IEEE - Aerospace and Electronic Systems - August 2022 - 10

Maximization of LEO Nanosatellite's Transmission Capacity to Multiple Ground Stations
Table 3.
MAC Characteristics
Parameter
Source frequency
Output wave power
FWHM
Figure 5.
Satellite's access sequence to the site.
where frS/Cg and frGSi
g are the position vector of the S/C
and the ground telescope in the ECI coordinate system,
respectively . The secondary alignment vector f^xS/Cg of
the S/C is in the plane of the orbit and perpendicular to
f^zS/Cg axis, in the direction of S/C travel. The f^yS/Cg
axis completes a three-axis right-hand orthogonal system.
Then it is possible to define the direction cosine matrix
½RS/C
input attitude quaternion fqECIg.
iii) A time interval equal to Dtm before coming into
the ith site access area, the S/C starts the alignment
maneuver. To connect the nadir pointing configuration to
the ground telescope pointing, a spline interpolating curve
with tangent ends has been used [31]. Since the spline
interpolation does not give unit quaternions, they have
been normalized after the interpolation. Spline interpolation
with tangent ending points allows angle profiles with
C2 continuity over time, which is advantageous to have a
ground telescope smooth tracking since the entry of the S/
C into the telescope field of view.
iv) The components of the input body frame's angular
velocity fvx; vy; vzg are retrieved using the derivative of
a quaternion [32]
d
dt
fqg¼ ½Vfqg
1
2
where
½V¼ 4 vy
2
6
6
vz
vz
vx
vy vx
vx vy
vxvyvz 0
3
7
7
0 vz 5:
(7)
(6)
Value
150 GHz
20 mW
2.80
vi) The RW torque required to perform the maneuver
has been estimated by using the Euler's equations [32],
which describe the rigid body dynamics
½IS/Cf _vgþfvg½IS/CfvgþfvgfhRWg
¼fTRWg:
ECI2 SOð3Þ of the satellite's attitude relative to the
ECI frame: ½RS/C
ECI¼ ½f^xS/Cg; f^yS/Cg; f^zS/Cg and the
RESULTS AND DISCUSSION
RESULTS OF SIGNAL DETECTABILITY
In order for the calibration signal to be identifiable, it was
considered that the SNR must be greater than 30 dB.
Moreover, the pointing accuracy of the polarized calibrator
toward the receiving telescope shall be sufficient so
that the signal attenuation is not greater than 50% compared
to the ideal pointing conditions. These requirements
affect the minimum elevation for which the MAC signal
is useful for calibration purposes and the pointing accuracy
needed by the calibration satellite AOCS system.
To calculate the expected SNR, MAC calibrator characteristics
have been used (see Table 3). The calibrator is
(9)
v) Considering that the wheel has no stored angular
momentum yet, the maximum momentum storage
required by the RW is given by the following equation:
fhRW;maxg¼½IS/Cfvmaxg
(8)
where vmax is the maximum angular velocity of the satellite
and where ½IS/C¼ diagðJx;Jy;JzÞ is the S/C inertia
matrix.
10
Figure 6.
SNR of the calibration signal as a function of the radio telescope
aperture, tested orbits, and CubeSat elevation as seen by the TUT.
The noise rms is equal to 6 105 pW, a 1 s of integration with
telescope bolometer NEP equal to 6 1017 W/Hz0:5 has been
assumed.
IEEE A&E SYSTEMS MAGAZINE
AUGUST 2022
IEEE - Aerospace and Electronic Systems - August 2022

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