Development of a Modified Link Budget for Low Earth Orbiting (Leo)-Based Land Mobile Satellite Communications System

Development of a Modified Link Budget for Low Earth Orbiting (Leo)-Based Land Mobile Satellite Communications System

1 M. B Sidiku,

1National Space Research & Development Agency, Abuja

2 S. M Sani, 2M. B Mu'azu & 2A. Mohammad 2Dept of Electrical & Computer Engineering Ahmadu Bello University, Zaria

Abstract: In this paper, a modified link budget model for Low Earth Orbiting (LEO)-based land mobile satellite communications system operating at Ku, K and Ka frequency bands is presented. The model takes into account the effect of additional loss due to Doppler frequency shift. Effect of losses due to Doppler frequency shift on satellite link budget was investigated at different satellite orbits (LEO, MEO and GEO). The results obtained show that at maximum satellite converge angle and central frequencies for Ku, K and Ka bands, the Doppler frequencies for LEO (780 km) are: 325.50 kHz, 423.20 kHz and 726.90 kHz; for MEO (20000 km) we have 88.33 kHz,

114.80 kHz and 197.30 kHz; while GEO (35786 km) stood at

55.26 kHz, 71.84 kHz and 123.40 kHz. Comparative analyses between the conventional and the modified link budget at Ku, K and Ka bands was carried out thereof. The results showed that the Carrier to Noise density ratio ( ) at Ku frequency

band dropped by 58% (from 31dB without Doppler shift to 13dB with Doppler shift). Similarly, at K band, the

dropped by 62% (from 54dB without Doppler shift to 20dB

Earths climate change, Earths imagery with high resolution and astronomical purposes (Ajayi, 2007). Low earth orbit satellites are also used for data relay and navigation as well as low-cost store-and-forward communications systems (Ajayi, 2007). This technology is currently being used for communicating with mobile terminals and with personal terminals that need stronger signals to function. Unfortunately, Satellite systems operating in LEO are inevitably affected by orbit perturbation such as Doppler frequency shift during signal transmissions between the satellite and earth stations (Ogundele, 2010). The Doppler frequency shift poses the problem of receiving higher or lower frequencies than the original transmitted frequency. The concept of Doppler frequency shift is applicable to the land mobile radio, including digital cellular transmission link (Gataullin et al., 2010). Here, the cause of Doppler effect could be due to the movement of a mobile unit or natural and constructed

with Doppler shift). At Ka band, 55% drop of

(from 85dB

obstacles (Levano, 1988 and Gataullin et al., 2010). Natural

calamities like torrential rains, raging storms, heavy

without Doppler shift to 38dB with Doppler shift) was also observed. With these, it could be concluded that Doppler shift is most pronounced at LEO orbit and therefore, should not be ignored during satellite link budget analysis; because it will give the designer an insightful view as to the amount of margins required for most efficient communication link design.

Key words: Carrier to Noise Density ratio, Doppler Frequency Shift, K, Ka and Ku frequency band, Land mobile satellite communications link budget, Low Earth Orbit (LEO), Medium Earth Orbit (MEO), Geostationary Earth Orbit (GEO)

SECTION I

1.0 INTRODUCTION

Since the launch of the first world known satellite SPUTNIK – in 1957, the world has made a tremendous progress in the course of advancing the frontiers of Space science and engineering. The use of Space environment, as many nations now recognize the strategic value and practical benefits of space asset, led to active and aggressive pursuit of space capabilities (Qingchong, 1999 and Ray, 2000). Achieving effective utilization of abundant resources that space science and technology presented could be well categorised into Global Navigation Satellite Systems, Metrological and Terrestrial System, fixed communications satellites and Low Earth Orbit Satellites Systems. LEO satellites have very wide scientific applications such as but not limited to; remote sensing of oceans, analyses of

snowfall e.t.c also cause significant Doppler effect in wireless communication (Kausik et. al, 2007). A satellite link margin prediction model used for evaluation of the performance of ASTRO Malaysia was developed by (Khairi, 2009). In (Nikolaos Tsakalozos et al., 2010), Doppler effect in both a classical and a relativistic setting were derived the input-output model by considering Doppler effect as a channel in itself and not necessarily as impairment. (Andrew et al., 2010) investigated methods of exploiting the communication link of small satellites that are required to use fixed data rates. In conjunction with global pass coverage analysis, the methods presented can help designers plan for optimal placement of ground stations and the optimal fixed data rate to use for the ground stations planned. In the work of (Shkelzen et al (2011), antenna noise temperature for Low Earth Orbiting satellite ground stations at L and S Band under the worst propagation case for a hypothetical satellite ground station implemented in different cities of Europe was presented. A software based application for satellite link budget analysis at Ka band was developed by (Mebrek et al., 2012). (Marie Rieche et al., 2014) worked on the modeling of land mobile satellite channel considering the terminals driving direction based on the channel between a satellite and a mobile terminal. In (Snehasis et al., 2014), a data sheet approach to computing the performance and link budget of LEO satellite (Iridium) for communications operated at the

frequency range 1650 – 1550MHz was presented. Similarly, (Snehasis & Barsha 2014) presented a data sheet

G(dB) 10log 109.66 f 2d 2

(2.3)

A

approach to calculating the performance and link budget of LEO satellite (Sky Bridge) communication operated at Ku band frequency range (12-14) GHz.

In a LEO satellite system, Doppler shift can be introduced in the both uplink and downlink reasons being that if not accounted for during link budget, it can invariably lead to comparatively weak signal or sometimes complete signal loss.

The rest of the paper is organized as follows: section II presents the review of the pertinent theoretical background. Section III explains the methods and materials used. Results and analysis and presented in section IV. Finally in section

Where; d = Physical diameter of the antenna,

f = Carrier wave frequency.

2.4 Link Power Equation

The received power is commonly referred to as carrier power; because most satellite links use either frequency modulation for analog transmission or phase modulation for digital transmission (Ogundele, 2010). To compute the received power at the satellite receiver input, the isotropic

power gain of the satellite antenna Gsat and any receiver

feeder losses rflmust to be taken into account (Adria, 2010);

V, we present the conclusion.

SECTION II

Pri

EIRPtpl GT

rfl dBW

(2.4)

1. CLASSICAL LINK BUDGET ANALYSIS

   A link budget is simply the addition and subtraction of gains and losses in a radio link. When the gains and losses of

   Where; = Effective Isotropic Radiated Power, tpl = Transmission path loss

   various system components are summed together, the result

   = Satellite antennae gain to temperature and rfl =

   is an estimation of the system performance in the real world (Maral, 2002). To arrive at an accurate answer, every componen or factor that contributes to gain or loss must be included. Detailed reviews of these factors are provided in the following subsections:

2. Effective Isotropic Radiated Power (EIRP)

Receiver feeder loss.

1. Figure of Merit

   The figure of merit (G/T ratio) is another parameter of interest in link budgeting used to specifying the system performance (Dennis, 2001).

   sat

   s

   EIRP describes the combination of a transmitter power and antenna gain in terms of an equivalent isotropic source with

   [G / T ]Uplin k

   G

   T (measured in dBK 1)

   (2.5)

   power Pt watts, radiating uniformly in all directions (Pratt, 2003). EIRP is expressed mathematically as (Pratt, 2003):

   EIRPUplink phpa tflUplink Ges (2.1)

   Where: [] = transmitted power, [] = transmitter to antennae line loss (feeder loss) and [ ] = transmit

   Where, G = Antenna gain of the satellite and

   Ts = System noise temperature.

2. Carrier to Noise Density Ratio

Carrier to noise density ratio ( ) is the ratio of the average

wideband carrier power to noise density (Ogundele, 2010).

antenna gain.

1. Total Transmission Path Loss ()

   C EIRPtplG T 228.6 (dB) (2.6)

   N

   sat s

   o

   The transmission path loss or tplis the summation of all the losses and it is defined as (NIIT, 2007);

   tpl fsl pl aml aal Gal Rl fl sl tp (2.2)

   Where: fsl = free space loss, aml = antenna misalignment loss, pl = polarization loss and aal = atmospheric absorption loss, Gal = gaseous absorption loss, Rl = rain attenuation, fl = attenuation caused by clouds and fog, sl = loss due to snow and tp = tropospheric attenuation.

   It is worthy to note that in conventional approach to satellite link budget analysis, the effect of Doppler frequency shift is neglected as it can be seen in equations (2.6). Furthermore, a complete communication system consists of an uplink and downlink; and the overall C / N0 ratio is the combine effect of these two (Vijitha et al, 2011). The carrier to noise ratio component of the uplink gives the carrier to noise power ratio for the link from the transmit terminal to the satellite receiver, and the carrier to noise ratio component of the downlink gives the carrier to noise power ratio for the link from the satellite antenna output to the ground receiver (Vijitha et al, 2011). The overall C / N0 is expressed as: (Vijitha et al, 2011).

   N N

2. Antenna Gain

C C

C

(2.7)

Antenna gain in dB for satellite applications is usually expressed as the dB value (Louis, 2008);

N0 Total

0 Uplink 0 Dowlink

1. Energy-Per-Bit to Noise Density Figure 3.1 shows a typical representation of a satellite

   Eb Pt Gttpl Gr 228.6 T R (2.8)

   dynamics in orbit.

   No

   s b

   V

   S

   SECTION III P

   1. METHODOLOGY

      1. Selection of key parameters.

      2. Development of a mathematical model of Doppler

         A

         Earth

         Satellite

         h

         `

         R

         rel

         Q

         `

         frequency shift

      3. Development of a modified model of a satellite link budget by including Doppler effect

      4. Simulation of the modified link budget at Ku, K and Ka bands using MATLAB R 2014a version.

      5. Comparison between the simulated modified and conventional link budgets at Ku, K and Ka bands.

      6. Validation

1. Selection of the Satellite Transmitter Power

   The power necessary for the transmission of a signal with a given level of quality depends on the method of modulation, satellite size and power limits. The high power amplifier

   Station

   R

   Sat

   R

   e

   R e

   `

   O

   Earth

   Orbit

   Figure 3.1: Typical Representation of Satellite Dynamics in an Orbit (Naser et al., 2001)

   To compute the relative velocity of the Earths terminal and the satellite, the ground station and the satellite velocity vectors must be in the same coordinate reference frame

   (HPA) in an earth station facility provides the RF carrier power to the input terminals of the antenna that, when

   (Naser et al., 2001). If Re and

   RSat

   are the position vectors

   combined with the antenna gain, yields the equivalent isotropic radiated power (EIRP) required for the uplink to

   the satellite. The output power ratings of different HPA (KPA, SSPA and TWTA) are provided in Table 3.1. For the

   of the user terminal or Earths station terminal and satellite

   respectively, then relative position of the satellite and Earths terminal is given by (You et al., 2000):

   purpose of this research work, Traveling Wave Tube Amplifier (TWTA) is used due to its linearity, efficiency and

   Rrel RSat Re

   (3.1)

   reliability. The TWTAs also gives the widest bandwidth, with the best power consumption at a cost effective price when compared to KPA and SSPA.

   The relative velocity of the satellite and Earths terminal is

   given by;

   d R

   d RSat Re

   Table 3.1: Power ratings of HPA (KPA, SSPA and TWTA) operating at Ku, K and Ka-bands (www.ATIcourses.com)

   Vrel

   rel

   dt dt

   (3.2)

   Type of Higher Power Amplifier (HPA)	Frequency Band (GHz)	Output Power (W)	Gain (dB)
   	Ku	10W-60W	45dB
   KPA	K	10W-100W	80dB
   	Ka	15W-250W	80dB
   	Ku	10W-100W	60dB 60dB
   SSPA	K	10W-120W	60dB
   	Ka	10W-120W
   	Ku	10W-700W	40Db
   TWTA	K	10W-700W	40dB
   	Ka	10W-700W	40dB

   Equation (3.2) can further be expressed in terms of

   magnitude and direction by as;

   Vrel VS Rrel

   (3.3)

   Where Rrel is the position vector of Rrel given by;

   R

   Rrel rel

   R rel

   (3.4)

   During Doppler effect, the received and transmitted signal frequencies are related by the following equation (Gataullin et al., 2010);

   Vrel fc

   fr ft fds ft C (3.5)

   Where:

   fr and ft are the received and transmitted signal

2. Development of a Mathematical Model of Doppler Frequency Shift

   Doppler frequency shift could be best computed from the geometry of the satellite dynamic in orbit. In order to accurately calculate the Doppler frequency shift, a relative velocity between satellite and ground terminal is required.

   frequencies respectively.

   fc is the carrier wave frequency.

   fds is the Doppler shift frequency.

   Vrel is the magnitude of the relative velocity between the satellite and the Earths terminal, C is the velocity of electromagnetic wave. It can be deduced from equation (3.5)

   that the Doppler shift frequency is given by (Gataullin et al., 2010);

   Vrel fc

   Where ( ) is the angle between the satellite and the line joining it with the Earths terminal.

   To compute the relative velocity between the satellite and the Earths terminal, a radial vector component of he

   satellite velocity ( Vrel ) in the direction relative to the Earths terminal is obtain by the transformation of satellite

   fds C

   (3.6)

   velocity

   Vs along line AB (lining joining the satellite and

   fds = Doppler shift frequency,

   Vrel = relative velocity of

   Earths terminal).

   the satellite and the Earths terminal sometimes called relative radial velocity between the satellite and the Earths,

   Vrel VS cos( )

   (3.11)

   fc = Carrier frequency and C = Velocity of electromagnetic

   Where VS

   is the satellite orbital velocity. Using equation

   wave. The ambiguous sign in equation (3.6) explains the scenarios where the satellite is either ascending towards horizon or receding below it with respect to the position of the Earths terminal. Figure 3.2 shown below is the

   (3.10), equation (3.11) becomes;

   Vrel VS sin

   (3.12)

   modification of figure 3.1 and was used to develop the appropriate mathematical representation of Doppler shift as the satellite sweeps over the orbit in an elliptical path.

   Substituting equations (3.8) and (3.12), the satellite radial velocity relative to the Earths terminal becomes;

   Satellite in an overhead

   V VS Re cos

   (3.13)

   position (Zero Doppler)

   `

   rel

   Re h

   vs

   Satellite sliding towards horizon

   P vs C

   h

   B

   `

   Satellite ascending above horizon

   With equations (3.13) and (3.6), the Doppler shift frequency is written as;

   `

   Q Srel

   h

   `

   A

   V R f cos

   R

   e

   User Terminal

   `

   v

   s

   O

   fds S e c

   C Re h

   (3.14)

   Earth

   Orbit

   Figure 3.2: Geometrical Representation of Satellite Orbital Dynamics

   Applying sine rule to AOB, ( ) and () are related to Earth radius ( R ) and height of the orbit ( h ) by the

   It can be seen from equation (3.14) that the Doppler shift is zero when the grazing or elevation angle, is equal to 900 . In this position, the satellite is directly overhead the Earths terminal. The relative distance between the satellite and the Earths terminal Srel is calculated from the cosine rule using

   2 1/2

   AOB as;

   rel e e e e

   S R2 R h 2R R hcos (3.15)

   e

   following equation;

   Similarly, Srel can be calculated from sine rule as;

   sin(900 ) sin

   Srel

   Re h

   (3.16)

   R h R

   (3.7)

   sin

   sin(900 )

   e e

   Hence,

   sin R e cos

   (3.8)

   cos Re h sin

   (3.17)

   Re h

   rel

   S

   Similarly, 900 ( )

   (3.9)

   Using equation (3.17), equation (3.14) is further expressed as;

   Using equations (3.8) and (3.9), the satellite coverage angle

   will be;

   fds

   VS Re fc sin

   CS

   (3.18)

   cos

   1 Re cos

   e

   R h

   (3.10)

   rel

   The magnitude of the velocity of satellite in orbit is calculated from law gravitation as (Carassa, 1989 and Valdoni, 1990);

   VS

   2 Re h T

   (3.19)

   Srel 2480.54km . Using these values and equation (3.18), the Doppler frequency shift for Ku, K and Ka bands in LEO

   Where T is the satellite orbital period. The period of the satellite can be calculated from Keplers equation as (Valdoni, 1990);

   were respectively calculated as:fdsku=325.483kHz,

   fdsk=423.129kHz and fdska=726.914kHz. The corresponding values of these frequencies in decibel are:

   fdsKu 55.125 (dB) , fdsK 56.265 (dB) and

   T 2

   Re

   p

   (3.20)

   fdsKa 58.615 (dB) . With these values, modified link budget equations at Ku, K and Ka bands can be respectively

   L written as;

   Equation (3.19) can also be written as;

   C EIRPtplG

   55.125 T 228.6 (dB)

   N Modified ( Ku )

   sat s

   V L

   (3.21)

   o

   (3.25)

   S R h

   e

   C EIRPtplG

   56.265 T 228.6 (dB)

   Where

   N Modified ( K )

   sat s

   L

   398 600 km3 sec2 3.8961014 m3 sec2

   o

   (3.26)

   (Keplers constant).

   It can be seen from equations (3.15) through (3.21) that the

   C EIRPtplG

   58.615 T 228.6 (dB)

   Doppler frequency shift depends on both the relative velocity and distance between the satellite and Earths terminal, the frequency of the carrier signal, the height of the orbit and the period of satellite on the orbit.

   N Modified ( Ka)

   sat s

   o

   (3.27)

   Eb

   Doppler frequency shift can be expressed in dB using equation (3.18) as follows;

   The modified equation for energy per noise density,

   N

   0

   using equations (2.8) with the Doppler Effect becomes;

   fds 10log VS Re fc sin 10log CSrel (dB)

   (3.22)

   Eb

   N Pt Gt Grtpl f

   ds 228.6 Ts Rb

   (3.28)

   o

3. Development of a Modified Model of a Satellite Link

The overall link budget equations taking into account the

Budget with Doppler Effect

The modified model of link budget is obtained by adding the Doppler equation in decibel to the classical link budget equation (2.6). The modified link budget equation is

C

effect of Doppler in terms of

N0

and down link can be written as;

and

Eb for both uplink

N0

expressed as;

C Pt

Gt

Gr

tpl f

228.6 T

N Modified

C

o

EIRP fsl pl aml aal Gal Rl fl sl tp fds

No Up link

C

ET ET Sat

ds Sat

(3.29)

sat

G

Ts 228.6

(3.23)

No Down link

Pt Gt Gr tpl fds 228.6 TET

Sat Sat ET

(3.30)

Where;

Eb

Pt

Gt Gr

tpl f

228.6 T

R

f 10log V R f

sin 10log CS

(dB)

No Up link

ET ET Sat

ds Sat

b

ds

S e c

rel

and; tpl fsl pl aml aal Gal Rl fl sl tp

(3.31)

Eb

Pt Gt Gr

tpl f

228.6 T R

Therefore equation (3.23) becomes;

No

Down link

Sat Sat ET

ds ET b

Modified ds sat s

C EIRPtpl f G T 228.6

N

(3.24)

(3.32)

The total carrier to noise density ratio is the summation of

o

As an illustration, Doppler effect was calculated at minimum grazing or elevation angle and the corresponding maximum satellite coverage angle,

equations (3.29) and (3.30). Similarly, the summation of equations (3.31) and (3.32) yields the total energy bit to noise density ratio. The two parameters are expressed as;

( 20.070 and

80 ) (Carassa, 1989) using the

C

Pt

Gt Gr Pt Gt Gr

min max

No Total

ET ET sat sat sat ET

1

e

following values: VS 7377.57 ms , R 6378km ,

T T 2tpl f 457.2

h 780km , fc (15.0GHz, 19.5GHz and 33.5GHz) and

sat ET ds

(3.33)

Eb Pt

Gt Gr Pt Gt Gr

4.1.2 Variation of Carrier to Noise Density Ratio with

No Total

ET ET sat sat sat ET

Tsat TET 2tpl fds Rb Rb 457.2

Transmission Path Loss at K-Band

(3.34)

The modified total path loss is thus;

tpl

Total

tp fds

SECTION IV

1. RESULTS DISCUSSION

   (3.35)

2. Variation of Carrier to Noise Density Ratio with Transmission Path Loss

In order to investigate the effect of Doppler frequency shift on the carrier signal, the overall carrier to noise density ratio

Figure 4.3:

against the Transmission Path Loss at K- Band

0

was plotted against the total transmission path loss at Ku, K

and Ka bands with and without the Doppler frequency shift. This relationship is depicted in Figures: 4.2, 4.3 and 4.4; which were obtained using equations: (2.6), (2.7), (3.33), (3.23) and the data in Table 3.1.

4.1.1 Variation of Carrier to Noise Density Ratio with Transmission Path Loss at Ku-Band

0

Figure 4.2: against the Transmission Path Loss at Ku-Band

From Figure 4.2 it can be seen that there is considerable decrease in carrier to noise density ratio. When the Doppler frequency shift was introduced, an appreciable decrease in

From Figure 4.3, excluding the Doppler frequency shift, carrier to noise density ratio decreases from 80dB to 40dB with corresponding increase in the total transmission path loss from 223dB to 261dB as indicated by the green line graph. With the inclusion of Doppler frequency shift however, a significant lowering of the value is seen with the carrier to noise density ratio plummeting from 33dB to 17dB (58.75% at 223dB transmission path loss and 57.5% at 264dB transmission path loss).

4.1.3 Variation of Carrier to Noise Density Ratio with Transmission Path Loss at Ka-Band

0

was observed. At 158 dB transmission path loss for

Figure 4.4: against the Transmission Path Loss at Ka-Band.

0

instance, the 0without the Doppler effect is 38 dB. This

0

value reduces by 41.67% (19 dB) with the inclusion of Doppler frequency shift. Similarly, the same scenarios were observed at both K and Ka bands (see Figures 4.3 and 4.4).

As it is illustrated in Figure 4.4 the carrier to noise density ratio decreased from 110dB at 271dB transmission path loss to 94.05dB at 304.9dB transmission path loss without the effect of Doppler frequency shift. When Doppler frequency shift was included, there was a significant fall in by

50.9% and 56.4% at 273dB and 312.9dB respectively.

4.2 Modified Link Model Validation

The modified model developed was validated through comparison with the work of Snehasis & Barsha (2014). The graphical plots obtained thereof were shown in Figures 4.5,

4.6 and 4.7. These figures further confirmed that with the inclusion of impairment due to Doppler frequency shift, there was a significant decline in carrier to noise density ratio when compared with the corresponding values obtained without the Doppler frequency effect (using conventional model).

0

Figure 4.7: Variation of with Transmission Path Loss at Ka-Band

The results at Ka band follows a similar pattern when compared with that observed in the Ku and K band. The

0

for Ka frequency band dropped by 55% (from 85dB

0

Figure 4.5: Variation of with Transmission Path Loss at Ku-Band

0

From Figure 4.5, it can be seen that at transmission path of 160dB for example, the Carrier to Noise density ratio for Ku frequency band dropped by 58% (from 31dB without Doppler shift to 13dB with Doppler shift).

without Doppler shift to 38dB with Doppler shift).

SECTION V

5.0 CONCLUSION

A detailed approach to the development of modified link budget for land mobile satellites communication systems was presented. The model took into account the additional impairment due to Doppler frequency shift, which is often neglected in the conventional satellite link budget model. The effect of losses due to Doppler frequency shift on satellite link budget was investigated at Ku, K and Ka bands.

Comparative analyses between the conventional (without Doppler shift) and the modified link budget (with the inclusion of Doppler shift) at Ku, K and Ka bands was achieved thereof. The results obtained show the Carrier to

0

Noise density ratio

for Ku frequency band dropped by

58% (from 31dB without Doppler shift to 13dB with

0

Doppler shift). The for K frequency band dropped by

62% (from 54dB without Doppler shift to 20dB with Doppler shift). The results at Ka band follows a similar pattern when compared with that observed in the Ku and K

0

band. The for Ka frequency band dropped by 55%

0

Figure 4.6: Variation of with Transmission Path Loss at K-Band

0

0

At K band, a considerable reduction in carrier to noise density ratio, is seen. The for K frequency band dropped by 62% (from 54dB without Doppler shift to 20dB with Doppler shift).

(from 85dB without Doppler shift to 38dB with Doppler

shift). It can be seen from the results obtained that with Doppler shift, Carrier to noise density ratio is worse when compared to the values obtained by snehasis and Barsha.

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