Linearized Mathematical Modelling of Integrated Baseband
Equipment of Satellite Ground Control Station
*Ogundele D.A. and **Adediran Y.A.
*National Space Research and Development Agency
Obasanjo Space Centre, Airport Road, Lugbe, Abuja, Nigeria
**Federal University of Technology, Minna, Nigeria
*delesolad@yahoo.com, **yinusaade@yahoo.com
satellites when they pass by the ground station
horizon[3].
ABSTRACT
Integrated
Baseband
Equipment
(IBBE) is located at the center of Satellite
Ground Control Station and it is responsible
for the processing of the information bearing
(baseband) signal; it is a high speed digital
equipment which provides signal processing
functions. IBBE, being integrated, enables the
processes carried out by it to share
information and initiate actions, thus allowing
decisions to be made faster and with fewer
errors.
In this
paper, the linearized mathematical models of
various components of Integrated Baseband
Equipment of a Satellite Ground Control
Station are presented. The non-linear system,
Integrated Baseband Equipment (IBBE), is
linearized assuming small signal conditions
and using ordinary differential equations
which can be easily modelled and solved
using standard methods. The linearization is
carried out in order to reduce the effects of
noise and interference.
I.
Satellite
RF
Antenna
TM Data
RF Subsystem
IF
Integrated Baseband
Ranging Data
Equipment
(IBBE)
Satellite Control
Center
(SCC)
Station Computer
Figure 1
Station Clock
Remote M & C
TC Data
Timing &
Frequency
Subsystem
(TFS)
Satellite ground control station
Satellite ground control station is made
up of six main subsystems and they are:
Antenna subsystem, RF subsystem, Integrated
Baseband Equipment, Satellite Control Center
(SCC), Monitoring and Control Subsystem
(MCS) and Time and Frequency Subsystem
(TFS). Figure 1 shows satellite ground control
station. The main functions of each of the
subsystems of satellite ground control station
shown in Figure 1 are as follows:
1. Antenna subsystem: Provides the vital
link between the ground and the
INTRODUCTION
Satellite ground control station is the
hub of a satellite communications system or
an unmanned aircraft system[1]. It consists of
ground station and control center working
together to support the spacecraft and the data
users[2]. The ground station performs like a
communication bridge between the satellites
and the ground, sending commands to
satellites as the ground center requests and
receiving the telemetry feedback data from
1
satellite, and maintains accurate
pointing between earth station and
satellite.
2. Radio-frequency (RF) subsystem: It is
made up of receiving side and transmit
side. On the receiving side, it contains
low noise amplifying equipment for
routing the received carriers to the
demodulating channels; on the
transmitting
side,
it
contains
equipment for coupling the transmitted
carriers and power amplifiers.
3. Integrated Baseband Equipment
(IBBE): It is the interface between the
SCC and the RF subsystem and it is
responsible for telemetry reception,
satellite telecommand transmission and
satellite
ranging
(distance
measurement).
4. Time and Frequency Subsystem
(TFS): It synchronizes the time of all
the equipment in the ground control
station.
5. Monitoring and Control Subsystem
(MCS): It monitors and displays
ground
station
equipment
configurations and status.
6. Satellite Control Center (SCC): It is
the ground operation decision centre of
any satellite mission; it ensures that the
satellite performance is kept high right
away from its injection up to the end
of its life.
From the papers reviewed, it was
discovered that there are no mathematical
details of the baseband equipment, thereby,
necessitated the development of a linearized
mathematical model of the system.
Figure 2. Each of the components is modelled
and linearized as shown below.
(a) Main Receiver:
The main receiver receives, from the
down converter of the RF subsystem, IF sum
signal
which is expressed as
where,
signal,
wave
input Phase Modulated (PM)
= center frequency of the carrier
= modulation index of telemetry
sub-carrier,
= initial phase of the
carrier
= modulation index of ranging
sub-carrier
= telemetry sub-carrier signal,
= ranging tone sub-carrier
Main receiver is made up of the IF
Channel and Costas loops. The IF channel
adjusts the amplitude of the IF signal and
filters the noise. Costas Loop performs
synchronization and tracking of the carrier; it
is made up of in-phase branch, quadrature
phase branch, low pass filters, phase detector,
loop filter and Numerically Controlled
Oscillator (NCO).
In-phase branch mixes in-phase carrier
signal generated by the local NCO and the
input carrier signal, and filters the sum signal
through low pass filter. The local in-phase
signal generated by NCO is
II.
LINEARIZED
MATHEMATICAL MODEL OF
INTEGRATED BASEBAND
EQUIPMENT (IBBE)
while
the
input
PM
signal
is,
The mathematical modelling of the mixture of
and
by the in-phase branch
is
The components of Integrated Baseband
Equipment are inter-related as shown in
2
The mathematical modelling of the mixture of
and
by the quadrature-phase
branch is
Satellite
Simulator
Low pass filter removes the sum item and the
resulting quadrature phase signal is,
Simulated
TM Subcarrier
IFΣ = s(t) = Acos
[ω1t+kp1m1(t)+kp2m2(
t)+θ1]
Telemetry
Receiver
Main
Receiver
TM Sub-carrier
Sk(t) = g(t – kTs) cos
(ωct + Ψk)
R Sub-carrier
m2(t)
TM Subcarrier
m1(t)
IFΔ= ΔAcos (ω1t + Ø) +
ΔEsin (ω1t + Ø)
Tracking Receiver
Simulated
TM Subcarrier
Telemetry
Processing
Ranging
Unit
Telemetry
Processing
TM
Data
where,
To satellite control center
TM IF signal
Ranging Data
(Phase
Difference)
After filtering,
produced
follows
TM Data
Ranging Tone
Generator
El = ΔE A0 cos (Δ Ø)
TC Subcarrier
Az = ΔA A0 cos (Δ Ø)
IF
Modulator
TC Frames
Telecommand
Unit
TC Frames
From satellite control center
To antenna control unit
Ranging Tones
Sub-carrier
.
produces
and
They are expressed as
and
enter the carrier phase
detector unit and complete the acquisition of
phase error,
Telemetry
Simulator
Agc
Lock
and
The linearization of main receiver is carried
out assuming
Then,
Time and Frequency
Subsystem (TFS)
Integrated Baseband Equipment
(IBBE)
is linearized as follows using eqn.
(12),
Figure 2
Inter-relationship among
different components of Integrated
Baseband Equipment
If
, the output
of
quadrature branch only consists of telemetry
sub-carrier and ranging tone sub-carrier
signal, and no phase error information exist.
Low pass filter removes the sum item and
produces the in-phase signal
Quadrature phase branch mixes the local
quadrature carrier signal generated by the
local NCO and the input carrier signal, and
filters the sum signal through low pass filter.
The local quadrature signal generated by NCO
is
(b)
Tracking Receiver:
The tracking receiver is made up of IF
Channel and Costas loop. The IF Channel and
Costas loop of tracking receiver performs the
same function as those of main receiver.
In-phase branch mixes input IF signal (
and the local in-phase signal generated by the
in-phase branch {
. The input IF signal
(
is given as
The input carrier signal is,
3
where，
= azimuth error signal and
=
elevation error signal.
The local in-phase signal generated by the inphase branch is given as
The
mixture of
mathematical model of
and
is given as
The low-pass filter removes the sum item and
produced the signal
the
Taking
(because the baseband signal
has a value near zero) and eliminating the
non-quadrature component we have,
The low-pass filter removes the sum item and
produces the signal
In order to get the exact azimuth and elevation
information, the residual phase offset
must
be eliminated. The automatic calibrate phase
is used to get
The linearization of tracking receiver is
carried out assuming
. Then,
where,
= phase offset information
between sum and error channel
= quantizing amplitude of local
carrier signature.
Taking
(because the baseband signal
has a frequency near zero) and eliminating the
non-quadrature
component
we
hav
can be linearized as follows using
Eqn. (28)
(c)
Telemetry Receiver:
IF signal is received by the telemetry
receiver from down converter of the RF
subsystem and it is expressed as
The linearization of tracking receiver is
carried out assuming
Then,
where,
= carrier’s phase of the data k,
angle frequency of carrier
= period of data,
= waveform of the modulated signal’s
envelope.
The linearization of telemetry receiver is
carried out assuming
Then,
is linearized as follows using Eqn.
(20)
Quadrature phase branch mixes the input IF
signal {
and quadrature signal
.
The quadrature signal
is given
as
The input IF signal is given as
can be linearized using Eqn. (31) as
The mathematical model of the mixture of
by the quadrature mixer is
follows
4
If
the
antenna
is
a
transceiver
then
and then
(d)
Telecommand Unit:
Telecommand unit receives Phase
Shift Keying (PSK) modulated telecommand
sub-carrier
signal
expressed
as
(f)
IF Modulator Unit:
IF modulator performs FM and PM
modulation. Its frequency is adjustable
between 68 and
. The time domain
expression of FM (e.g. ranging signal) signal
is
The linearization of telecommand unit is
carried out assuming
Then,
is linearized using Eqn. (34) as
follows
(e)
Ranging Unit:
The ranging unit processes the ranging
tone sub-carrier signal. Tone is a single
frequency sine wave signal given as
Let,
The FM signal could be expressed as
quadrature
vector
as
follows
Expression of PM Modulation signal (e.g.
telemetry and telecommand signal) is
The linearization of ranging unit is carried out
assuming
Then,
Let
Then,
37 as follows
can be linearized using Eqn.
, then
III. TESTING OF THE MODEL
The distance (S) between the launching and
receiving point is given as
The Integrated Baseband Equipment of
Satellite Ground Control Station of Nigeria
Communications Satellite uses two types of
ranging tones: major tone (27.778kHz) for
accurate distance measurement and minor
tones (3.968kHz, 283Hz, and 35Hz) for
ambiguity resolution Using Eqn. 40 and taking
the phase difference to be
, the range of
Nigeria communication satellite can be
calculated as
where,
distance between the satellite ground
control station and object
distance between the satellite and
satellite ground control station
= phase delay and
wavelength,
=
angular frequency
5
[4] “Integrated baseband equipment for TT &
C
stations.”
Available
at
http://www.thalesaleniaspace.com.
The value of range obtained using the
mathematical model developed,
is very close to the value of range of Nigeria
communication satellite given as
IV. CONCLUSIONS
The linearized mathematical model of
Integrated Baseband Equipment developed
gave a detailed description and mathematical
representation of the system. The system
modelled is an effective training tool which
will give the Satellite Ground Control Station
(GCS) operator the experience necessary to
handle and operate it effectively. In this paper,
every block of the system modelled was
individualy linearized in order to reduce the
effects of noise and interference on the
system. The result obtained by modelling is
nearly equal to the standard value of range.
ACKNOWLEDGEMENT
We would like to acknowledge National
Space Research and Development Agency
(NASRDA), Nigeria who sponsored this
research work and the academic staff of
Electrical
and
Computer
Engineering
Department of Federal University of
Technology, Minna, Nigeria who gave moral
support and advice in the course of writing
this paper.
REFERENCES
[1] S. A. Philip, “Development of an
unmanned aerial vehicle (UAV) ground
control station”, ;.Linköping University,
2002, pp. 1 – 92.
[2] R.W. James and J.L. Wiley, Space
mission analysis and design, Microcosm
Press, Third Edition, United States, 1999.
[3] B.G. Evans, Satellite communication
systems, The Institution of Electrical
Engineers, London, 1990, pp. 68 – 260.
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