivate the use of the two complementary configurations. As will be seen later on, this provides an additional flexibility to the optimization process.Figure 3
Phase shift versus slot lengths for different patch sizes (Lx) at f0=14.25GHz under normal incidence, and Wx=0.9mm.It can be highlighted that the considered cells are patches on air substrate which gives low loss elements. Nevertheless, the losses of the centered crossed slots configuration are higher when stubs are used due to the resonance of the cell which is shifted close to the operating frequency.


## 2.3. Dual-Polarization Capabilities

In this section, the dual polarization capabilities of the cell are investigated. As previously, the cell is excited by ay polarized electric field. The phase of the reflected wave is thus controlled by the x oriented main slot (Bx) and y oriented stubs (Sx) referred to as the excited slots. The orthogonal slots defined by By and Sy should not affect the reflected wave and are referred to as the parasitic slots. The evolution of the phase of the direct reflection coefficient is plotted in Figure 4 as a function of the lengths of the excited slots at the central frequency. Different lengths of parasitic slots are considered for the two cell configurations.Figure 4
Effect of the parasitic slots (By+Sy) on the phase of the direct reflection coefficient for the centered (+) and the emerging (□) slots configurations at f0=14.25GHz under normal incidence, and Wx=0.9mm.This figure shows that the reflected phase can be tuned by varying the excited slots while the effect of the parasitic slots is negligible. As a consequence, both orthogonal linear polarizations can be controlled independently.


## 2.4. Cell Diversity

One key issue in the reflectarray layout synthesis is to select the appropriate design for each cell in order to comply with the desired antenna performance. One cell design is defined by six geometrical parameters for each polarization. Consequently, a large number of cell designs can be obtained, with several ones that produce the same phase shift. This diversity gives flexibility to the synthesis process but increases its complexity.As an illustration, we consider the situation where each geometrical parameter has been sampled so that 1074 different cell designs are obtained. The resulting phase distribution, corresponding to the number of cell designs producing a given phase shift under normal incidence, is plotted in Figure5.Figure 5
Number of cell designs producing a given range of phase shift (20° by 20°) under normal incidence at14.25GHz for a uniform sampling of the geometrical parameter.This figure shows the multiplicity of cell designs available to reach a given phase shift. However, it can be noted that this distribution is not uniform. For instance, a  “pinched zone” can be observed from 40 to 100° where only few cell designs are available. This restricts the possible choices in this phase range for the optimization process. Nevertheless, the phase distribution is different for each incident angle. At the end, for a given reflectarray, many layouts can be generated satisfying the phase law at the central frequency. For instance, in [5], up to 6.45×103187 distinctive layouts could theoretically be generated for the studied antenna.In these conditions, cell selection strategies must be implemented in order to optimize the reflectarray layout.


## 3. Synthesis Process

### 3.1. Cell Selection Strategies

A cell selection strategy aims at choosing the best design for each element in the array. The minimum requirement is that the achieved phase at the central frequency,f0, matches the desired one:
(1)ϕiach(f0)=ϕides⁡(f0)
for i=1 to N, where N is the number of elements in the array.Thereference cell, defined as the starting point when filling up the layout, is arbitrarily located at the center of the array. The cells are then successively designed from the reference one and moving to the edges of the array. In this section, four cell selection strategies are proposed and described. (i)
TheRandom strategy only operates a random selection among available cell designs achieving the desired phase shift at f0 without any consideration on the geometry or other electrical characteristics. In this paper, these layouts are called “R layout” for “Random” strategy.(ii)
TheDispersion optimization consists in selecting cell designs that not only produce the required phase shifts at central frequency (f0) but also the best achievable ones at the bandwidth extremities (fmin and fmax). It is the most conventional strategy when designing large-bandwidth reflectarrays [11].The best cell design, for theith array element, is the one that minimizes the phase error between the desired and the achieved ones:
(2)ɛi(f)=|ϕides⁡(f)-ϕiach(f)|
at f=fmin and fmax.In this paper, such layouts are called  “D layout” for  “Dispersion” strategy. (iii)
The third strategy is calledGeometrical optimization and has been introduced in [12]. The aim of this original strategy is to maximize the geometrical similarity between contiguous cells in the reflectarray layout. The goal is to comply with the used Floquet simulation hypotheses and thus improve the prediction accuracy of the antenna performance.As it has been shown in Section2, each geometrical parameter does not equally affect the phase shift. Thus, to quantify the similarity between two cells i and j, a similarity factor is defined in which a different weight is attributed to each geometrical parameter:
(3)SF(i,j)=αLx⋅(Lxi-Lxj)2+αLy⋅(Lyi-Lyj)2+⋯.
In this paper, αLx=7 (patch size), αBx=4 (slot length), αSx=1 (stub length), αWx=10 (slot width), and αWSx=10 (stub width). In other words, a variation of slot width (Wx) leads to a larger SF(i,j) value than the same variation of stub length (Sx). The similarity between cell i and its neighbors is noted SF¯i. It is defined by averaging the similarity factor between this cell and each of its nearest neighbors (eight for a rectangular lattice). An iterative process is used that results in a layout which minimizes the SF¯i factor for each array element and thus ensures smooth geometrical variations. The first iteration initializes the geometry of each cell by minimizing the SF¯i factor only considering those of its 8 nearest neighbors that have already been defined. As a consequence, the geometry of the first cell is chosen arbitrarily (only complying with the desired phase). In the next steps, the cell's geometry is progressively updated until the average value of SF¯i converges to its lowest value.In this paper, these layouts are called  “G layout” for  “Geometrical” strategy. (iv)
The last proposed strategy is calledMRC optimization for  “Maximization of Reflection Coefficients” strategy. It has been developed to improve both the reflectarray losses and the cross-polarization level. To do so, the direct reflection coefficient magnitude, |Γyy(f0)|, is maximized for each array element at the central frequency (f0).The simpleRandom cell selection will be used to assess the relevance of these strategies for reflectarray synthesis.


### 3.2. Layout Selection

In addition to the proposed cell selection strategies, it is possible to synthesize layouts with different initial conditions associated to the reference cell. Indeed, any phase offset can theoretically be applied to the phase law in the radiating aperture without changing the associated radiation pattern. The phase of the reference cell at the central frequency,ϕ0=ϕ0des(f0), determines the absolute phase values for all the array elements at this frequency. Thus, the phase of the reference cell can be chosen arbitrarily. In practice, however, its choice is not neutral [13]. As seen in Figure 5, the phase distribution is not uniform. Thus, a judicious ϕ0 value is one that maximizes the number of possible cell designs for most of the array elements.Although this general principle is quite simple, its direct application is not straightforward as the phase distribution depends on the incident angle (in Figure5, it is only given for the normal incidence). As a consequence, in the following, the optimization process is repeated for different ϕ0 values. Then, the solution with the best simulated performance is selected.To do so, some indicators are defined as follows.(i)
The phase errors between the simulated and the desired phase shifts over the array at a given frequencyf are quantified by the following mean and standard deviation:ɛ
¯
(
f
)
=
(
1
/
N
)
∑
i
=
1
N
ɛ
i
(
f
) quantifies the mean phase errors over the array. Note that ɛ¯(f0)=0 as all proposed strategies match the specification at f0 (1). (ii)
The magnitude of the reflection coefficients is averaged over the array to quantify the ohmic losses and/or the polarization conversions of the generated layout but does not account for the tapering of the illumination on the array. It is notedΓyy¯(f).(iii)
To quantify the similarity over the layout, a global similarity criterion, notedSF¯, is defined by averaging the SF¯i values all over the array.Layouts can objectively be compared using these indicators and the best candidate can then be chosen.


## 3.1. Cell Selection Strategies

A cell selection strategy aims at choosing the best design for each element in the array. The minimum requirement is that the achieved phase at the central frequency,f0, matches the desired one:
(1)ϕiach(f0)=ϕides⁡(f0)
for i=1 to N, where N is the number of elements in the array.Thereference cell, defined as the starting point when filling up the layout, is arbitrarily located at the center of the array. The cells are then successively designed from the reference one and moving to the edges of the array. In this section, four cell selection strategies are proposed and described. (i)
TheRandom strategy only operates a random selection among available cell designs achieving the desired phase shift at f0 without any consideration on the geometry or other electrical characteristics. In this paper, these layouts are called “R layout” for “Random” strategy.(ii)
TheDispersion optimization consists in selecting cell designs that not only produce the required phase shifts at central frequency (f0) but also the best achievable ones at the bandwidth extremities (fmin and fmax). It is the most conventional strategy when designing large-bandwidth reflectarrays [11].The best cell design, for theith array element, is the one that minimizes the phase error between the desired and the achieved ones:
(2)ɛi(f)=|ϕides⁡(f)-ϕiach(f)|
at f=fmin and fmax.In this paper, such layouts are called  “D layout” for  “Dispersion” strategy. (iii)
The third strategy is calledGeometrical optimization and has been introduced in [12]. The aim of this original strategy is to maximize the geometrical similarity between contiguous cells in the reflectarray layout. The goal is to comply with the used Floquet simulation hypotheses and thus improve the prediction accuracy of the antenna performance.As it has been shown in Section2, each geometrical parameter does not equally affect the phase shift. Thus, to quantify the similarity between two cells i and j, a similarity factor is defined in which a different weight is attributed to each geometrical parameter:
(3)SF(i,j)=αLx⋅(Lxi-Lxj)2+αLy⋅(Lyi-Lyj)2+⋯.
In this paper, αLx=7 (patch size), αBx=4 (slot length), αSx=1 (stub length), αWx=10 (slot width), and αWSx=10 (stub width). In other words, a variation of slot width (Wx) leads to a larger SF(i,j) value than the same variation of stub length (Sx). The similarity between cell i and its neighbors is noted SF¯i. It is defined by averaging the similarity factor between this cell and each of its nearest neighbors (eight for a rectangular lattice). An iterative process is used that results in a layout which minimizes the SF¯i factor for each array element and thus ensures smooth geometrical variations. The first iteration initializes the geometry of each cell by minimizing the SF¯i factor only considering those of its 8 nearest neighbors that have already been defined. As a consequence, the geometry of the first cell is chosen arbitrarily (only complying with the desired phase). In the next steps, the cell's geometry is progressively updated until the average value of SF¯i converges to its lowest value.In this paper, these layouts are called  “G layout” for  “Geometrical” strategy. (iv)
The last proposed strategy is calledMRC optimization for  “Maximization of Reflection Coefficients” strategy. It has been developed to improve both the reflectarray losses and the cross-polarization level. To do so, the direct reflection coefficient magnitude, |Γyy(f0)|, is maximized for each array element at the central frequency (f0).The simpleRandom cell selection will be used to assess the relevance of these strategies for reflectarray synthesis.


## 3.2. Layout Selection

In addition to the proposed cell selection strategies, it is possible to synthesize layouts with different initial conditions associated to the reference cell. Indeed, any phase offset can theoretically be applied to the phase law in the radiating aperture without changing the associated radiation pattern. The phase of the reference cell at the central frequency,ϕ0=ϕ0des(f0), determines the absolute phase values for all the array elements at this frequency. Thus, the phase of the reference cell can be chosen arbitrarily. In practice, however, its choice is not neutral [13]. As seen in Figure 5, the phase distribution is not uniform. Thus, a judicious ϕ0 value is one that maximizes the number of possible cell designs for most of the array elements.Although this general principle is quite simple, its direct application is not straightforward as the phase distribution depends on the incident angle (in Figure5, it is only given for the normal incidence). As a consequence, in the following, the optimization process is repeated for different ϕ0 values. Then, the solution with the best simulated performance is selected.To do so, some indicators are defined as follows.(i)
The phase errors between the simulated and the desired phase shifts over the array at a given frequencyf are quantified by the following mean and standard deviation:ɛ
¯
(
f
)
=
(
1
/
N
)
∑
i
=
1
N
ɛ
i
(
f
) quantifies the mean phase errors over the array. Note that ɛ¯(f0)=0 as all proposed strategies match the specification at f0 (1). (ii)
The magnitude of the reflection coefficients is averaged over the array to quantify the ohmic losses and/or the polarization conversions of the generated layout but does not account for the tapering of the illumination on the array. It is notedΓyy¯(f).(iii)
To quantify the similarity over the layout, a global similarity criterion, notedSF¯, is defined by averaging the SF¯i values all over the array.Layouts can objectively be compared using these indicators and the best candidate can then be chosen.


## 4. Application to a Specific Antenna  Configuration

### 4.1. RF Requirements

The synthesis process is applied to the design of a dual-polarized reflectarray antenna for spatial communications in the Ku band (from 14 to14.5GHz). The considered antenna configuration is depicted in Figure 6(a). The size of the antenna aperture is 22λ0×22λ0. The F/D ratio is set to 1.3 as a trade-off between frequency dispersion and spillover effects. Moreover, an offset configuration is chosen to limit feed blockage.Antenna configuration (F/D=1.3, maximum cell incidence angle =38°, radiating aperture = 22λ0×22λ0, and interelement spacing =0.5λ0).
(a)
Offset configuration
(b)
Desired aperture phase shift atf0=14.25GHzThe same radiation pattern is required for both polarizations with a CONUS type coverage (for CONtinental United States). To get the phase shift required in the reflectarray aperture, a complex ratio between the field coming from the primary feed and the field reconstructed from the desired shaped radiation pattern in the aperture is performed. The desired aperture phase shift atf0=14.25GHz is shown in Figure 6(b).


### 4.2. Layout Synthesis and Optimization

#### 4.2.1. Layouts Generation and Selection

Different layouts are generated using the four cell selection strategies. For each strategy, eight layouts are synthesized by considering eight initial conditions (ϕ0) regularly distributed over the 360° range. Among the eight layouts, the best one is then selected using the indicators defined in Section 3.2.For illustrative purpose, the procedure is detailed only for theMRC strategy. The results obtained with the four cell selection approaches are summarized in the next section.Table1 reports the indicators associated to each synthesized MRC layout. Note that ɛ¯(f0) is not reported in Table 1 as it is null.Table 1
Indicators of layouts synthesized with theMRC strategy for eight ϕ0 values.
f
min
f
0
f
max
ϕ
0
SF
¯
Γ
y
y
¯
ε
¯
Γ
y
y
¯
Γ
y
y
¯
ε
¯
0
1.17
0.917
5.2
0.951
0.948
7.9
50
1.12
0.915
5.0
0.950
0.949
8.2
100
1.12
0.912
3.8
0.950
0.948
8.6
150
1.10
0.908
4.3
0.948
0.949
8.8
200
1.07
0.907
3.6
0.948
0.949
8.6
250
1.10
0.907
4.3
0.947
0.945
8.1
300
1.16
0.913
4.7
0.948
0.947
7.5
350
1.19
0.917
5.4
0.950
0.947
8.0The relatively low values ofΓyy¯ shown in Table 1 might be related to cross-polarization generated by cells distant from the center of the array, with high incidence angle (38°). To mitigate this phenomenon, nonsymmetrical cells could be used. Γyy¯ is an arbitrary indicator used for layout selection and is not directly related to the losses and cross-polarization levels radiated by the reflectarray (does not account for the tapering on the array). It can be noticed that the Γyy¯ parameter is not really affected by the ϕ0 value. This is consistent with the used MRC strategy that aims at maximizing |Γyy| for each array element. However, larger variations can be observed for the nonoptimized indicators (SF¯ and ɛ¯).As a consequence, the selection consists in choosing theϕ0 value that results in the best trade-off among these indicators. For the MRC strategy, the layout obtained with ϕ0=50∘ is selected.


#### 4.2.2. Selected Layouts

The same layout selection is applied for each strategy. The RF performance of the four resulting layouts are summarized in Table2. It can be observed that each strategy leads to a layout that optimizes its own indicator. This characteristic is highlighted by bold numbers in Table 2. The bad RF performance of the R layout confirms the interest to use a specific cell selection strategy.Table 2
Indicators of the four layouts synthesized with the four cell selection strategies.
f
min
f
0
f
max
Name
ϕ
0
SF
¯
Γ
y
y
¯
ε
¯
Γ
y
y
¯
Γ
y
y
¯
ε
¯
MRC
50
1.12
0.92
13.6
0.90
0.95
9.5
D
100
0.97
0.86
10.4
0.89
0.89
7.5
G
100
0.17
0.82
38.1
0.77
0.87
29.6
R
150
1.41
0.85
32.7
0.79
0.83
31.8The four layouts are depicted in Figure7(a). As expected, the G layout has the smoothest geometrical variations to provide the best accuracy between simulation and measurement. Nevertheless, the accuracy of the prediction also relies on the number of resonant cells in the array: mutual coupling is larger for cells close to resonance [7] which makes these cells more sensitive to their actual environment. The R layout has large geometrical variations distributed all over the panel while for MRC and D layouts, variations are localized only at transition areas. This regularity results from the restricted cell choice imposed by the MRC and D approaches. Indeed, the R layout is synthesized with only one criterion whereas the MRC and the D layouts are optimized with two criteria. A zoom of a 12 by 12 array elements area on the layouts is presented in Figure 8 to show more clearly the evolution of the geometry of the chosen cells in the four layouts (Figure 7).Visualization of the four selected layouts.
(a)
MRC layout
(b)
D layout
(c)
G layout
(d)
R layoutZoom in on the top right area of the four layouts (12 by 12 elements area).
(a)
MRC layout
(b)
D layout
(c)
G layout
(d)
R layout


## 4.1. RF Requirements

The synthesis process is applied to the design of a dual-polarized reflectarray antenna for spatial communications in the Ku band (from 14 to14.5GHz). The considered antenna configuration is depicted in Figure 6(a). The size of the antenna aperture is 22λ0×22λ0. The F/D ratio is set to 1.3 as a trade-off between frequency dispersion and spillover effects. Moreover, an offset configuration is chosen to limit feed blockage.Antenna configuration (F/D=1.3, maximum cell incidence angle =38°, radiating aperture = 22λ0×22λ0, and interelement spacing =0.5λ0).
(a)
Offset configuration
(b)
Desired aperture phase shift atf0=14.25GHzThe same radiation pattern is required for both polarizations with a CONUS type coverage (for CONtinental United States). To get the phase shift required in the reflectarray aperture, a complex ratio between the field coming from the primary feed and the field reconstructed from the desired shaped radiation pattern in the aperture is performed. The desired aperture phase shift atf0=14.25GHz is shown in Figure 6(b).


## 4.2. Layout Synthesis and Optimization

### 4.2.1. Layouts Generation and Selection

Different layouts are generated using the four cell selection strategies. For each strategy, eight layouts are synthesized by considering eight initial conditions (ϕ0) regularly distributed over the 360° range. Among the eight layouts, the best one is then selected using the indicators defined in Section 3.2.For illustrative purpose, the procedure is detailed only for theMRC strategy. The results obtained with the four cell selection approaches are summarized in the next section.Table1 reports the indicators associated to each synthesized MRC layout. Note that ɛ¯(f0) is not reported in Table 1 as it is null.Table 1
Indicators of layouts synthesized with theMRC strategy for eight ϕ0 values.
f
min
f
0
f
max
ϕ
0
SF
¯
Γ
y
y
¯
ε
¯
Γ
y
y
¯
Γ
y
y
¯
ε
¯
0
1.17
0.917
5.2
0.951
0.948
7.9
50
1.12
0.915
5.0
0.950
0.949
8.2
100
1.12
0.912
3.8
0.950
0.948
8.6
150
1.10
0.908
4.3
0.948
0.949
8.8
200
1.07
0.907
3.6
0.948
0.949
8.6
250
1.10
0.907
4.3
0.947
0.945
8.1
300
1.16
0.913
4.7
0.948
0.947
7.5
350
1.19
0.917
5.4
0.950
0.947
8.0The relatively low values ofΓyy¯ shown in Table 1 might be related to cross-polarization generated by cells distant from the center of the array, with high incidence angle (38°). To mitigate this phenomenon, nonsymmetrical cells could be used. Γyy¯ is an arbitrary indicator used for layout selection and is not directly related to the losses and cross-polarization levels radiated by the reflectarray (does not account for the tapering on the array). It can be noticed that the Γyy¯ parameter is not really affected by the ϕ0 value. This is consistent with the used MRC strategy that aims at maximizing |Γyy| for each array element. However, larger variations can be observed for the nonoptimized indicators (SF¯ and ɛ¯).As a consequence, the selection consists in choosing theϕ0 value that results in the best trade-off among these indicators. For the MRC strategy, the layout obtained with ϕ0=50∘ is selected.


### 4.2.2. Selected Layouts

The same layout selection is applied for each strategy. The RF performance of the four resulting layouts are summarized in Table2. It can be observed that each strategy leads to a layout that optimizes its own indicator. This characteristic is highlighted by bold numbers in Table 2. The bad RF performance of the R layout confirms the interest to use a specific cell selection strategy.Table 2
Indicators of the four layouts synthesized with the four cell selection strategies.
f
min
f
0
f
max
Name
ϕ
0
SF
¯
Γ
y
y
¯
ε
¯
Γ
y
y
¯
Γ
y
y
¯
ε
¯
MRC
50
1.12
0.92
13.6
0.90
0.95
9.5
D
100
0.97
0.86
10.4
0.89
0.89
7.5
G
100
0.17
0.82
38.1
0.77
0.87
29.6
R
150
1.41
0.85
32.7
0.79
0.83
31.8The four layouts are depicted in Figure7(a). As expected, the G layout has the smoothest geometrical variations to provide the best accuracy between simulation and measurement. Nevertheless, the accuracy of the prediction also relies on the number of resonant cells in the array: mutual coupling is larger for cells close to resonance [7] which makes these cells more sensitive to their actual environment. The R layout has large geometrical variations distributed all over the panel while for MRC and D layouts, variations are localized only at transition areas. This regularity results from the restricted cell choice imposed by the MRC and D approaches. Indeed, the R layout is synthesized with only one criterion whereas the MRC and the D layouts are optimized with two criteria. A zoom of a 12 by 12 array elements area on the layouts is presented in Figure 8 to show more clearly the evolution of the geometry of the chosen cells in the four layouts (Figure 7).Visualization of the four selected layouts.
(a)
MRC layout
(b)
D layout
(c)
G layout
(d)
R layoutZoom in on the top right area of the four layouts (12 by 12 elements area).
(a)
MRC layout
(b)
D layout
(c)
G layout
(d)
R layout


## 4.2.1. Layouts Generation and Selection

Different layouts are generated using the four cell selection strategies. For each strategy, eight layouts are synthesized by considering eight initial conditions (ϕ0) regularly distributed over the 360° range. Among the eight layouts, the best one is then selected using the indicators defined in Section 3.2.For illustrative purpose, the procedure is detailed only for theMRC strategy. The results obtained with the four cell selection approaches are summarized in the next section.Table1 reports the indicators associated to each synthesized MRC layout. Note that ɛ¯(f0) is not reported in Table 1 as it is null.Table 1
Indicators of layouts synthesized with theMRC strategy for eight ϕ0 values.
f
min
f
0
f
max
ϕ
0
SF
¯
Γ
y
y
¯
ε
¯
Γ
y
y
¯
Γ
y
y
¯
ε
¯
0
1.17
0.917
5.2
0.951
0.948
7.9
50
1.12
0.915
5.0
0.950
0.949
8.2
100
1.12
0.912
3.8
0.950
0.948
8.6
150
1.10
0.908
4.3
0.948
0.949
8.8
200
1.07
0.907
3.6
0.948
0.949
8.6
250
1.10
0.907
4.3
0.947
0.945
8.1
300
1.16
0.913
4.7
0.948
0.947
7.5
350
1.19
0.917
5.4
0.950
0.947
8.0The relatively low values ofΓyy¯ shown in Table 1 might be related to cross-polarization generated by cells distant from the center of the array, with high incidence angle (38°). To mitigate this phenomenon, nonsymmetrical cells could be used. Γyy¯ is an arbitrary indicator used for layout selection and is not directly related to the losses and cross-polarization levels radiated by the reflectarray (does not account for the tapering on the array). It can be noticed that the Γyy¯ parameter is not really affected by the ϕ0 value. This is consistent with the used MRC strategy that aims at maximizing |Γyy| for each array element. However, larger variations can be observed for the nonoptimized indicators (SF¯ and ɛ¯).As a consequence, the selection consists in choosing theϕ0 value that results in the best trade-off among these indicators. For the MRC strategy, the layout obtained with ϕ0=50∘ is selected.


## 4.2.2. Selected Layouts

The same layout selection is applied for each strategy. The RF performance of the four resulting layouts are summarized in Table2. It can be observed that each strategy leads to a layout that optimizes its own indicator. This characteristic is highlighted by bold numbers in Table 2. The bad RF performance of the R layout confirms the interest to use a specific cell selection strategy.Table 2
Indicators of the four layouts synthesized with the four cell selection strategies.
f
min
f
0
f
max
Name
ϕ
0
SF
¯
Γ
y
y
¯
ε
¯
Γ
y
y
¯
Γ
y
y
¯
ε
¯
MRC
50
1.12
0.92
13.6
0.90
0.95
9.5
D
100
0.97
0.86
10.4
0.89
0.89
7.5
G
100
0.17
0.82
38.1
0.77
0.87
29.6
R
150
1.41
0.85
32.7
0.79
0.83
31.8The four layouts are depicted in Figure7(a). As expected, the G layout has the smoothest geometrical variations to provide the best accuracy between simulation and measurement. Nevertheless, the accuracy of the prediction also relies on the number of resonant cells in the array: mutual coupling is larger for cells close to resonance [7] which makes these cells more sensitive to their actual environment. The R layout has large geometrical variations distributed all over the panel while for MRC and D layouts, variations are localized only at transition areas. This regularity results from the restricted cell choice imposed by the MRC and D approaches. Indeed, the R layout is synthesized with only one criterion whereas the MRC and the D layouts are optimized with two criteria. A zoom of a 12 by 12 array elements area on the layouts is presented in Figure 8 to show more clearly the evolution of the geometry of the chosen cells in the four layouts (Figure 7).Visualization of the four selected layouts.
(a)
MRC layout
(b)
D layout
(c)
G layout
(d)
R layoutZoom in on the top right area of the four layouts (12 by 12 elements area).
(a)
MRC layout
(b)
D layout
(c)
G layout
(d)
R layout


## 5. Measurement Results

The chosen layouts have been manufactured and measured. This section compares the results in order to assess the proposed strategies.


### 5.1. Radiation Patterns at the Central Frequency

The required radiation pattern is presented in Figure9. We can observe one main beam for the continental USA, Canada, and Puerto-Rico and another one for Hawaii. Figures 10(a)–10(d) show the superimposition of the required and measured radiation patterns of the four manufactured layouts for a conical view of the earth (±8° angles).Figure 9
Required radiation patterns in the direct polarization at14.25GHz.Superimposition of the required (solid) and measured (dashed) radiation patterns at14.25GHz in the direct polarization.
(a)
MRC layout
(b)
D layout
(c)
G layout
(d)
R layoutThe measured radiation patterns of theMRC, D, and the G layouts match the required coverage quite well regarding the small size of the considered antenna while for the R layout, large differences occur. For this layout which presents the largest geometrical irregularities, the local periodicity assumed in the simulation process is strongly violated. This results in poor RF performance which confirms the necessity to use a specific cell selection process. As a consequence, this layout is no longer studied in the following.


### 5.2. Losses and Cross-Polarization

Table3 summarizes the measured ohmic losses for the three layouts at the central frequency and the extremities of the band. The MRC layout does not only provide a good spatial coverage, it also exhibits the lowest losses. This is consistent with the optimization of |Γyy(f0)| performed for this layout. The losses exhibited by the D layout are high compared to the other measured layouts. This phenomenon is explained by the use of a larger number of dispersive cells in order to match the phase law requirements over the frequency band.Table 3
Measured losses of three manufactured layouts.
Measured losses (dB)
Name
14 GHz
14.25 GHz
14.5 GHz
MRC
0.5
0.2
0.1
D
1.4
1.2
1.27
G
0.63
0.5
0.53Table4 summarizes the maximum measured cross-polarization level for the three layouts. The cross-polarization levels remain under −25 dB for the G and MRC layouts whereas for the D layout, it goes up to −22.4 dB at the lower frequency. However, these levels are suitable with the specifications for all cases.Table 4
Measured cross-polarization of three manufactured layouts.
Measured cross-polarization (dB)
Name
14 GHz
14.25 GHz
14.5 GHz
MRC
-
25.7
-
26.3
-
26.8
D
-
22.4
-
25.4
-
27.1
G
-
27.3
-
26.9
-
26.6


### 5.3. Radiation Patterns over the Frequency Band

Figures11(a)–11(f) show the superimposition of the required and measured radiation patterns at 14 and 14.5GHz for the conical view of the earth.Superimposition of the required (solid) and measured (dashed) radiation patterns in the direct polarization of synthesized layouts.
(a)
MRC layout at 14 GHz
(b)
MRC layout at 14.5 GHz
(c)
D layout at 14 GHz
(d)
D layout at 14.5 GHz
(e)
G layout at 14 GHz
(f)
G layout at 14.5 GHzThese layouts exhibit quite stable radiation patterns over the frequency band. As expected, theD layout has a very good matching with the required coverage at the extremities of the frequency band. However, in the present case, the best performance over the frequency band are exhibited by the MRC layout. It can be explained because, unlike the other strategies, it is not a “phase only synthesis” as the module of the direct reflection coefficients are also optimized. It should be noticed that the small size of the breadboard is certainly favorable to the MRC layout. In a larger array, the frequency dispersion would be higher and the improvement brought by the D strategy would be more obvious.


### 5.4. Radiation Pattern of the MRC Layout

The two main cut views corresponding to theMRC layout are presented in Figures 12(a) and 12(b) at 14.25GHz for the direct and the cross-polarizations.Superimposition of the required (red) and measured (blue) radiation patterns at14.25GHz in direct (solid) and crossed (dashed) polarizations.
(a)
MRClayout at 0° longitude
(b)
MRC layout at 0° latitudeThe good coverage matching is confirmed by a maximum gain difference in the direct polarization of 1.5 dB between the required and the measured ones within the −10 dB bandwidth.


## 5.1. Radiation Patterns at the Central Frequency

The required radiation pattern is presented in Figure9. We can observe one main beam for the continental USA, Canada, and Puerto-Rico and another one for Hawaii. Figures 10(a)–10(d) show the superimposition of the required and measured radiation patterns of the four manufactured layouts for a conical view of the earth (±8° angles).Figure 9
Required radiation patterns in the direct polarization at14.25GHz.Superimposition of the required (solid) and measured (dashed) radiation patterns at14.25GHz in the direct polarization.
(a)
MRC layout
(b)
D layout
(c)
G layout
(d)
R layoutThe measured radiation patterns of theMRC, D, and the G layouts match the required coverage quite well regarding the small size of the considered antenna while for the R layout, large differences occur. For this layout which presents the largest geometrical irregularities, the local periodicity assumed in the simulation process is strongly violated. This results in poor RF performance which confirms the necessity to use a specific cell selection process. As a consequence, this layout is no longer studied in the following.


## 5.2. Losses and Cross-Polarization

Table3 summarizes the measured ohmic losses for the three layouts at the central frequency and the extremities of the band. The MRC layout does not only provide a good spatial coverage, it also exhibits the lowest losses. This is consistent with the optimization of |Γyy(f0)| performed for this layout. The losses exhibited by the D layout are high compared to the other measured layouts. This phenomenon is explained by the use of a larger number of dispersive cells in order to match the phase law requirements over the frequency band.Table 3
Measured losses of three manufactured layouts.
Measured losses (dB)
Name
14 GHz
14.25 GHz
14.5 GHz
MRC
0.5
0.2
0.1
D
1.4
1.2
1.27
G
0.63
0.5
0.53Table4 summarizes the maximum measured cross-polarization level for the three layouts. The cross-polarization levels remain under −25 dB for the G and MRC layouts whereas for the D layout, it goes up to −22.4 dB at the lower frequency. However, these levels are suitable with the specifications for all cases.Table 4
Measured cross-polarization of three manufactured layouts.
Measured cross-polarization (dB)
Name
14 GHz
14.25 GHz
14.5 GHz
MRC
-
25.7
-
26.3
-
26.8
D
-
22.4
-
25.4
-
27.1
G
-
27.3
-
26.9
-
26.6


## 5.3. Radiation Patterns over the Frequency Band

Figures11(a)–11(f) show the superimposition of the required and measured radiation patterns at 14 and 14.5GHz for the conical view of the earth.Superimposition of the required (solid) and measured (dashed) radiation patterns in the direct polarization of synthesized layouts.
(a)
MRC layout at 14 GHz
(b)
MRC layout at 14.5 GHz
(c)
D layout at 14 GHz
(d)
D layout at 14.5 GHz
(e)
G layout at 14 GHz
(f)
G layout at 14.5 GHzThese layouts exhibit quite stable radiation patterns over the frequency band. As expected, theD layout has a very good matching with the required coverage at the extremities of the frequency band. However, in the present case, the best performance over the frequency band are exhibited by the MRC layout. It can be explained because, unlike the other strategies, it is not a “phase only synthesis” as the module of the direct reflection coefficients are also optimized. It should be noticed that the small size of the breadboard is certainly favorable to the MRC layout. In a larger array, the frequency dispersion would be higher and the improvement brought by the D strategy would be more obvious.


## 5.4. Radiation Pattern of the MRC Layout

The two main cut views corresponding to theMRC layout are presented in Figures 12(a) and 12(b) at 14.25GHz for the direct and the cross-polarizations.Superimposition of the required (red) and measured (blue) radiation patterns at14.25GHz in direct (solid) and crossed (dashed) polarizations.
(a)
MRClayout at 0° longitude
(b)
MRC layout at 0° latitudeThe good coverage matching is confirmed by a maximum gain difference in the direct polarization of 1.5 dB between the required and the measured ones within the −10 dB bandwidth.


## 6. Conclusion

In this paper, optimization strategies have been proposed to select the geometry of the radiating cells when designing a reflectarray. They have been applied to improve the performance of a dual-polarized reflectarray with slot-loaded patches. It has been shown that such advanced synthesis procedures are required to take full benefit of the numerous geometrical degrees of freedom provided by this radiating cell. Comparisons of measured performance have confirmed the superiority of the optimization strategies combining phase and magnitude goals. The correspondingMRC layout reveals low losses and a satisfactory cross-polarization level. Moreover, its radiation pattern is quite stable over the considered frequency band (0.5GHz centered on 14.25GHz).



---

*Source: 708429-2012-07-12.xml*