The unintentional radio frequency interference (RFI) from ground radars has not been a concern for the link performance of a geostationary satellite system because, as compared to the desired signal power, the received interference power has been negligible. In recent years, however, due to the adoption of advanced communication techniques, the uplink signal power level at a satellite needed to achieve reliable data transmission has become smaller and smaller. Therefore, the effect of RFI from ground radars may not be ignored. This paper illustrates an approach to assess the impact of such RFI on a geostationary satellite. A commonly used scanning pattern is utilized to compute the spatial probability of interference for azimuthal scanning radars. Several factors in geography, frequency, power, and time (due to pulse repetition frequency) are considered as well. This paper presents a good and realistic RFI analysis methodology to evaluate the impact of ground radars to a satellite uplink.
INTRODUCTION
For satellite communications, especially for geostationary Earth orbit (GEO) satellites, the radio frequency interference (RFI) from ground radar sources has never been a concern. This is due to the fact that the received interference power from ground radars at the geostationary orbit is far below the power level of the desired signal so as not to cause any noticeable performance degradation. But, in recent years, numerous advanced communication technologies such as phased-array antennas, turbo coding, space-time diversity, etc., have been or will be implemented in satellite communication systems. With these technologies, reliable data transmission can be achieved with a very low signal-to-noise ratio (SNR). This implies that the uplink becomes more susceptible to RFI from ground radars. This paper presents a systematic approach to assess the impact of such RFI on a
GEO satellite uplink. Our approach considers various factors, including geographic location, cell distribution (for spot beam antennas), frequency, power, spatial relationship within the scanning frame, and temporal spread of radar pulses.
MODELING A SCANNING RADAR
The most commonly used radar is azimuthal scanning radar. In order to achieve high power-efficiency, this type of radar uses a narrow beam antenna. The antenna pattern can be modeled as
G(θ)=2[J1(αθ)/αθ]2 (1)
where J1(θ) is the Bessel function of the first order and α is a constant such that the one-sided 3-dB beam width can be specified at a particular angle θ. Figure 1 shows the antenna pattern as a function of the normalized angle (α=1) in degrees. The one-sided 3-dB beamwidth of a radar is typically from 1º to 3º. Throughout this paper, the “beamwidth” is always referred to as the one-sided 3-dB beamwidth unless otherwise specified.
Figure 1. Normalized Antenna Gain Pattern for a Scanning Radar
In order to cover a relatively large spatial area, the radar antenna scans, by either mechanical or electronic means, azimuthally back and forth with elevation starting from the horizon up to some maximum elevation angle ϕmax (or from an elevation to the horizon). Because the nature of radar is to detect any low-flying objects, the elevation angle of the scanning region (referred to
Angular Offset x, Degrees
0
0.2
0.4
0.6
0.8
1
-5 -3 -1 1 3 5
No
rmal
ized
An
tenn
aG
ain
G(x
)
Null atTmax = 3.83
3dB Beamwidth at x = 1.62
Angular Offset x, Degrees
0
0.2
0.4
0.6
0.8
1
-5 -3 -1 1 3 5
No
rmal
ized
An
tenn
a G
ain
G(x
)
Null atTmax = 3.83
3dB Beamwidth at x = 1.62
20th AIAA International Communication Satellite Systems Conference and Exhibit12-15 May 2002, Montreal, Quebec, Canada
American Institute of Aeronautics and Astronautics
2
as the scanning frame) usually has an upper limit. The typical spatial frame of an azimuthal scanning radar is from the horizon (0º) to 33º in elevation and –150º to 150º in azimuth as shown in Fig. 2. The coordinates in Figure 2 are in angles. Figure 2 also indicates the radar scanning paths. Let us assume that the horizontal scanning lines are equally spaced across the elevation. Therefore, the scanning strips, i.e. the area the radar covers with one horizontal sweep, between adjacent horizontal scans may overlap and the angular separation (AS), θs, between two adjacent lines is not necessarily 2 times the beamwidth. Table 1 lists, for beamwidths of 1º, 2º, and 3º, the numbers of scanning lines, θs, and maximum angles, θmax, below which there is always antenna gain.
Because the scanning frame is upper-limited by θmax, when the radar is located too close to the nadir point of the satellite, the radar cannot view the satellite (within its scanning frame). Figure 3 shows that when the radar is located at the leftmost position, it is impossible for the radar to interfere with the satellite. Therefore, there essentially exists an “RFI-Free Zone” (RFZ) centered at the nadir. The radius of RFZ is
)]cos(sincos[ max1
max ϕϕGEO
ee R
RRr −+= (2)
where Re and RGEO are radii of the Earth and geostationary orbit (measuring from the center of the Earth), respectively. Any radar located within the RFZ shall be excluded from being considered as potential interferers. Figure 4 is a ground map of RFZ associated with a GEO satellite located at 25ºE.
Figure 3. RFI-Free Zone (RFZ)
Figure 4. Typical Ground Map for RFZ
Cell Consideration
When the spot beam antenna is utilized, the footprint (referred to as the “cell”) of each beam needs to be identified. Potential interfering radars need to be sorted according to cell numbers. The purpose of this screening process is to associate a particular free space loss (Ls) with a cluster of radars located within the same cell. Typically, the size of a cell is small so that the difference of Ls at different locations within the same cell is negligible as compared to the loss itself. Therefore, it is a
Azi
mu
th =
150q
Horizon Elevation = 0q
Elevation = 33qA
zim
uth
= 1
50
q
Scanning FrameScanning Frame
Radar Trace Path
sθRadar Beam
Tmax
Azi
mu
th =
150q
Horizon Elevation = 0q
Elevation = 33qA
zim
uth
= 1
50
q
Scanning FrameScanning Frame
Radar Trace Path
sθRadar Beam
Tmax
25oW 0o 25oE 50o E 75o E
50oS
25oS
0o
25oN
50oN
RFZfor 33°
25oW 0o 25oE 50o E 75o E
50oS
25oS
0o
25oN
50oN
25oW 0o 25oE 50o E 75o E
50oS
25oS
0o
25oN
50oN
RFZfor 33°
Victim Satellite
ϕmax
ϕmaxϕmax
RFI Free Zone
Victim is in the Scanning Frame
Victim is NOT in the Scanning Frame
Horizon
r
To the center of earth
Victim Satellite
ϕmax
ϕmaxϕmax
RFI Free Zone
Victim is in the Scanning Frame
Victim is NOT in the Scanning Frame
Horizon
r
To the center of earth
American Institute of Aeronautics and Astronautics
3
good approximation that the Ls associated with the center of the cell is applied to all radars within the same cluster. The free space loss is given by
Ls=(4πD/λ)2 (3)
where D is the slant path distance between the satellite and the center of the cell of interest, and λ is the wavelength of the interfering carrier.
Frequency Consideration
The carrier of the radar signal may or may not be spectrally located within the frequency band of the victim satellite. In either case, the interference power within the victim band shall be computed. Assuming the radar signal is a stream of rectangular pulses, the normalized interfering power (normalized to the total radar power) within the victim band is, as shown in Figure 5,
dffTcinTPBf
Bf dd∫+∆
−∆⋅= )(s 2
0 (4)
where B is the one-sided frequency band of the victim, ∆f is the center frequency offset between victim and interferer, and sinc(x)≡sin(x)/x is the PDF of rectangular pulses.
Figure 5. In-Band Interference Power
Power Consideration
The interference power is the aggregate power collected at the front end of the satellite’s low noise amplifier (LNA) from all interfering ground radars. The received interference power Pint from each radar source can be expressed as
Pint=Ppeak/(LTLR)=(PTXP0GTmaxGRmax)/Ls/(LTLR) (5)
where PTX is the transmit power of radar signal, GTmax and GRmax are the transmit and receive antenna boresight gains, respectively, and LT and LR are the antenna gain losses due to off-boresight angles for the transmit and receive antennas, respectively. Depending on the type of concern, e.g., damage to satellite LNA or bit-error-rate (BER) degradation, the aggregate interference power is compared against a threshold.
Now let us proceed with a worst-case analysis for which the victim satellite receives multiple interfering signals, all temporally aligned. Furthermore, assume that the satellite is spatially
aligned with the scanning line, and that all ground radars have the same transmit power. Based on the threshold used, the minimum number of radars required, Nmin, for the aggregate interference power to exceed the threshold can be identified:
Nmin=smallest N such that N⋅Ppeak > threshold
Depending on the number of interferers n (>Nmin), the exceeding power Pexc allocated to each interferer can be calculated as
Pexc = (n⋅Ppeak − threshold)/n (6)
Spatial Consideration
Even though the victim satellite is in view of a scanning radar, the radar does not illuminate the satellite for the entire scanning frame. Now, we proceed to calculate the spatial probability of interference conditioned on the victim satellite being in view of a ground radar. Figure 6 illustrates that the only time period the radar can illuminate the victim satellite is from point a1 to a2, when the victim is within the antenna beamwidth θmax. Therefore, the time duration that the radar illuminates the victim is
)ondssecin(/2 22max Ω−=∆ ha θ (7)
where h is the angular distance from the victim satellite to the scanning line of interest and Ω is the radar’s angular speed. It can be seen that this “illumination interval” can occur more than once per frame, depending on the relative distance from satellite to the scanning lines.
Figure 6. Illumination Interval
As the antenna scans the entire frame, the magnitude of the received power from a single radar can create multiple humps, as illustrated in Figure 7. Based on Pexc, the interference threshold THRint allocated to each interferer, above which the power (from each individual
Victim
a1a2
h
a1: time instance that radar beam touches ESa2: time instance that radar beam leaves ESh: nearest angle between ES and the tracking lineθmax: at the null of radar antenna pattern
∆a
Angular speed = Ω (°/sec)
Tmax
Radar Beam
Victim
a1a2
h
a1: time instance that radar beam touches ESa2: time instance that radar beam leaves ESh: nearest angle between ES and the tracking lineθmax: at the null of radar antenna pattern
∆a
Angular speed = Ω (°/sec)
Tmax
Radar Beam
PDF of Interfering Radar
f
PDF of Interfering RadarVictim Band
f
∆f
PDF of Interfering Radar
f
PDF of Interfering RadarVictim Band
fff
∆f
American Institute of Aeronautics and Astronautics
4
interferer) will result in the aggregate interference exceeding the threshold, is
THRint = Ppeak − Pexc (8)
Figure 7. Profile of Interference Power
The time duration from b1 to b2 shown in Fig. 7, during which the power exceeds THRint, represents the actual interference interval. Let px(h) denote the probability of the satellite being interfered with by an individual radar when there are a total of n interfering radars, given a satellite location being h degrees away from the nearest scanning line. Then,
∑∑ −=∆= ffx TbbTbhp /)(/)( 12 (9)
where the summation is over all possible interference intervals from multiple humps in Fig. 7 and Tf is the time period of a scanning frame. Ignoring the boundary condition, the probability of interference by a single radar, pn, can be obtained by averaging px(h) over h=[−θs,θs], that is,
∫−= s
s
dhhpp xs
n
θ
θθ)(
2
1 (10)
The reason why pn is a function of n is that THRint depends on n and, consequently, ∆b depends on
n as well. Therefore, the probability of spatial interference conditioned on a total of n radars causing power exceedance can be determined as
=
thresholdexceed power toenough
with alignedspatially radars ),(Pr max
nPNnsp
nNn
nn pp
n
N −− −
= max)1(1max (11)
where Nmax is the number of radars within the same cell that can view the victim satellite.
Temporal Consideration
A typical radar signal is a continuous stream of pulses with pulse width PW and pulse repetition frequency PRF, as shown in Figure 8. Assume that scanning phases and pulse train phases of all radars are independent and identically uniformly distributed. Therefore, the probability that i radar signals are temporally aligned given n spatially aligned radar beams is
=
alignedspatially arebeamsradar n
alignedy temporallare signalsradar ),(Pr
iPnitemp
int
it pp
i
n −− −
= )1(1
(12)
where pt = PW⋅PRF.
Figure 8. A Typical Radar Signal
Probability of Satellite being Interfered
The victim satellite is actually interfered with when Nmin or more radar signals hit the satellite concurrently. Therefore,
________________________________________
∑=
=
max
min thresholdexceed power toenough with
alignedspatiallyandy temporallareradars )Pr(
N
Nn
nPexceededisthresholdthe
( )∑=
⋅
=
max
min
alignedspatially areradars alignedspatially areradars thresholdexceed power to
enough with alignedy temporallareradars moreor minN
Nn
nPn
Np
( )∑ ∑= =
⋅
=
max
min min
alignedspatially areradars alignedspatially areradars thresholdexceed to
powerenough with alignedy temporallareradars N
Nn
n
Ni
nPn
iP
0.4995 0.5 0.5005
0
0.2
0.4
0.6
0.8
1
0.441 0.442 0.5586 0.5588 0.559
Time (Normalized to Frame Time)
No
rmal
ized
Inte
rfer
ence
Po
wer
Threshold
a1 a2
b1 b2
b1: starting time for theinterference interval
b2: ending time for the interference interval
0.4995 0.5 0.5005
0
0.2
0.4
0.6
0.8
1
0.441 0.442 0.5586 0.5588 0.559
Time (Normalized to Frame Time)
No
rmal
ized
Inte
rfer
ence
Po
wer
Threshold
a1 a2
b1 b2
b1: starting time for theinterference interval
b2: ending time for the interference interval
PW
1/PRF
PW
1/PRF
American Institute of Aeronautics and Astronautics
5
∑ ∑=
−−
=
−− −
⋅
−
=
max
min
max
min
)1()1( 1max1N
Nn
nNn
nn
n
Ni
int
it pp
n
Npp
i
n (13)
_________________________________________
AN EXAMPLE
Let us consider an example where the received isotropic power (RIP) at a GEO satellite from a potential interfering ground radar within a cell of interest is, after satellite front-end filtering, –173.7 dBW. Assuming a bandwidth of 250 MHz, the received Ppeak at the victim satellite from an interfering radar is –257.7 dBW/Hz. The threshold considered is –252 dBW/Hz and the maximum number of radars located in a cell that can view the victim satellite is Nmax = 30. Assume that the radar’s pulse width is 1 µsec, the pulse repetition frequency is 1 kHz, and the scanning rate is 12 frames per minute. The scanning frame considered is 0º to 33º in elevation and –150º to 150º in azimuth.
We have developed a program to evaluate pn based on which Prsp(n,Nmax) can be calculated. It can be seen that Nmin=4. Table 2 shows pn and Prsp(n,30) for n≤15 with an antenna beamwidth of 3º.
Using Eq. 13, as given in Table 3, we can compute the probability that the aggregate RIP exceeds the threshold. Note that the values for n=16 to 30 are not shown since they can be neglected.
In this paper, we have presented an approach to analyze the potential RFI from ground radars to a GEO satellite. This approach has considered several factors: geographic position, cell distribution, frequency, power, spatial relationship within the scanning pattern, and temporal spread of pulses.
ACKNOWLEDGEMENT
The authors want to acknowledge Miss Florence Wong for her contribution of developing computer program that leads the results described in this paper.
