Spectral Coexistence between LEO and GEO Satellites by Optimizing Direction Normal of Phased Array Antennas

Chen Zhang＊, Jin Jin Hao Zhang, Ting Li

1 Tsinghua Space Center, Tsinghua University, Beijing 100084, China

2 Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences, Beijing 100091, China

I. INTRODUCTION

In recent years, a number of Non Geostationary Orbits (NGEO) communication systems working in the Ku and Ka-band were proposed, creating a new era of commercial communication applications (e.g., Oneweb,SpaceX, Leo Sat, Sumsung and others)[1,2,3,4]. These NGEO constellations which contain hundreds or even thousands of small satellites can provide high-capacity and low-latency multimedia services but may generate harmful interference to other satellite systems,especially geostationary (GEO) satellite networks. This potential has attracted a great deal of research interest and various interference mitigation methodologies have proposed. Nelson [5] described the principle features of satellite-to-satellite and satellite-to-station interference analysis for NGEO satellite systems.Lansard [6,7] provided a concept of doublets constellation to cope with the coverage requirements under the constraint of frequency sharing with GEO. Fortes [8] formalized an analytical approach to assess interference involving NGEO satellite networks, and the statistical interfering signal power levels can be evaluated without requiring lengthy computer simulation runs. In [9], Fortes presented modifications to the implementation of the socalled analytical method, in this approach, the position of reference satellite is expressed with a new formulation by using mean anomaly and longitude of ascending node. Wang [10,11] investigated the key issues for spectrum sharing optimization on constellation selection and design, and several proposed NGEO systems are compared from an interference reduction point of view. Zhang [12] proposed a constellation design methodology considering frequency sharing which took the angle between the LEO and GEO communication links as design con-straints, but the constellation needs to support high dual or more satellites visibility at most latitudes. Sharma [13] proposed an adaptive power control technique to mitigate the inline interference of GEO and LEO satellites,the approach demonstrates that the adaptive power control technique can satisfy the desired quality of service of the MEO link while guaranteeing the interference limit of the GEO link. Previous mitigation methods usually focused on optimizing constellation parameters or transmit power to facilitate the sharing of spectrum resources among multiple satellite networks. Recently, the company Oneweb proposed to solve this problem by turning the satellite pitch angle during their span in the equatorial zone [14, 15], but the control strategy and the effect of this method call for further investigation.

In this paper, a specific method is proposed to mitigate the in-line interference between LEO constellation and GEO belt. The contribution of the paper is twofold. First, it suggests a novel look at the spectrum sharing by optimizing the direction normal of phased array antennas, and the configuration of the constellation has not changed. Second, the link performance for global distributed earth stations are analyzed with different direction normal of phased array antenna, and the optimal direction normal is found by solving an optimization problem.

The structure of this paper is as follows.The introduction is stated in section one. The interference scenario is formulated in section two. The visibility condition, antenna radiation patterns, coordinate transformations and interference calculation with analytic approach are introduced in detail in section three. In section four, a case study is performed to prove the validity of methods, then the simulation results are analyzed. In the last section, the conclusions are presented.

II. PROBLEM DESCRIPTION

The interference problem is formulated in this section. Figure 1 illustrates a simplified interference scenario, where green solid dots denote overlapped LEO and GEO earth stations in the most serious interference cases.Blue circles are LEO satellites and red star is a GEO satellite on the equator. Denoteβas the angle separation between LEO and GEO links for each earth station. It can be concluded that theβincreases as the latitude of earth stations decreases, which means low latitude earth stations most likely to receive interference from LEO systems.

For LEO constellations, phased array antennas have become the antenna system of choice [16]. In this paper, the envelope of the phased array antenna is formulated as a cone directing to the earth center in order to simplify the discussion and implementation. Figure 2 illustrates the downlink interference scenario for low latitude earth stations when single coverage is considered. In figure 2(a), nadir pointing arrays with limited boresight angle are used for LEO constellations, it can be seen that LEO links with high visibility elevation most likely to create in-line interference with GEO system. in figure 2(b), the angular separation β is increased by tilting the direction normal of the phased array antennas with same angle, thus avoiding the interference to the GEO system. As can be seen that the interference is mitigated at the expense of reduced signal level at the LEO earth station, therefore the optimal direction normal of phased array is desired, and its evaluation is described in detail in the following sections.

Fig. 1. A simplified interference scenario between LEO constellation and a GEO satellite.

III. METHODOLOGY

3.1 The visibility condition between earth station and satellite

This section describes the visibility condition between earth station and satellite. Denote[ν, φ]┬as the latitude and longitude of the earth station, then the position vector under Earth-Centered-Fixed (ECF) frame can be given by

where,Reis the equatorial radius. Denote Rsatas the position vector of the satellite under Earth-Centered-Inertial (ECI) frame, then the position vector rsatunder ECF frame can be

Fig. 2. The downlink interference scenario of low latitude overlapped earth stations.

expressed as

where, θgis Greenwich sidereal time and it can be obtained by

where, θg0is the Greenwich sidereal time att0, ωeis earth rotation rate and ?tis the time difference between any timetand the initial timet0. Define ξ as the minimum visibility elevation, and the vector from earth station to satellite is defined asDenote rantas the direction normal of phased array,and ζ as the cone angle. Then the visibility conditions between satellite and earth station are expressed as

The above equations denote that the satellite is visible only if it can be seen by the earth station, and the earth station is located in the footprint of the phased array antenna.

3.2 Antenna radiation patterns

Three types of antenna radiation patterns involved in the simulation are given in this section. According to ITU-R S.1528, the reference pattern for an LEO satellite antenna having antenna aperture diameter to wavelength ratio (D/λ)＜ 35 is given by

where, ψ is the off-axis angle, ψbis one-halthe 3dB beam width.Gm=20log(D/λ)represents the maximum gain in the main lobe (dBi).Z=Y×100.04(Gm+Ls?LF), whereLSis the main beam and near-in side-lobe mask cross point (dB) below the peak gain,LFis the far-out side-lobe level (dBi) and the value is 0 dBi for ideal patterns. For MEO satellite,Ls=?1 2 and Y=2ψb, and for LEO satellite,Ls= ?6.75 andY= ?1.5ψb.

According to ITU-R S.672-4, the reference radiation pattern employing for GEO satellites is given by (6) shown in the bottom at this page, whereGmis the maximum gain in the main lobe (dBi), ψ0is the one half the 3 dB beam width in the plane of interest, ψ1is the value of the ψ when theG(ψ) =Gm+Ls+ 20 ?25log(ψ / ψ0) is equal to 0 dBi,Lsis the required near-in-side-lobe level (dB) relative to peak gain, and (a,b) are numeric values based on the value ofLs. ForLs=?20 dB, the values ofaandbare 2.58 and 6.32, respectively.

According to ITU-R S.465-6, the reference radiation pattern employing for earth stations is given by

Figure 3 shows the gain patterns of GEO/LEO satellites and earth terminals using the relevant ITU-R recommendations in the downlink mode.

3.3 Coordinate transformation

This section evaluates the direction normal of phased array after tilting. Five relating coordinates are defined as below

● ECF coordinatesE?Xf Yf Zf’: It has its origin at the center of mass of the Earth,Xfis along the Greenwich or prime meridian.Zfpoints along the rotation axis of the Earth, and theYfaxis completes a right-handed coordinate system.

● ECI coordinatesE?X iYiZi’: It has its origin at the center of mass of the Earth,Xiis along the intersection of the Earth equatorial plane and the ecliptic plane,Zipoints along the rotation axis of the Earth, and theYiaxis completes a right-handed coordinate system.

● LVLH(Local Vertical, Local Horizontal)coordinatesS?X lYlZl’: It has its origin at the mass center of satellite,Zlaxis points toward earth’s center,Ylaxis is the direction of the negative unit angular momentum vector, and theXlaxis completes a right-handed coordinate system.

● VVLH(Vehicle Velocity, Local Horizontal)coordinatesS?Xv Yv Zv’: It has its origin at the mass center of satellite,Xvis directed toward the satellite from earth’s center,Zvaxis is the orbit normal and perpendicular to the orbit plane, and theYvaxis completes a right-handed coordinate system.

● Antenna coordinatesS?Xp Yp Zp’: It has its origin at the mass center of satellite, the antenna coordinates consist with the `LVLH’frame when nadir pointing is implemented.Figure.4 illustrates the relation between

VVLH and LVLH coordinates. Suppose the direction normal in the antenna frame is Ap=[0,0,1]┬. If the direction normal of the antenna is changed, the components of direc-tion normal in the VVLH coordinates is given by

Fig. 3. Antenna radiation patterns in the downlink.

where Ψ , Θ and Φ are roll angle, pitch angle and yaw angle, and Rx, Ryand Rzare the Euler rotation matrix respect tox,yandzaxis respectively (see [17]). Then the components of the direction normal in the LVLH coordinates is given by

The components of the direction normal in the ECI coordinates is given by

where ? is Right Ascension of Ascending Node (RAAN),iis inclination and ω is argument of perigee. The components of the direction normal in the ECF coordinates is given by

Finally, the components of the direction normal in the ECF coordinates are evaluated with Eq.(11), and the interference calculation are introduced in the following section.

3.4 Interference calculation with analytic approach

For simplicity, lets assume an interference scenario in the down link mode with tilted phased array antenna, which is illustrated in figure 2(b). The expression for Carrier to Noise ratio(C/N) at the LEO earth station can be expressed as

Fig. 4. VVLH and LVLH coordinates.

wherePtlsis the transmit power of the LEO satellite,GtlsandGrleare the gain of LEO satellite and LEO earth station respectively. λ is wavelength anddis the distance between the LEO station and the LEO satellite. In addition,Kis Boltzmann’s constant,Trleis the receive noise temperature of the LEO earth station antenna, andWis the bandwidth.

Furthermore, the Interference to Noise ratio(I/N) at the GEO earth station due to the presence of LEO link can be written as

whereGrge(β) is the gain of GEO earth station when the angular separation between two links equals to β.Trgeis the receive noise temperature of the GEO earth station. In order to ensure the desired Quality of Service(QoS) of LEO system without interfering with the existing GEO system, the value ofC/Nat the LEO earth station should exceed the threshold of (C/N)th, and the value ofI/Nat the GEO earth station should not exceed the threshold of (I/N)th.

Let’s assume a more complex interference scenario with a LEO constellation and a set of GEO satellites uniformly placed on the equator. For a fixed earth station, suppose there existNivisible LEO satellites andNjvisible GEO satellites at time instancetbased on the visible condition (i.e., Eq.(4)). Denote (C/N)iand (I/N)i,j,i=1,2,…,Ni,j=1,2,…,Njas Carrier to Noise ratio and Interference to Noise ratio involving thei-th LEO satellite and thej-th GEO satellite. The variable δiof thei-th LEO link is defined as

where δiis a 0-1 variable, and it is used to measure thei-th LEO link can satisfy the desired (C/N)thof the LEO link while guaranteeing the interference limit (I/N)thwith all visible GEO satellites. Define δ~ as the availability function for the earth station compressingNiLEO links, which is given by

where δ~ is a 0-1 variable, 1 means there exist at least one available LEO link for the earth station. Suppose only one LEO link with the best Carrier to Noise ratio is connected by the earth station, the corresponding (C/N)*is given by

In order to obtain the statistical significant results of the earth station, the available percentageand effective signal levelcan be evaluated at a number of sampling points, which is given by

wherek=1,2,…,Nkis the index of sampling points.

In general, statistical analysis via computer simulation of Eq.(17) requires an extremely long computer time, an analytical approach proposed by Fortes [8] can be implemented to assess interference without requiring lengthy computer simulation runs. The rationale behind it takes into account the fact that the position of constellation can be defined once the positions of the reference satellite x are given. As a special case, if Walker constellation[18, 19] is used in the LEO system. Denote x=[?0,M0]┬as the position of the reference satellite, where ?0andM0are the RAAN and mean anomaly. The location of all other satellites can be given by

where,Nis the number of satellites,Pis the number of planes, andFis the phasing factor, the transformation from orbital elements to the corresponding Cartesian components under ECI frame can be found in [20, 21]. For analytic approach, by modeling x as a random variable with probability density function(PDF)px(,M) , where the argument of ascending nodeand mean anomalyMare considered to be continuous random variables,uniformly distributed over interval (?π , π].When non-repeated track satellite system is involved, the PDF function of the vector x is given by (see [9] for PDF function of repeated ground track system)

Because the available percentage and desired average signal levels (i.e.,andare deterministic functions of the position of the reference satellites, their statistical characterization can be obtained while considering the reference satellite location varies in theandMspace.

Suppose theandMspace are equally divided intoNddiscrete points. The calculation process ofandwith analytic approach is illustrated in algorithm 1.

The algorithm 1 can be further extended to analyze global distributed earth stations, supposeNesearth stations are uniformly placed on the earth surface, and the tilted phased array is used to improve the link performance for all earth stations, the optimization problem can be formalized as below

The formalization of Eq.(20) target to maximize the effective signal level while guarantying the available percentage greater than 95% by tilting the phased array (suppose yaw angle Φ=0).

IV. SIMULATION

In this section, the method proposed in the previous section is implemented in a complex simulation scenario, whereNes=337 earth stations, a Walker type LEO constellation anda GEO belt with equally spaced satellites on the equator are considered. The orbital parameters of the two constellations are listed in the Table 1, and the simulation parameters are listed in Table 2.

Algorithm 1. The evaluation of and(C/ N)* with analytic approach

Algorithm 1. The evaluation of and(C/ N)* with analytic approach

1: Initialize Earth stations, LEO constellation and GEO belt.2: Evaluate Earth station positon res with Eq.(1)3: Determine all visible GEO satellites with Eq.(2) and Eq.(4).4: for i=1→Nd do 5: ?= ? ?π(i )(N )6: for j=1→Nd do 7: 2 1/ 1~0,id 2 1/ 1 π( )( )8: Evaluate LEO constellation position with Eq.(18).9: Determine all visible LEO satellite positions with Eq.(2) and Eq.(4).10: Evaluate δ~ and (C/ N)* with Eq.(14). to Eq.(16).11: end for 12: end for 13: Evaluate MjN 0,jd=? ?δ~ and (C/ N)*.

Table I. Parameters of LEO constellation and GEO belt.

Suppose the same strategy is implemented for all phased array antennas in the LEO constellation. Figure 5 illustrates the surface of min available percentage and min effective signal level of all earth stations with different tilting angles, wherexandyaxis are the roll and pitch angles respectively. It can be found that if nadir pointing array is implemented(i.e., Ψ =0°and Θ =0°, which is marked by red point), the min available percentage is 69.23%, and the effective signal level is 23.18 dB. Because the saddle shape and the symmetrical feature of figure 5(a), antenna tilting in the pitch direction (both positive or negative)significantly improves the performance of available percentage with minor reduction of received signal level. The optimal direction normal which is marked by blue circle can be found by solving the nonlinear programming program stated in Eq.(20). Table 3 compares simulation results of nadir pointing array with the optimal tilted array. It can be found that the min available percentage is greatly improved from 69.23% to 95.11% at the expense of tolerable loss of effective signal level, which is decreased from 23.18 dB to 22.08 dB. Figure 6 and figure 7 compare the contour map of available percentage and effective signal level for two cases in Table 3. It can be found that latitude earth stations most likely to receive interference from LEO constellation, which is consistent with the conclusion illustrated in figure 1, and the minor reduction of received signal level is the cost of improving available percentage for low latitude earth stations.Figure 8 shows the coverage area of two LEO constellations listed in Table 3 respectively,it can be found that the coverage area of each satellite is enlarged, which leads to better coverage performance of the constellation.

Fig. 5. Min available percentage and effective signal level of all Earth stations with different tilting angles.

Fig. 6. Available percentage of global distributed Earth stations.

Fig. 7. Effective signal level of global distributed Earth stations.

Fig. 8. The constellation and coverage area of two cases (black line is direction normal of phased array).

Table II. Simulation parameters.

Table III. Comparison of nadir pointing array and optimal tilted array.

V. CONCLUSION

To ensure the desired link quality of the LEO constellation while mitigating the aggressive interference to the GEO belt, a specific mitigation method is proposed by tilting the phased array antennas of the LEO constellation without changing the configuration of constellation, the variation of direction normal of phased array antenna is analyzed and the optimal direction is found by solving a nonlinear programming problem. The simulation result demonstrates that the LEO constellation can be coordinated with the GEO system while guaranteeing the desired signal level of the LEO earth stations.

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (grant no.91738101 and 91438206).

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