Sky Radio Quiet Zones for Mitigating RFI From Large-Scale NGSO Satellites to Ground Radio Astronomy System

Emerging large-scale non-geostationary orbit (NGSO) satellite communication (SatCom) systems with more than thousands of satellites raise a serious concern of radio frequency interference (RFI) to the ground-based radio astronomy system (RAS). This situation becomes more serious as the SatCom industry is rapidly expanding the number of communication satellites which increases RFI, while the RAS is also advancing with enhanced radio astronomical observation (RAO) capability requiring better protection against RFI. To address this impending RFI issue, we analyze the corresponding RFI to identify dominant RFI contributors and then propose two types of sky radio quiet zone (SRQZ), namely, telescope-centered (TC)-SRQZ and RAO direction-centered (DC)-SRQZ. We investigate peak RFI and average RFI suppression characteristics of the two SRQZ types when applied individually alone and jointly. We evaluate the RFI characteristics with/without SRQZs for a few representative ground RAS receiver locations under a low earth orbit SatCom system as well as a medium earth orbit SatCom system. We present and discuss extensive RFI performance results and their dependency on the specifics of the RFI scenarios. These results show that appropriately designed SRQZs provide significant RFI suppression. We also offer guidance on the choice of SRQZ type/deployment, related parameter settings, and practical implementation aspects.

Union (ITU) has regulated the usage of spectrum to guide any services that may cause a possible conflict. The regulatory entities have also enacted multiple protection mechanisms to reduce the RFI impact of any active services on RASs. An example is imposing a ground radio quiet zone (RQZ) [29], [30], [31], [32] to limit the transmit power level and prevent harmful RFI in a certain ground region for some ground passive services. However, these ground RQZs cannot address RFI coming from the sky. Other solutions like space-based RASs deployment [33], [34], [35], [36], [37] move RAO functionality from the ground to space to avoid RFI from terrestrial and lower orbit active transmission systems. Such a space-based approach is expensive and it does not protect the existing ground RASs. Commonly used RFI mitigation techniques such as blanking and excision [38], [39], [40] can remove RFI to the ground RAS but at the cost of RAO data loss. However, such techniques will become inefficient when high RFI occurs more frequently. The emerging NGSO SatCom systems will cause such type of scenarios, thus needing new forms of RFI mitigation.
To address this imminent problem of RFI to the ground RAS caused by the emerging mega-constellation SatCom systems, we explore an efficient RFI mitigation strategy by means of introducing two types of sky radio quiet zone (SRQZ). We investigate characteristics of the RFI caused by mega-constellation low earth orbit (LEO) and medium earth orbit (MEO) SatCom systems at three representative ground RAS receiver locations, and based on the obtained insight we propose two types of SRQZ. We then study their RFI suppression performances in terms of the SRQZ size under three deployment scenarios. The first two scenarios correspond to applying one of the two SRQZ types individually. In the third scenario, both types of SRQZ are jointly applied. Then, based on the results, we provide guidelines on the SRQZ type, the deployment scenario, and the zone size, for the LEO and MEO SatCom systems.
The main technical contributions are summarized below.
• We introduce the SRQZ concept as an efficient RFI mitigation strategy for the coexistence of emerging mega-constellation NGSO SatCom systems and ground RASs.
• We propose two types of SRQZ. In the first type, the SRQZ is centered at the zenith direction of the ground RAS telescope on the considered SatCom orbit, and we term it a telescope-centered (TC) SRQZ. In the second type, the SRQZ is centered at the intersection point of the RAS antenna main beam direction and the considered SatCom orbital surface, which we name a directioncentered (DC) SRQZ.
• Our extensive investigation reveals various peak RFI and average RFI suppression performances of these SRQZs under three deployment scenarios (individual applications of one of the two types and the joint application of both types) for a few representative ground RAS receiver locations under the LEO and MEO SatCom systems.
• We provide insights on their RFI suppression characteristics with reference to the SatCom and RAS parameters and then offer guidelines on the type, parameter settings, and deployment scenarios of SRQZs, as well as their practical implementation aspects.
The structure of this paper is as follows. In Section I, we provide an introduction and motivation for the considered research and a summary of our technical contributions. Section II describes details of the components of the considered system in the context of RFI. Next, Section III introduces the two types of the proposed SRQZs. Then, in Section IV, we present and discuss extensive RFI suppression performances, their characteristics, and practical implementation aspects. Finally, we summarize the key points of our investigation results and draw conclusions in Section V.

II. SYSTEM MODEL
Our considered RFI scenario consists of downlinks of LEO and MEO SatCom systems as the RFI sources and ground RASs as the RFI victim systems. We use OneWeb's LEO/MEO system as our LEO/MEO SatCom system model [41], [42]. In consideration of potentially different RFI impacts at different locations of the ground RAS, we consider three representative ground RAS locations. Details of the components of these systems in the context of RFI are described in the following sub-sections.

A. OneWeb NGSO SatCom SYSTEM
The downlink band of the Oneweb LEO SatCom is 10.7 − 12.7 GHz which is adjacent to the 10.6 − 10.7 GHz RAS band. The Oneweb MEO SatCom downlink band is 40 − 42 GHz and the adjacent RAS band is 42.5 − 43.5 GHz. As the two RAS bands susceptible to the RFI of the LEO and MEO SatCom systems are quite distant, we can consider RFI issues separately for the LEO and MEO SatCom systems. OneWeb LEO SatCom system has 720 satellites operating at an altitude of 1200 km. The LEO satellites are evenly distributed on 18 different orbits with 40 satellites on each and an orbital inclination of 87.9 • . Oneweb MEO SatCom system has 1280 satellites at around 8500 km altitude. MEO satellites are allocated on 16 orbits with 80 satellites on each and a nominal orbital inclination of 45 • . There exist slight variations of altitudes and inclination angles among MEO satellite orbits. Fig. 1 shows a snap-shot of the satellites of the OneWeb LEO and MEO SatCom systems, where red stars indicate the LEO satellites and red lines represent the paths of the orbital planes. Similarly, blues stars and lines are for the MEO satellites case.
In the following, we describe how to generate individual satellite positions as a function of time t by using the orbital parameters of the considered SatCom system according to orbital mechanics [43].
i) Using the eccentricity e of the considered SatCom orbit and the initial true anomaly value v 0,i of the i-th satellite, VOLUME 11, 2023 we obtain the initial eccentric anomaly E o,i by first computing and then where atan2(·, ·) is the four-quadrant inverse tangent function. ii) With the satellite orbital period T , the satellite angular velocity V in radian/second is V = 2π T . Then, according to Kepler's equation, we can trace back the pass time at perigee, denoted by t p,i , of satellite i as: Then, we compute the corresponding i-th satellite's mean anomaly M e,i,t at time t as: iii) Solving Kepler's equation f (E i,t ) = E i,t − e sin E i,t − M e,i,t = 0, e.g., by using Newton's method, we obtain the corresponding eccentric anomaly E i,t . iv) Next, we get the corresponding true anomaly v i,t of satellite i at time t by computing sin and then v) Based on the orbital parameters like orbital inclination I , right ascension of the ascending node (RAAN) i of the satellite i's orbital plane, argument of perigee ω, and the true anomaly v i,t , we obtain i-th satellite's position vector in the earth-centered inertial coordinate system (ECI) with the Cartesian coordinates as follows:x where r i (t) is the satellite orbital height from the earth center at time t given by with a being the semi-major axis of the orbit. vi) Next, we obtain the position vector s, in the earth-centered earth-fixed coordinate system (ECEF) with the spherical coordinates. Here, r i (t)) is the radius given in (12) while l s,i (t) and w s,i (t) are the latitude and the longitude respectively given by where the effect of the earth's rotation with the angular velocity V e is incorporated in (14) by subtracting V e t. vii) Then, we can obtain i-th satellite's position vector S s,i (t) = [x i (t), y i (t), z i (t)] in the ECEF coordinate system with the Cartesian coordinates as follows: Generally, the orbital eccentricity e of SatCom system is close to zero (e.g., e ≈ 0.0818 for OneWeb SatCom systems based on earth ellipsoid WGS-84 model) and hence their orbits are nearly circular. For such a system, one can use a circular orbit as a simple equivalent system. In the following, we use R orb to denote the nominal value of r i (t) or the radius of the equivalent circular orbit in defining the virtual position vector of the RAO target direction and in developing the satellite downlink beam models.

B. ANALYSIS OF RFI AT GROUND RAS
Due to the SatCom orbital inclination, the number of communication satellites within the line-of-sight (LOS) region of a ground RAS could vary with the ground RAS locations.
Thus, we consider three representative ground RAS locations from south to north within the North America around Large Millimeter Telescope (LMT) [44]  The position vector of a considered ground RAS in the spherical ECEF coordinate system can also be defined by g = [l g , w g , R e ] where l g and w g are the latitude and longitude of the ground RAS and R e is the radius of the earth. The corresponding Cartesian coordinate position vector S g = [x g , y g , z g ] can be obtained similar to the transformations in (15), (16), and (17). Similarly, we can define the virtual position vector for the RAO target direction as tgt = [l tgt , w tgt , R orb ] and denote its Cartesian coordinate vector by S tgt . Note that S tgt originates at the earth center with its direction parallel to the main beam direction of the RAS receiver (see Fig. 6).
Suppose the considered NGSO SatCom system has N sat satellites and N beam downlink beams from each satellite. The satellite transmit-beam radiation pattern as defined in ITU-R S.672 [47] and the RAS receive antenna gain pattern from ITU-R S.1428 [48] are shown in Fig. 2. Note that the transmit antenna beams are quite sharp, but the RAS antenna pattern is even much sharper (its off-axis angle is shown in log-scale in Fig. 2(b) for better presentation) with a much larger peak gain, 78 dBi for the RAO band near the MEO downlink band and 67 dBi for the RAO band adjacent to the LEO downlink band. We will utilize these facts when developing our SRQZs in a later section. Fig. 3 illustrates the RFI paths (dash-lines) from the downlinks of NGSO satellites which are within the LOS region of the considered RAS telescope. The LOS region is defined by an angle φ LOS formed at the earth center by the telescope and an edge of the LOS region on the satellite orbital spherical surface. We can compute φ LOS as Define angle(X, Y ) to be the angle between two vectors X and Y . Then, we have ∥X∥∥Y ∥ where X · Y represents the dot product of X and Y . Denote the indices of the satellites within the LOS region of the considered RAS telescope r at time t by J r (t), i.e., Let us consider the RFI from the k-th beam of satellite i ∈ J r (t) to the RAS telescope r. Denote P UE,i,k as the unwanted emission power inside the considered RAO band caused by the transmission of the k-th beam of satellite i. Let θ T,r,i,k (t) and θ R,r,i (t) represent the considered RFI path's off-axis angles in the satellite transmit antenna gain pattern G T (·) and the RAS receive antenna gain pattern G R (·), respectively, in the RAO band. They will be detailed in Fig. 6 and its related part later. The corresponding antenna gains for the RFI path are denoted by G T (θ T,r,i,k (t)) and G R (θ R,r,i (t)), respectively. Let d r,i (t) denote the distance at time t between satellite i located at S s,i (t) and the telescope r located at S g , i.e., d r, Then, we can follow the ITU-R document [49] to calculate the instantaneous equivalent power flux density (epfd) epfd r,i,k (t) received at telescope r caused by the k-th beam of satellite i at time t as follows: .
The total instantaneous RFI (in terms of epfd) at time t at telescope r is Typically, to detect extremely weak RAO signal levels, RAO signal power is integrated over a long time interval t. Thus, VOLUME 11, 2023 a relevant RFI performance is the average RFI in terms of average epfd over the time interval [t 0 , t 0 + t] which can be computed as: The average RFI computation also requires knowledge of the unwanted emission power. For the sake of better protection of the passive services against RFI, the use of an upper bound for P UE,i,k is desired. For this, we can use the existing emission mask regulated by NTIA for space service [50] to compute P UE,i,k within the RAO band [f R,L , f R,U ] as: where S EM (f off ) is the NTIA space service emission mask in dB defined as: S EM (f off ) = max{−40 · log 10 ( 2f off B assign ) − 8, −60}, (24) p beam is the satellite transmit beam power, f off is the frequency offset from the center frequency f c of the transmitter assigned band with the bandwidth B assign .

C. USER DOWNLINK BEAM COVERAGE PATTERN AND ANTENNA BEAM ANGLES
For the satellite user downlink (UD) beam structure model, we consider a commonly used fixed central symmetric 7-cell structure for both LEO and MEO SatCom systems as shown in Fig. 4. The center cell is with the earth-centered downward beam and the six outer cells are distributed around the center one. We set the UD beams such that the beam's onesided cell size angle corresponds to −10 dB of the maximum gain of the antenna pattern (based on the average wavelength of the downlink sub-bands) and the angle between the two adjacent beam centers is twice that angle. The Oneweb LEO SatCom system has seven downlink sub-bands denoted by {UD1, · · · , UD7} in Fig. 4(a) (see Table 1 for details), and we simply consider a random allocation of these seven sub-bands to the seven cells of the considered satellite. The Oneweb MEO SatCom system has only four downlink sub-bands denoted by {UD1, · · · , UD4} (see Table 1 for details), and we need to avoid allocating the same downlink sub-band to adjacent cells. The basic design is that the center cell randomly picks one of the four sub-bands (e.g. UD1), and the three consecutive outer cells are assigned with the remaining three sub-bands (UD2, UD3, UD4), as shown in Fig. 4(b). Next, the remaining three outer cells are allocated with the three sub-bands of the first three outer cells in such a way that adjacent cells have different sub-bands as shown by the different colors for different sub-bands in Fig. 4(b). The same downlink sub-band allocation pattern is applied to different satellites. Next, we present how to compute θ T,r,i,k (t) and θ R,r,i (t). For a considered satellite S, let C 0 denote the center point of the center cell and C 1 to C 6 denote the center points of the outer cells on the earth surface as shown in Fig. 5. Suppose C 0 , C 1 , and C 4 are at the same latitude; C 2 /C 6 , and C 3 /C 5 are symmetric to the line formed by C 1 and C 4 , which is intersected at point B with the line connected between the considered satellite S and the earth center O. We use this setting for simplicity and it does not affect the distances between the cell centers. We denote the beamwidth angle of a beam cell (corresponding to a −10 dB drop from the 91340 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. maximum in the antenna gain pattern) by ̸ OSC 1 = θ b . Then, we can express β = ̸ OC 1 S as: where R orb is the distance from the satellite to the earth center and R e is the radius of the earth. Equation (25) has incorporated the fact that β > π 2 . Then, θ o = ̸ SOC 1 can be calculated as: The distances of outer cell centers {C i i = 1, · · · , 6} to the center point B, denoted by {BC i : i = 1, · · · , 6} are the same and after simplification we have: Next, we project BC 2 onto the latitude and longitude directions and obtain the corresponding projected lengths d l and d w as: The corresponding shifts in latitude and longitude, denoted by δ l and δ w for C 2 with reference to C 0 are: Then, for satellite i with the position vector s,i (t) = [l s,i , w s,i , R orb ], utilizing the symmetry of the cells, we can obtain the position vectors b,i,k (t) of all the beam cell centers {C i } on the earth surface as The corresponding Cartesian coordinate position vectors } by using the transformation approach as in (15), (16), and (17).
Next, we introduce a virtual vector S tgt,o representing the position vector of the point where the center of the RAS antenna beam intercepts with the orbital surface. This point could be viewed as a virtual RAO target on the orbital surface. We can compute S tgt,o as where From the above position vectors, we can compute θ T,r,i,k (t) and θ R,r,i (t) as: Note that (35) and (36) are used in computing RFI in (20). Fig. 6 illustrates the relevant position vectors and the antenna beam angles related to the RFI path.   (20) and (21) together with the antenna gain patterns in Fig. 2, we find that the satellites whose RFI path directions fall within the main-lobe of the satellite transmit or/and RAS receive antenna gain patterns are the dominant contributors to the RFI. To be more specific, the satellites with |θ T,r,i,k (t)| or |θ R,r,i (t))| being close to 0 are dominant. This leads us to two types of SRQZs as described below.

A. TELESCOPE-CENTERED SRQZ
For the considered ground telescope r located at [l g , w g , R e ], let us first consider the satellite orbital region which contains the satellites with |θ T,r,i,k (t)| being around 0. This region corresponds to the spherical cap centered around the zenith direction of the telescope and is defined as the telescopecentered (TC) SRQZ. Downlink transmissions of the satellites within this region are associated with large transmit antenna gains as well as smaller propagation distances to the telescope, both of which contribute to higher RFI levels. We define the SRQZ by two parameters, namely, the center point position vector TC and the one-sided angular zone size φ 1z,TC (or simply φ 1z if no ambiguity arises). The center point of the SRQZ is defined on the satellite's orbital spherical surface and hence, for TC-SRQZ, we have TC = [l g , w g , R orb ] and its Cartesian coordinate vector is denoted by S TC . φ 1z is defined as the angle between the SRQZ center point and the SRQZ edge point on the satellite's orbital spherical surface formed at the earth center. Fig. 7 illustrates a TC-SRQZ. The indices of the satellites inside the TC-SRQZ are represented by When TC-SRQZ is imposed, the downlink transmissions of the satellites inside J TC r (t) are muted.

B. RAO DIRECTION-CENTERED SRQZ
Here, we consider the satellite orbital region which contains the satellites with |θ R,r,i (t))| being around 0. Suppose the telescope r located at [l g , w g , R e ] has an RAO target direction defined by the latitude and longitude as (l tgt (t), w tgt (t)) at time t. Then, the region with |θ R,r,i (t))| being around 0 corresponds to the region centered around the virtual RAO target point on the satellite orbital surface defined by S tgt,o (see eq. (33) and Fig. 6). We define this region as the RAO direction-centered (DC) SRQZ, which is represented by the SRQZ center point vector S DC = S tgt,o and the one-sided SRQZ angular zone size φ 1z,DC (or simply φ 1z if no confusion arises) measured at the earth center. The introduction of DC-SRQZ is justified by the fact that the RAS receiver antenna peak gain is the most dominant factor to the RFI. Note that a TC-SRQZ is at a fixed location in the ECEF coordinate system but a DC-SRQZ can be with a time-varying location according to the RAO direction. An illustration of a DC-SRQZ is shown in Fig. 7. The indices of the satellites inside the DC-SRQZ are represented by When DC-SRQZ is imposed, the downlink transmissions of the satellites inside J DC r (t) are muted.

C. SRQZ DEPLOYMENT SCENARIOS AND RFI
In general, we have three SRQZ deployment scenarios: i) TC-SRQZ only, ii) DC-SRQZ only, and iii) TC+DC SRQZ. The RFI expression in (21) for the above SRQZ scenarios can be given by where J TCDC The average RFI is obtained by substituting epfd r (t) in (22) with the corresponding term from (39), (40), or (41).
As will be seen in the section on performance results, the RFI suppression performances of TC-SRQZ and DC-SRQZ depend on several factors such as the satellite orbital parameters, telescope location, and RAO direction. Note that the satellites with the orbital inclination of l 0 are orbiting within the latitude region [−l 0 , l 0 ]. Thus, if the virtual RAO target point on the SatCom orbital surface (defined by S tgt,o ) is well outside this latitude region, a DC-SRQZ may not be needed. On the other hand, as RAS will have different RAO directions at different times, a DC-SRQZ may be needed again at a later time. Similarly, if a ground radio telescope is located well outside the latitude region [−l 0 , l 0 ], the TC-SRQZ will not be needed. Thus, the deployment of SRQZs needs to be developed for each ground telescope based on its location, RAO bands, RAO projects, and NGSO SatCom system information. Due to the time-varying nature of the RAO direction, the deployment of DC-SRQZ would be time-varying as well. Fundamentally important to the design and deployment of SRQZ is the knowledge of RFI suppression characteristics of TC-SRQZ, DC-SRQZ, and TC+DC SRQZ under various system conditions. Thus, we present our extensive investigations of their RFI suppression characteristics in the next section.

A. SIMULATION PARAMETER SETTING AND PERFORMANCE METRICS
We use OneWeb LEO and MEO SatCom systems and three ground RAS telescopes approximately at LMT, VLA, and ARO locations. The corresponding system models are described in Section II. The SatCom orbital parameters are according to [41] and [42] and other related parameter settings are given in Table 1. A detailed description of simulation is given in the Appendix.
We use peak RFI and average RFI as our performance metrics. As RAO signals are extremely weak, signal power averaging over a long time interval is used to retrieve the radio astronomical signal information. Thus, average RFI is an important performance metric for RAS, On the other hand, strong peak RFI could damage the RAS receiver. Thus, peak RFI also needs to be assessed and mitigated to protect the RAS receiver. We use a discrete-time system with a one-second sampling interval and an observation duration of 240 minutes. The peak RFI is the maximum RFI among the observation instants and the average RFI is the average of RFI across all the observation instants. As the performance depends on the RAO target direction, we consider several RAO target directions defined by the latitude l g + l and longitude w g + w.

B. RESULTS IN LEO SYSTEMS 1) TC-SRQZ PERFORMANCE
We first assess the peak-RFI mitigation capability of TC-SRQZ. The peak RFI results of TC-SRQZ with several zone sizes are shown in Fig. 8 for the three different RAS receiver locations, respectively. The scenario where the RAO target direction is the zenith direction of the RAS telescope, i.e., ( l = 0 • , w = 0 • ), has the largest RFI when no SRQZ is applied (i.e., φ 1z = 0 case) but for this scenario, the TC-SRQZ efficiently reduces RFI with a small zone size of one to five degrees. Other RAO target direction scenarios show some plateau without any RFI reduction up to certain TC-SRQZ sizes, and then RFI falls off steeply when the zone size is further increased. The RFI plateau width in terms of φ 1z value varies across different scenarios.
To explain the above characteristics, we introduce a parameter γ which is defined as the angle formed at the earth center by the RAS receiver and the virtual RAO target point S tgt,o on the SatCom orbital surface. In other words, γ is the angle between (l g , w g ) and (l to , w to ), or equivalently between the zone centers of TC-SRQZ and DC-SRQZ, formed at the earth center. We can compute γ as γ = cos −1 cos(l g ) cos(l to ) cos(w g − w to ) + sin(l g ) sin(l to ) (42) Table 2 presents the values of γ for different RAO directions and RAS receiver locations, in the RFI scenarios with the LEO and MEO SatCom systems. We can observe that a larger value of | w|, | l|, or R orb yields a larger γ . Furthermore, the values of γ for different RAS locations are different for an RAO direction with w ̸ = 0, but they are the same for an RAO direction with ( l ̸ = 0, w = 0).
The characteristics of the TC zone with no RFI reduction can be explained as follows. First, the RAS receiver has a very sharp antenna gain pattern with a very large maximum gain (see Fig. 2b), which will become a dominant factor to RFI if there is any transmitting satellite in the RAS receiver's main beam direction. When the TC-SRQZ size φ 1z is smaller than γ , the satellite orbital region intersecting with the RAS receiver main beam is outside the TC-SRQZ, and hence the dominant contributor to RFI is not suppressed by TC-SRQZ. Thus, we can see in the results that only when φ 1z > γ , RFI falls off sharply. For example, for LMT with ( l = 30 • , w = 0 • ) and ( l = 0 • , w = 60 • ), we have γ = 5.12 • and γ = 12.04 • , and the steep RFI drop occurs at φ 1z = 6 • and φ 1z = 13 • , respectively (the plots are with a 1 • step size in φ 1z ). The same cases for VLA have γ = 5.12 • and γ = 9.57 • , and the steep RFI drops at φ 1z = 6 • and φ 1z = 10 • . The zone size where RFI drops steeply does not change with the latitude location of the RAS receiver for the same | l| but it changes for the same | w|. This is a direct consequence of the same characteristics of γ shown in Table 2.
Peak RFI levels without any SRQZ are contributed by several factors, such as the RAS receiver location, satellite orbital parameters, and RAO target direction. The first two factors influence the number of satellites inside the LOS region of the RAS receiver. The RAO target direction affects the propagation distance of the dominant RFI source satellite(s). Furthermore, due to the very sharp RAS receiver antenna pattern and moving discrete points of transmitting satellites, the occurrence of a transmitting satellite at the vicinity of the peak antenna gain direction of the RAS receiver is infrequent. Thus, given a limited observation time, occasionally two scenarios with very similar RFI environments may show noticeable differences in peak RFI level. As an example, the scenarios of ( l = 0 • , w = 60 • ) and ( l = 0 • , w = −60 • ) for LMT have very similar RFI environments due to the same longitude deviation of target direction from the zenith direction) but their peak RFI levels in the figures are quite different. As a confirmation of our explanation, we present in Fig. 9 two sets of RFI across time with different starting time instants. The peak RFI for w = −60 • case in Fig. 9(b) is substantially larger than that for w = 60 • case in Fig. 9(a) for the time interval [0, 240] minutes but the situation reverses for the time interval [720, 960] minutes as shown in Fig. 9(d) and Fig. 9(c).
The average RFI results of TC-SRQZ with several zone sizes are shown in Fig. 10 for the three RAS receiver locations. The performance characteristics exhibit very similar trends to their respective peak RFI results except that they are at the scaled down levels. This is due to the dominance of RFI peak spikes on the overall RFI results. The scenario with ( l = 0 • , w = 0 • ) shows a significant RFI suppression for the zone size up to φ 1z = 5 • and a much slower rate of RFI decrease for larger zone sizes, but without any RFI plateau. For other scenarios, the RFI plateau in the region of φ 1z < γ now shows a marginal RFI reduction as the zone size φ 1z increases. Within the region, the TC-SRQZ suppresses some non-dominant RFI sources but not the ones causing the RFI peak and hence the plateau remains flat for the peak RFI results and marginally decreases for the average RFI results. Overall, the TC-SRQZ size mainly depends on the value of γ for the considered LEO SatCom system. The RAS receiver location influences γ and hence the RFI plateau region size. However, when the zone size φ 1z is a few degrees larger than γ , the RFI levels of the different RAS receiver locations are very similar.

2) DC-SRQZ PERFORMANCE
In this section, we investigate the RFI mitigation capability of DC-SRQZ. Fig. 11 presents the peak RFI results of DC-SRQZ with various zone sizes for the three RAS receiver locations. We can observe a completely different set of performance characteristics if compared to TC-SRQZ cases. With the zone size of φ 1z = 1 • , DC-SRQZ greatly suppresses peak RFI. This can be explained as follows. As mentioned before, the peak RAS receiver gain is the most dominant factor for the peak (as well as average) RFI. As the center of DC-SRQZ on the SatCom orbital surface coincides with the peak RAS receiver gain direction, DC-SRQZ effectively removes the dominant RFI contributor, thus, giving a significant RFI suppression with one degree zone size.
Note that when ( l = 0 • , w = 0 • ), TC-SRQZ and DC-SRQZ coincide, and hence the performance discussion for this scenario of TC-SRQZ applies here as well. Recall that there is no RFI plateau for this scenario. For other target direction scenarios, right after DC-SRQZ suppresses the dominant RFI contributor in the direction of peak RAS receiver gain, the peak RFI shows a plateau region for the zone size up to φ 1z ≈ γ . Then, another steep decline of RFI happens within γ < φ 1z < γ + 2 • and beyond which a very slow rate of RFI decrease follows. This characteristic indicates that the satellite's transmit antenna main beam is the second most dominant RFI contributing factor. Only when the DC-SRQZ includes the orbital region where the satellite transmit antenna main beam coverage overlaps with the RAS receiver location, the removal of the corresponding RFI contributors yields a steep RFI decline. Also note that the first RFI drop at φ 1z = 1 • is much larger than the second drop at φ 1z ≈ γ since the RAS receive antenna peak gain is much larger than the satellite transmit antenna peak gain.
Next, we present the average RFI results of DC-SRQZ with various zone sizes for the three RAS receiver locations in Fig. 12. We can observe similar characteristics to the peak RFI performance but in a scaled down version. Another difference is that the RFI plateau region is now replaced by 91344 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.  a noticeable RFI decrease slope especially for the scenarios with γ < 6 • . It can be explained as follows. In these scenarios, the two most dominant RFI contributing regions corresponding to the peak RAS receiver antenna gain and the peak satellite transmit antenna gain are close to each other and the role of the outer part gain of the transmit antenna main beam becomes noticeable due to their closer propagation distances to the RAS receiver than the scenarios with larger γ values. The characteristic of the impact of RAS receiver location is the same as that discussed in the TC-SRQZ case. When comparing the RFI performances of TC-SRQZ and DC-SRQZ, we can conclude that for small zone sizes up to VOLUME 11, 2023   φ 1z = 5 • , DC-SRQZ has a clear advantage with significant performance gain for all considered scenarios. As an overall, DC-SRQZ can be chosen over TC-SRQZ for zone sizes up to φ 1z = 13 • for all the considered scenarios with the LEO-SatCom system.

3) TC+DC SRQZ PERFORMANCE
Here, we assess the average RFI performance when both TC-SRQZ and DC-SRQZ are applied. The results corresponding to six representative relative RAO target directions are shown for an RAS receiver approximately at LMT in Fig. 13, at VLA in Fig. 14, and at ARO in Fig. 15. At each RAS receiver location, the RFI suppression performances with respect to different relative RAO target directions are mainly dominated by the value of γ as discussed in the previous sections. On the other hand, the RFI suppression performances are very similar for different RAS receiver locations under the LEO SatCom system. Although the zone size to avoid RFI plateau when applying TC-SRQZ only can be quite large, the results indicate that we should not discard TC-SRQZ. After suppressing the effect of RAS receiver peak gain by means of DC-SRQZ, the satellite transmit antenna main beam becomes the dominant factor for which TC-SRQZ is effective. Thus, applying both TC and DC SRQZs represents an efficient solution. In general, the zone sizes of TC-SRQZ and DC-SRQZ can be set differently depending on the considered situations. As an overall simple guideline, we observe that φ 1z = 4 • or 5 • are efficient design settings for both types of SRQZ in the considered LEO SatCom system.
Next, we show in Fig. 16 a more vivid performance comparison among TC-SRQZ, DC-SRQZ, and TC+DC-SRQZ (with the same zone size for TC and DC in TC+DC) in terms of peak RFI results for different relative RAO target directions. RFI suppression performances of TC only or DC only largely depend on the relative RAO target directions. However, those of TC+DC show consistent and very similar RFI suppression performances for all the target directions.  For the target directions with large γ values, the advantage of TC+DC over TC or DC alone are very significant.
Another aspect for practical consideration is the total spherical cap surface area of the SRQZ. A smaller surface area of SRQZ is preferred to minimize interruption to Sat-Com service provisioning. For TC or DC only zone with φ 1z = θ 1 , the spherical surface area of the zone is A 1 = 2πR 2 orb (1 − cos(θ 1 )). For TC+DC with each zone defined by φ 1z = θ 2 , the total spherical surface area (of TC+DC) is A 2 = 4πR 2 orb (1 − cos(θ 2 )). For example, if θ 2 = 4 • , we will have θ 1 = 5.658 • for A 1 = A 2 . With this setting, let alone | l| = 60 • cases, even at l = 30 • , the use of TC+DC is more advantageous, as can be observed in the figures.

C. RESULTS IN MEO SYSTEMS 1) TC-SRQZ PERFORMANCE
The peak RFI performances of TC-SRQZ in the MEO Sat-Com system are presented in Fig. 17 for an RAS receiver approximately at LMT, VLA, and ARO, respectively. The MEO SatCom system causes higher RFI levels than the LEO SatCom system does and the RFI difference is over 20 dB after suppressing with TC-SRQZ. This could be ascribed to the much higher peak gains of the RAS receive antenna and the SatCom transmit antenna as well as the larger number of satellites in the considered MEO SatCom system than the LEO SatCom system. TC-SRQZ efficiently suppresses RFI for the RAO in the zenith direction. But a slightly different VOLUME 11, 2023  behavior from the LEO SatCom system is a narrow region of very slow RFI decline at φ 1z = 2 • . This is due to the earlier appearance (i.e., at a smaller offset angle) of transmit antenna gain flat region in the MEO SatCom system than in the LEO SatCom system, (1.4 • versus 5 • offset from the bore-sight of antenna beam pattern). After that, there is a steep RFI drop which is due to exclusion of transmit antenna peak gains by the SRQZ.
TC-SRQZs with other non-zenith RAO directions exhibit peak RFI plateaus up to the zone size φ 1z < γ after which RFI declines steeply. This is the same behavior as explained in the LEO SatCom case. However, the values of γ are larger for the MEO SatCom system than the LEO SatCom system (see Table 2). We also observe some exceptions to the steep decline from the peak RFI plateau which do not occur in the LEO SatCom system. Specifically, ( l = 60 • , w = 0 • ) for for ARO show already low RFI levels. The reason is that for these cases the RAS receiver antenna points to the region without any MEO satellites, i.e., at the latitudes higher than the orbital inclination angle of MEO SatCom system, thus the effect of the peak RAS antenna gain is already excluded. The cases of ( l = 0 • , w = 60 • ) and ( l = 0 • , w = −60 • ) for ARO also exhibit similar characteristics and this is due to the low RAS receiver antenna gain associated with large γ values of these cases and the half of the TC zone being without MEO satellites (as the latitude of ARO is approximately the same as the MEO inclination angle).
Next, to demonstrate that very strong peak RFI can occur occasionally at different time instants for different RAO directions, we present in Fig. 18 the peak RFI at two different sets of times for LMT under MEO SatCom system. We use two RAO directions ( l = 0 • , w = −30 • ) and ( l = 0 • , w = 30 • ) which have very similar RFI environments. Yet, the very strong RFI peaks occur at substantially different time intervals. Furthermore, we notice that the RFI peaks are less frequent in MEO SatCom system than in LEO SatCom system. This could be ascribed to the longer orbital period of MEO SatCom system.
The average RFI performances of TC-SRQZ in the MEO SatCom system are presented in Fig. 19 for the three RAS receiver locations. They show scaled down characteristics of their peak RFI results. The average RFI levels after suppression with TC-SRQZ in the MEO SatCom system are over 20 dB higher than those in the LEO SatCom system. This aspect and its reason follow those of the peak RFI performance comparison.

2) DC-SRQZ PERFORMANCE
The peak RFI performances of DC-SRQZ in the MEO Sat-Com system are presented in Fig. 20 for the three RAS receiver locations. For the RAO in the zenith direction, TC is equivalent to DC and the performance characteristics and discussions are provided in the previous section. For several other RAO directions, the peak RFI characteristics consist of a steep drop at φ 1z = 1 • due to the exclusion of the peak RAS receive antenna gain followed by a plateau until or near φ 1z = γ . Then, there is another RFI drop due to the exclusion of the transmit antenna peak gains. The same cases of exceptions as in the TC-SRQZ occur for the DC-SRQZ and the discussion points are referred to the TC-SRQZ section. A minor difference is a small RFI drop at φ 1z = 3 • or 4 • for the TC-SRQZ which can be ascribed to the exclusion of some satellites with main transmit antenna gains inside the zone. Such behavior does not happen for DC-SRQZ until near φ 1z = γ and hence the RFI curves for those exception cases are flat for DC-SRQZ.
Next, Fig. 21 shows average RFI performances of DC-SRQZ in the MEO SatCom system for the three RAS receiver locations. Same as other cases, the average RFI results are scaled down version of their peak RFI results. We also note that for the LEO SatCom system the zone size of DC-SRQZ is typically smaller than that of TC-SRQZ to achieve similar RFI suppression. But for MEO SatCom system, the two zone sizes are similar.

3) TC+DC SRQZ PERFORMANCE
We present the average RFI performances when both TC and DC SRQZs are applied in the MEO SatCom system for some representative relative RAO directions for an RAS receiver approximately located at LMT in Fig. 22, at VLA in Fig. 23, and at ARO in Fig. 24. TC-SRQZ only case corresponds to φ 1z = 0 • for DC, and DC-SRQZ only case is where φ 1z = 0 • for TC. At LMT, DC-SRQZ outperforms TC-SRQZ for all cases except ( l = 60 • , w = 0 • ). This exception case corresponds to the situation where the RAS receiver peak antenna gain points to the region with no satellites  (i.e., the region with a latitude higher than the orbital inclination angle). As the main RFI contributor is already excluded, its RFI is relatively lower than other cases and the role of DC, which is to suppress the main RFI contributor, is irrelevant. Thus, for this case, TC only can be considered if the requirement on RFI is met by φ 1z = 10 • . For all other cases, we can observe that applying both TC and DC is more efficient. For example, with φ 1z = 10 • for both TC and DC, quite substantial RFI suppression is achieved. At VLA, DC-SRQZ outperforms TC-SRQZ for all relative RAO directions except two cases, ( l = 30 • , w = 0 • ) and ( l = 60 • , w = 0 • ). These exception cases correspond to the scenarios where the 91350 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.  peak RAS receive antenna gain points to the region with no satellites. For the case of ( l = 60 • , w = 0 • ), we can apply TC-SRQZ only. For all other cases, applying both TC and DC is more advantageous. Setting φ 1z = 10 • could be a good design tradeoff between RFI suppression and MEO SatCom service disruption.
However, at ARO which sits at approximately the same latitude as the MEO orbital inclination angle, TC-SRQZ outperforms DC-SRQZ for the cases of ( l = 30 • , w = 0 • ), ( l = 0 • , w = 60 • ) and ( l = 60 • , w = 0 • ). For ( l = −60 • , w = 0 • ), the performance of TC and DC are similar. For ( l = 0 • , w = 30 • ) and ( l = −30 • , w = 0 • ), DC-SRQZ is better. The better performance of TC-SRQZ can be explained by either the peak RAS antenna gain pointing to a region with no satellite or very large relative RAO direction from the zenith direction for which DC will have smaller transmit antenna gains and larger propagation distances to offset the peak RAS receive antenna gain while TC still suppresses peak transmit antenna gain. For ( l = 30 • , w = 0 • ) and ( l = 60 • , w = 0 • ) cases, we can choose TC-SRQZ only. For other cases, applying both TC and DC is more efficient and we view that at least φ 1z = 10 • would be needed to achieve significant RFI suppression.
Next, in Fig. 25 we present peak RFI performance comparison among TC-SRQZ, DC-SRQZ, and TC+DC-SRQZ (with the same zone size for TC and DC in TC+DC) for different relative RAO target directions. RFI suppression performances of TC only or DC only largely depend on the relative RAO target directions and whether the peak RAS antenna gain points to a region with no satellites. However, those of TC+DC show consistent and very similar RFI suppression performances for all the target directions. The performance curves of TC-SRQZ and TC+DC SRQZ overlap for ( l = 60 • , w = 0 • ) up to φ 1z = 11 • at LMT, for  ( l = 60 • , w = 0 • ) at VLA, and for ( l = 30 • , w = 0 • ) and ( l = 60 • , w = 0 • ) at ARO. For these cases, we can apply TC-SRQZ only. For all other cases, we can apply TC+DC SRQZ with φ 1z = 10 • for the MEO system.

D. APPLICABILITY FOR OTHER CONTINENTS
Here, we illustrate applicability of our approach and results for other continents by presenting the average RFI performance of TC+DC SRQZs with various zone sizes for an RAS receiver at ATCA location in Australia. The performances under the LEO and MEO systems are shown in Fig. 26 and Fig. 27, respectively. Note that RAS receivers located at similar latitudes have similar RFI characteristics. As ATCA is located about 30 • S while VLA is around 34 • N, we can expect that they have similar average RFI characteristics for mirrored latitude shifts (e.g., l = X • versus l = −X • ) of RAO directions. To verify this fact, we compare the results for VLA and ATCA, i.e., Fig. 14 versus Fig. 26 for the LEO case and Fig. 23 versus Fig. 27 for the MEO case. We can observe close similarity of RFI performance characteristics between ATCA with l = −30 • and VLA with l = 30 • , between ATCA with l = −60 • and VLA with l = 60 • , and vice versa.

E. OPERATIONALIZATION OR IMPLEMENTATION
Based on our investigation results, we discuss the operationalization or implementation aspects below. The main  parameters of the SRQZs are zone centers and zone sizes which depend on SatCom system parameters, RAS observatory location, RAO directions, and acceptable RFI level to be achieved by SRQZs. For each observatory location and each RAO band which is subject to the NGSO SatCom RFI, we can define disjoint regions of RAO directions in terms of regions of l and w, and assign each region with a zone size for TC-SRQZ and that for DC-SRQZ. We can introduce a maximum limit on the zone size to avoid unacceptable service interruption for SatCom which depends on the SatCom's beam management capability which needs a further separate study. The maximum zone size sets the limit on the RFI level achievable by the SRQZ. If needed, SatCom systems must implement additional RFI suppression approaches, e.g., using better spectrum sidelobe suppression, operating below peak capacity, etc, to meet the overall acceptable RFI level  as defined by ITU in [51]. Depending on the considered RAO direction region, the RFI level to be realized by the SRQZ approach may be less stringent than the RFI level corresponding to the maximum zone size.
To find a single pair of TC and DC zone sizes for the considered RAO direction region, we can first consider a representative candidate points of ( l, w) in the RAO direction region and obtain their corresponding pairs of TC and DC zone sizes. For each pair, the TC and DC zone sizes are jointly selected to meet the desired RFI level to be achieved by SRQZs while minimizing the total zone surface area. Then, the assigned TC and DC zone sizes for the RAO direction region are chosen to be those with the largest zone sizes.
The above designs need to be done offline once, and the results are stored and used to generate the list of SRQZs (zone centers and zone sizes) together with their time intervals according to the RAO project schedule of the observatory. Note that if the observatory's RAO bands within a time interval are not subject to the SatCom RFI, the SRQZs need not be included in the list for that time interval.
For implementation, the above list needs to be conveyed (e.g., via an online database system) in advance to the SatCom operators, which then implement downlink muting for their satellites according to the SRQZ list. For example, each satellite obtains the SRQZ list, computes the angle between its position and each SRQZ center formed at the earth center, and if the angle is less than the zone size φ 1z , its downlink beams are muted.

V. CONCLUSION
To mitigate impending RFI from emerging mega-constellation NGSO SatCom systems to the ground RAS, we analyzed dominant RFI contributors based on the analytical RFI expression together with the system parameters/characteristics, and proposed two types of sky RQZs. Using OneWeb LEO and MEO SatCom systems as an example, we investigated peak RFI and average RFI performances without any SRQZ (φ 1z = 0 • case), with TC-SRQZ only, with DC-SRQZ only, and with TC+DC SRQZs. The RFI suppression performances of various SRQZ deployments differ according to the underlying system conditions but with an appropriate choice/setting of the SRQZ deployment, very significant RFI suppression can be achieved for both peak and average RFI. The preferred choice of SRQZ type and zone size would depend on several system parameters/conditions such as the RAS telescope location, the relative RAO target direction, and the SatCom orbital altitude and inclination. In general, TC+DC SRQZ offers the best RFI suppression performance. And the zone size φ 1z of 5 • for the OneWeb LEO SatCom system and 10 • for the OneWeb MEO SatCom system yields efficient RFI suppression. Accounting for the time-varying nature of the RAO direction, the DC-SRQZ center point needs to be accordingly updated. Such timedependent DC-SRQZ center and associated time need to be conveyed in advance to the SatCom system for its implementation. Our SRQZ approach is also applicable to co-located or distributed telescope antenna arrays by applying it to each telescope antenna and taking the union of the SRQZs. Further research directions include developing analytical RFI models for SRQZs, fine-tuning the SRQZs by jointly considering multiple RFI mitigation approaches as well as SatCom service provisioning, and adapting SRQZs according to region and time dependent SatCom traffic statistics.
The unwanted emission power P UE,i,k is computed by (23) and (24) based on NTIA emission mask and SatCom downlink subbands (see Table 1). Note that if desired, a specific SatCom transmission power spectral density (PSD) can be used to compute P UE,i,k by integrating the PSD over the RAO band of interest.
The satellites in the LOS region are identified by (18) and (19). Similarly, the satellites inside TC-SRQZ and DC-SRQZ are identified by (37) and (38), respectively. Removing the satellites inside TC-SRQZ (DC-SRQZ) from those of LOS region, we obtain the satellites that contribute to RFI for the TC-SRQZ (DC-SRQZ) only case. Removing union of the satellites inside TC-SRQZ and DC-SRQZ from those of the LOS region, we obtain the RFI contributing satellites for TC+DC SRQZ case.
For each of the RAO target direction, obtain the position vector of the virtual target on the orbital surface by (33) and (34). It also represents the DC-SRQZ center point position vector S DC .
For each RFI-contributing satellite, its transmit antenna gain angle and RAS receive antenna gain angle are computed by (35) and (36), respectively. Using these angles in the antenna gain patterns give the corresponding antenna gains.
Finally, the RFI in terms of epfd is computed by (21) for no SRQZ case, (39) for TC-SRQZ case, (40) for DC-SRQZ case, or (41) for TC+DC SRQZ case at each discrete-time instant, where RFI contributed by satellite i is obtained by (20). The peak RFI is given by the maximum epfd among all the discrete-time instants of the corresponding case. The average RFI is obtained by averaging of epfds across all the discrete-time instants of the corresponding case, which is the discrete-time implementation of (22).