W. Tomasi - Pp

Eb

No

= 52 x !i N

fb

The E,jNo ratio is the product of the carrier-to-noise ratio (GIN) and the noise bandwidth-to-bit rate ratio (B/fb).Expressed as a log, Eb (dB) = G (dB) No N

+!i fb

(dB)

(7-6)

The energy per bit (Eb) will remain constant as long as the total wideband carrier power (C) and the transmission rate (bps) remain unchanged. Also, the noise density (No) will remain constant as long as the noise temperature remains constant. The following conclusion can be made: For a given carrier power, bit rate, and noise temperature, the E,jNo ratio will ~main constant regardless of the encoding technique, modulation scheme, or bandwidth used. Figure 7-17 graphically illustrates the relationship between an expected probability of error P(e) and the minimum GIN ratio required to achieve the P(e). The GIN specified is for the minimum double-sided Nyquist bandwidth. Figure 7-18 graphically illustrates the relationship between an expected P(e) and the minimum E,jNo ratio required to achieve that P(e). A P(e) of 10-5 (1/105) indicates a probability that 1 bit will be in error for every 100,000 bits transmitted. P(e) is analogous to the bit error rate (BER). EXAMPLE7-6 A coherent binary phase-shift-keyed (BPSK) transmitter operates at a bit rate of 20 Mbps. For a probability of error P(e) of 10-4: (a) Determine the minimum theoretical CIN and EJNo ratios for a receiver bandwidth equal to the minimum double-sided Nyquist bandwidth. (b) Determine the CIN if the noise is measured at a point prior to the bandpass filter, where the bandwidth is equal to twice the Nyquist bandwidth. (c) Determine the CIN if the noise is measured at a point prior to the bandpass filter where the bandwidth is equal to three times the Nyquist bandwidth.

Solution (a) With BPSK, the minimum bandwidth is equal to the bit rate, 20 MHz. From Figure 7-17, the minimum ClNis 8.8 dB. Substituting into Equation 7-6 gives us Eb (dB) No

=

C (dB) +

N

= 8.8

!i

fb

(dB)

20 X 106 dB + 10 log 2 XI 6 0 0

= 8.8 dB +

0 dB

= 8.8 dB

Note: The minimum E~o equals the minimum CIN when the receiver noise bandwidth equals the minimum Nyquist bandwidth. The minimum E~o of 8.8 can be verified from Figure 7-18. What effect does increasing the noise bandwidth have on the minimum CIN and E~o ratios? The wideband carrier power is totally independent of the noise bandwidth. Similarly, an increase in the bandwidth causes a corresponding increase in the noise power. Consequently, a decrease in CIN is realized that is directly proportional to the increase in the noise bandwidth. Eb is dependent on the wideband carrier power and the bit rate only. Therefore, Eb is unaffected by an increase in the noise bandwidth. No is the noise power normalized to a I-Hz bandwidth and, consequently, is also unaffected by an increase in the noise bandwidth.

Satellite System

Parameters

287

P(e)

~ C<{ cb

~ !/) Coo

~ !/) C~

~ !/) Ceo

~

I

10-3

~ !/) Ccb

I\ \ \ \ \ \ \ \

10-4

\ \ \ \ \ \ \ \ \ \ \

10-6

,

,, \ ,\ 8-PSK

10-6

16-PSK

,"

I

i ,, ,, : ,, : ,, : ,~ :: , : :' :, : : ,, : :, : ":' [:

v

160AM

10-7

I II I

II I I

10-6

10-9

10-10

I

I

"

I

I

I

:, :' :'I, "

: : :I

C/N (dB) 6

8

10

12

14

16

18

20

22

24

26

Figure 7-17 Pre) performance of M-ary PSK, GAM, QPR, and M-ary APK coherent systems. The rms cm is specified in the double-sided Nyquist bandwidth.

(b) Since Ei/No is independent of bandwidth, measuring the C/N at a point in the receiver where the bandwidth is equal to twice the minimum Nyquist bandwidth has absolutely no effect on Ei/No. Therefore, Ei/No becomes the constant in Equation 7-6 and is used to solve for the new value of C/N. Rearranging Equation 7-6 and using the calculated Ei/No ratio, we have 288

Chap. 7

Satellite Communications

, I,: 10-1 I:

10-2

II II

10-3

I'

~

II~

e 10-4 ~

..... 0

i.l

,£ :0 co

:

IIl I~

"2 10-5 c...

I

I

1111"

10-<3

'II

10-7 'II II,

~II

10-<3 7

8

9

10

11

12

13

15

14

16

17

18

19

EbiNo (dB)

III

Figure 7 -18 Probability of error P(e) versus Ebl No ratio for various digital modulation schemes. Iii

C (dB)

N

=

Eb

No

(dB)

-

!i

fb

(dB)

40 X 106

II

= 8.8dB - 10 log 20 X 106 = 8.8 dB

-

10 log 2

= 8.8 dB

-

3 dB

= 5.8

II

dB

(c) Measuring the CIN ratio at a point in the receiver where the bandwidth equals three times the minimum bandwidth yields the following results for CIN.

£ = N

Eb - 10 1 60 X 106 No og 20 X 106

= 8.8dB - 10 log 3 = 4.03 dB The CIN ratios of 8.8, 5.8, and 4.03 dB indicate the CIN ratios that would be measured at the three specified points in the receiver to achieve the desired minimum E~o and Pee).

Satellite System Parameters

289

Because Et/No cannot be directly measured to determine the Et/No ratio, the wideband carrier-to-noise ratio is measured and then substituted into Equation 7-6. Consequently, to accurately determine the Et/No ratio, the noise bandwidth of the receiver must be known. EXAMPLE 7-7 A coherent 8-PSK transmitter operates at a bit rate of 90 Mbps. For a probability of error of 10-5: (a) Determine the minimum theoretical CIN and Et/No ratios for a receiver bandwidth equal to the minimum double-sided Nyquist bandwidth. (b) Determine the CIN if the noise is measured at a point prior to the bandpass filter where the bandwidth is equal to twice the Nyquist bandwidth. (c) Determi~e the CIN if the noise is measured at a point prior to the bandpass filter where the bandwidth is equal to three times the Nyquist bandwidth. Solution (a) 8-PSK has a bandwidth efficiency of 3 bps/Hz and, consequently, requires a minimum bandwidth of one-third the bit rate or 30 MHz. Froin Figure 7-17, the minimum CIN is 18.5 dB. Substituting into Equation 7-6, we obtain Eb (dB) = 18.5 dB + 10 log 30 MHz No 90 Mbps = 18.5 dB + (-4.8 dB) = 13.7 dB (b) Rearranging Equation 7-6 and substituting for Et/No yields C (dB) N

= 13 7 (dB) .

= 13.7dB -

10 1 60 MHz og 90 Mbps

(- 1.77 dB) = 15.47dB

(c) Again, rearranging Equation 7-6 and substituting for E,jNo gives us

52(dB = 13.7 (dB) -

10 1

N

= 13.7 dB -

90 MHz

og 90 Mbps

0 dB

= 13.7 dB

It should be evident from Examples 7-6 and 7-7 that the Et/No and CIN ratios are equal only when the noise bandwidth is equal to the bit rate. Also, as the bandwidth at the point of measurement increases, the CIN decreases. When the modulation scheme, bit rate, bandwidth, and CIN ratios of two digital radio systems are different it is often difficult to determine which system has the lower probability of error. Because Et/No is independent of bit rate, bandwidth, and modulation scheme; it is a convenient common denominator to use for comparing the probability of error performance of two digital radio systems. EXAMPLE 7-8 Compare the performance characteristics of the two digital systems listed below, and determine which system has the lower probability of error.

Bit rate Bandwidth CIN

Solution 290

QPSK

8-PSK

4DMbps 1.5 X minimum 10.75 dB

60 Mbps 2 X minimum 13.76 dB

Substituting into Equation 7-6 for the QPSK system gives us Chap. 7

Satellite Communications

E

C

-1L No (dB)

= -N

B (dB) + 10 log Jb 7

= 10.75 dB +

10 log 1.5 X 20 MHz 40 Mbps

= 10.75 dB +

(-1.25 dB)

= 9.5

dB

From Figure 7-18, the Pee) is 10-4. Substituting into Equation 7-6 for the 8-PSK system gives us

~

Eb (dB)

No

= 13.76 dB +

10 10 2 X 20 MHz

= 13.76dB +

(-1.76 dB)

g

60 Mbps

= 12dB From Figure 7-18, the Pee) is 10-3. Although the QPSK system has a lower C/N and E~o ratio, the Pee) of the QPSK system is 10 times lower (better) than the 8-PSK system.

Gain-to-Equivalent

Noise Temperature

Ratio

Essentially, gain-to-equivalent noise temperature ratio (GITe) is a figure of merit used to represent the quality of a satellite or an earth station receiver. The GITeof a receiver is the ratio of the receive antenna gain to the equivalent noise temperature (Te) of the receiver. Because of the extremely small receive carrier powers typically experienced with satellite systems, very often an LNA is physically located at the feedpoint of the antenna. When this is the case, GITe is a ratio of the gain of the receiving antenna plus the gain of the LNA to the equivalent noise temperature. Mathematically, gain-to-equivalent noise temperature ratio is Q Te

=

Ar

+ A(LNA) Te

(7-7)

Expressed in logs, we have Q (dBK-1) = Ar (dB) + A(LNA)(dB) - Te (dBK) Te

(7-8)

GITeis a very useful parameter for determining the EtfNo and C/N ratios at the satellite transponder and earth station receivers. GITeis essentially the only parameter required at a satellite or an earth station receiver when completing a link budget. EXAMPLE7-9 For a satellite transponder with a receiver antenna gain of 22 dB, an LNA gain of 10 dB, and an equivalent noise temperature of 22 dBK; determine the GlTe figure of merit. Solution

Substituting into Equation 7-8 yields Q (dBK-1) Te

= 22 dB +

10 dB

-

22 dBK

= 10 dBK-1

Satellite System Parameters

291

SATELLITE SYSTEM LINK EQQAnONS The error performance

of a digital satellite system is quite predictable.

Figure 7-19 shows

a simplified block diagram of a digital satellite system and identifies the various gains and losses that may affect the system performance. When evaluating the performance of a digital satellite system, the uplink and downlink parameters are first considered separately, then the overall performance is determined by combining them in the appropriate manner. Keep in mind, a digital microwave or satellite radio simply means the original and demodulated baseband signals are digital in nature. The RF portion of the radio is analog; that is, FSK, PSK, QAM, or some other higher-level modulation riding on an analog microwave carner.

~ Ar

C'1

Lf

I Lb I

Lb

I Lf

At

Grre

LNA

Lbo

HPA

Satellite transponder

C' At,

HPA

Pt

Ar

Pr Lf

Lf

Lp

Pr Lb

Lbo

Et/No LNA Grre

C/N

Earth station receiver

Earth station transmitter

Figure 7-19 Overall satellite system showing the gains and losses incurred in both the uplink and downlink sections. HPA, High-power amplifier; Pto HPA output power; Lbo, back-off loss; Lf, feeder loss; Lb, branching loss; At, transmit antenna gain; Prototal radiated power = Pt - Lbo - Lb - L,; EIRP, effective isotropic radiated power = PrAt; Lu, additional uplink losses due to atmosphere; Lp, path loss; An receive antenna gain; GITe, gain-to-equivalent noise ratio; Ld, additional downlink losses due to atmosphere; LNA, low-noise amplifier; CITe, carrier-to-equivalent noise ratio; CINo, carrier-to-noise density ratio; EblNo, energy of bit-to-noise density ratio; CIN, carrier-to-noise ratio.

LINK EQQATIONS The following link equations are used to separately analyze the uplink and the downlink sections of a single radio-frequency carrier satellite system. These equations consider only the ideal gains and losses and effects of thermal noise associated with the earth station transmitter, earth station receiver, and the satellite transponder. The nonideal aspects of the system are discussed later in this chapter. QpIink Equation AtPrCLpLu)Ar- AtPr(LpLu) x- G --C No KTe K Te 292

Chap. 7

Satellite Communications

where Ld and Lu are the additional uplink and downlink atmospheric losses, respectively. The uplink and downlink signals must pass through Earth's atmosphere, where they are partially absorbed by the moisture, oxygen, and particulates in the air. Depending on the elevation angle, the distance the RF signal travels through the atmosphere varies from one earth station to another. Because Lp, Lw and Ld represent losses, they are decimal values less than 1. Grre is the receive antenna gain plus the gain of the LNA divided by the equivalent input noise temperature. Expressed as a log, C -

~

= 10 log At? r

-

20 log

~~~~~

-

~

EIRP earth station

41TD

( -

A )

free-space path loss

+ 10 log

+

G

-

(~ ) -

satellite G/Te

10 log Lu - 10 log K

- additional - Boltzmann's atmospheric constant losses

= EIRP (dBW) - Lp (dB) + Q (dBK-1) - Lu (dB) - K(dBWK) Te Downlink Equation f.. = At? r(LpLd)Ar = At? r(LvLd)

No

KTe

x Q

K

Te

Expressed as a log C -

~

= 10 log At?r

41TD

-

(

20 log -

~~~~~ EIRP satellite

A )

G + 10 log -

free-space path loss

(~ ) -

+

satellite G/Te

10 log Ld - 10 log K

- additional - Boltzmann's atmospheric constant losses

= EIRP (dEW) - Lp (dB) + Q (dBK-1) - Ld (dB) - K (dBWK) Te

LINK BUDGET Table 7-4 lists the system parameters for three typical satellite communication systems. The systems and their parameters are not necessarily for an existing or future system; they are hypothetical examples only. The system parameters are used to construct a link budget. A link budget identifies the system parameters and is used to determine the projected C/N and Ei/No ratios at both the satellite and earth station receivers for a given modulation scheme and desired Pee). EXAMPLE 7 -1 0 ,I,

Complete the link budget for a satellite system with the following parameters.

"

I,

Uplink 1. Earth station transmitter output power at saturation, 2000 W

33 dBW

293

Link Budget

r

111__""., " ",,_~ILill':II~::"~"'fi'

1'1!::::,~~Ii'I'::iii:::ij:I:':f

~

,'f_1

III,::,. "

:""

"""~lII,:I::IIIII~:liil:'IIIII;I:'FI;I!11

i::I:Hl:ll>lllm:lliIIilliliilllli

I

.i

TABLE 7-4 SYSTEM PARAMETERS FOR THREE HYPOTHETICAL SATELLITE SYSTEMS

"

'" 0-

~~

.... "0 .. >'0 0 ~ u c S -'" .8

" 'g .. ~>. ""5 -"0 ::c s O~

CI) N 0

::tCl)

'0 A.. CI

~

" '" 0-

01).<:; ~::E >0 00\

.. <.) ~-",c S 'g .g B ,,~ '" - '" >.N"O CI)::CO 0 S N~ -CI) ~A.. -""

'" ~2' ~::E "0 >N

0- -

oo <.) u-"'c S " 'g " .g ,. ~ -"5 >.N"O CI)::Co

0 s

8~
Uplink 35 2 3 0.6 55 200 20 1 1000 -10

25 2 3 0.4 45 208 45 1 800 16

33 3 4 0.6 64 206.5 23.7 0 800 -5.3

18 0.5 1 0.8 16 197 51 3 250 27

20 0.2 1 1.4 44 206 44 3 1000 14

10 0.1 0.5 0.4 30.8 205.6 62 0 270 37.7

3. Earth station branching and feeder losses 4. Earth station transmit antenna gain (from Figure 7-20, 15 mat 14 GHz) 5. Additional uplink atmospheric losses 6. Free-space path loss (from Figure 7-21, at 14 GHz) 7. Satellite receiver GtTeratio 8. Satellite branching and feeder losses 9. Bit rate 10. Modulation scheme

4dB

Transmitter output power (saturation, dBW) Earth station back-off loss (dB) Earth station branching and feeder loss (dB) Additional atmospheric (dB) Earth station antenna gain (dB) Free-space path loss (dB) Satellite receive antenna gain (dB) Satellite branching and feeder loss (dB) Satellite equivalent noise temperature (K) Satellite GlTe (dBK-1)

Downlink Transmitter output power (saturation, dBW) Satellite back -off loss (dB) Satellite branching and feeder loss (dB) Additional atmospheric loss (dB) Satellite antenna gain (dB) Free-space path loss (dB) Earth station receive antenna gain (dB) Earth station branching and feeder loss (dB) Earth station equivalent noise temperature (K) Earth station GlTe (dBK-1)

2. Earth station back-off loss

3 dB 64 dB 0.6 dB 206.5 dB -5.3 dBK-1 OdB 120 Mbps 8-PSK

Downlink 1. Satellite transmitter output power at saturation 10 W

294

10 dBW

2. Satellite back-off loss

0.1 dB

3. Satellite branching and feeder losses

0.5 dB

Chap. 7

Satellite Communications

60

50

~

40

~

30

c: .~ C> .,c: c: 2

Figure 7-20 Antenna gain based on the gain equation for a parabolic antenna:

10

A (db) = 10 log 1'] ('IT 0/'11.)2

0

0.5

2

3

4

5

where 0 is the antenna diameter, '11.= the wavelength, and 1']= the antenna efficiency. Here 1']= 0.55. To correct for a 100% efficient antenna, add 2.66 dB to the value.

10 15

Antenna diameter (m)

4. Satellite transmit antenna gain (from Figure 7-20, 0.37 mat 12 GHz) 5. Additional downlink atmospheric losses 6. Free-space path loss (from Figure 7-21, at 12 GHz) 7. Earth station receive antenna gain (15 m, 12 GHz) 8. Earth station branching and feeder losses 9. Earth station equivalent noise temperature 10. Earth station GlTe ratio II. Bit rate 12. Modulation scheme Solution

30.8 dB

0.4 dB 205.6 dB 62 dB OdB 270K 37.7 dBK-1 120 Mbps 8-PSK

Uplink budget: Expressed as a log,

EIRP(earthstation)= Pt + At -

Lbo

= 33 dBW +

-

Lbf

64 dB - 3 dB - 4 dB

= 90 dBW

Carrier power density at the satellite antenna:

Link Budget

295

1

210

208

206

204

i:D ~

'"

.2

202

Elevation angle correction:

.;; co Co

Angle 90° 45° 0°

~ 200 co

'" Co

., ~ 198 u.

+dB 0 0.44 1.33

196

194

192 3

4

5

6

7

8

9

10 11 12 13 14 15

Frequency (GHz)

Figure 7-21 Free-space path 1055 (Lp) determined from Lp = 183.5 + 20 log f(GHz}, elevation angle = 90°, and distance = 35,930 km.

C' = EIRP (earth station) - Lp - Lu

= 90 dBw - 206.5 dB - 0.6 dB =

-117.1

dBW

C/No at the satellite:

~=~=~XJ... No KIe

Te

K

C G where - = C' X Te Te

Thus C -=C'x-xNo

G Te

1 K

Expressed as a log,

~No (dB)

= C' (dBW) + Q (dBK-1) - 10 log (1.38 X 10-23)

Te

~ = -117.1 No

dBW + (-5.3 dBK-1) - (-228.6dBWK)

= 106.2dB

Thus Eb (dB) No Eb

No 296

=

C/fb (dB) No

= 106.2 dB -

=~

No

(dB) - 10 logfb

10 (log 120 X 106) = 25.4 dB

Chap. 7

Satellite Communications

and for a minimum bandwidth system, C = Eb - .!i = 25.4 - 10 10 40 X 106 = 30.2 dB N No fb g 120 X 106 Downlink budget: Expressed as a log,

EIRP (satellite transponder)

= Pt

+ At

- Lbo - Lbf

= 10 dBW + 30.8 dB - 0.1 dB - 0.5 dB = 40.2 dBW Carrier power density at earth station antenna: C' = EIRP (dBW) - Lp (dB) - Ld (dB)

~

= 40.2 dBW - 205.6 dB - 0.4 dB = -165.8

dBW

C/No at the earth station receiver:

~=-.£=~X~ No KTe

Te

K

i

C G where - = C' X Te Te

I

Thus

! ~=C'X.QX~ No

Te

K

t

Expressed as a log,

~No

r

(dB) = C' (dBW) + .Q (dBK-1) - 10 log (1.38 X 10-23)

Te

= -165.8 dBW + (37.7 dBK-1) - (-228.6 dBWK) = 100.5 dB

I I.

An alternative method of solving for C/No is I!I I

~No (dB) = C' (dBW)+ Ar (dB) -

ii

Te(dBK-1) - K (dBWK)

II l

= -165.8 dBW + 62 dB - 10 log 270 - (-228.6 dBWK)

I~

~

No

=

-165.8

dBW + 62 dB - 24.3 dBK-1 + 228.6 dBWK = 100.5 dB

E C !L (dB) = (dB) - 10logfb No No = 100.5 dB - 10 log (120 X 106)

~

= 100.5dB - 80.8dB = 19.7dB and for a minimum bandwidth system, C = Eb - .!i = 19.7 - 10 1 40 X 106 = 24.5 dB N No fb og 120 X 106

With careful analysis and a little algebra, it can be shown that the overall energy of bitto-noise density ratio (Et/No), which includes the combined effects of the uplink ratio (Et/No)u and the downlink ratio (E,/No)d, is a standard product over the sum relationship and is expressed mathematically as Eb (Et/NoL (Et/NO)d No (overall) = (Et/NoL + (Et/NO)d Link Budget

(7-9)

297

J

where all E,jNo ratios are in absolute values. For Example 7-10, the overall E,jNo ratio is Eb (overall)

No

=

(346.7)(93.3)

346.7+ 93.3

= 73.5

= 10 log 73.5 = 18.7 dB

As with all product-over-sum relationships, the smaller of the two numbers dominates. If one number is substantially smaller than the other, the overall result is approximately equal to the smaller of the two numbers. The system parameters used for Example 7-10 were taken from system C in Table 7-4. A complete link budget for the system is shown in Table 7-5. 1 TABLE 7-5

LINK BUDGET FOR EXAMPLE7-10

Uplink 1. Earth station transmitter output power at saturation, 2000 W 2. Earth station back -offloss 3. Earth station branching and feeder losses 4. Earth station transmit antenna gain 5. Earth station EIRP 6. Additional uplink atmospheric losses 7. 8. 9. 10. 11. 12. 13.

Free-space path loss Carrier power density at satellite Satellite branching and feeder losses Satellite Glfe ratio Satellite Clfe ratio Satellite C/No ratio Satellite C/N ratio

14. Satellite Ei/No ratio 15. Bit rate 16. Modulation scheme

33 dBW 3dB 4dB 64 dB 90 dBW 0.6 dB 206.5 dB -117.1 dBW OdB -5.3 dBK-1 -122.4 dBWK-1 106.2 dB 30.2 dB 25.4 dB 120 Mbps 8-PSK

Downlink 10 dBW

1. Satellite transmitter output power at saturation, 10 W 2. Satellite back-off loss 3. Satellite branching and feeder losses 4. Satellite transmit antenna gain 5. Satellite EIRP 6. Additional downlink atmospheric losses 7. 8. 9. 10. 11. 12. 13. 14. 15.

Free-space path loss Earth station receive antenna gain Earth station equivalent noise temperature Earth station branching and feeder losses Earth station G/Te ratio Carrier power density at earth station Earth station C/Te ratio Earth station C/No ratio Earth station C/N ratio

16. Earth station Ei/No ratio 17. Bit rate 18. Modulation scheme

298

Chap. 7

0.1 dB 0.5 dB 30.8 dB 40.2 dBW 0.4 dB 205.6 dB 62 dB 270 K OdB 37.7 dBK-1 -165.8 dBW . -128.1 dBWK-1 100.5 dB 24.5 dB 19.7 dB 120 Mbps 8-PSK

Satellite Communications

NONIDEAL SYSTEM PARAMETERS Additional nonideal parameters include the following impairments: AMlAM conversion and AMIPM conversion, which result from nonlinear amplification in HPAs and limiters; pointing error, which occurs when the earth station and satellite antennas are not exactly aligned; phase jitter, which results from imperfect carrier recovery in receivers; nonideal filtering, due to the imperfections introduced in bandpass filters; timing error, due to imperfect clock recovery in receivers; andfrequency translation errors introduced in the satellite transponders. The degradation caused by the preceding impairments effectively reduces the Ei/No ratios determined in the link budget calculations. Consequently, they have to be included in the link budget as equivalent losses. An in-depth coverage of the nonideal par~eters is beyond the intent of this text.

QUESTIONS 7-1. 7-2. 7-3. 7-4. 7-5. 7-6. 7-7. 7-8. 7-9. 7-10. 7-11. 7-12. 7-13. 7-14. 7-15. 7-16. 7-17. 7-18. 7-19. 7-20. 7-21. 7-22.

Briefly describe a satellite. What is a passive satellite? An active satellite? Contrast nonsynchronous and synchronous satellites. Define prograde and retrograde. Define apogee and perigee. Briefly explain the characteristics of low-, medium-, and high-altitude satellite orbits. Explain equatorial, polar, and inclined orbits. Contrast the advantages and disadvantages of geosynchronous satellites. Define look angles, angle of elevation, and azimuth. Define satellite spatial separation and list its restrictions. Describe a "footprint." Describe spot, zonal, and earth coverage radiation patterns. Explain reuse. Briefly describe the functional characteristics of an uplink, a transponder, and a downlink model for a satellite system. Define back-off loss and its relationship to saturated and transmit power. Define bit energy. Define effective isotropic radiated power. Define equivalent noise temperature. Define noise density. Define carrier-to-noise density ratio and energy of bit-to-noise density ratio. Define gain-to-equivalent noise temperature ratio. Describe what a satellite link budget is and how it is used.

PROBLEMS 7-1. An earth station is located at Houston, Texas, which has a longitude of99.5° and a latitude of 29.5° north. The satellite of interest is Satcom 2. Determine the look angles for the earth station antenna. 299

Problems

._-~

.,

",-

!I:' ~",":i"''',''''"''''" ""'"

-..-

"'-- - ._-""" ,

-

".",,,""

7-2. A satellite system operates at l4-GHz uplink and ll-GHz downlink and has a projected P(e) of 10-7. The modulation scheme is 8-PSK, and the system will carry 120 Mbps. The equivalent noise temperature of the receiver is 400 K, and the receiver noise bandwidth is equal to the minimum Nyquist frequency. Determine the following parameters: minimum theoretical C/N ratio, minimum theoretical Ei/No ratio, noise density, total receiver input noise, minimum receive carrier power, and the minimum energy per bit at the receiver input. 7-3. A satellite system operates at 6-GHz uplink and 4-GHz downlink and has a projected P(e) of 10-6. The modulation scheme is QPSK and the system will carry 100 Mbps. The equivalent receiver noise temperature is 290 K, and the receiver noise bandwidth is equal to the minimum Nyquist frequency. Determine the C/N ratio that would be measured at a point in the receiver prior to the BPF where the bandwidth is equal to (a) It times the minimum Nyquist frequency, and (b) 3 times the minimum Nyquist frequency. 7-4. Which systlm has the best projected BER? (a) 8-QAM, C/N = 15 dB, B = 2fN'fb = 60 Mbps. (b) QPSK, C/N = 16 dB, B = fN,fb = 40 Mbps. 7-5. An earth station satellite transmitter has an HPA with a rated saturated output power of 10,000 W. The back-off ratio is 6 dB, the branching loss is 2 dB, the feeder loss is 4 dB, and the antenna gain is 40 dB. Determine the actual radiated power and the EIRP. 7-6. Determine the total noise power for a receiver with an input bandwidth of 20 MHz and an equivalent noise temperature of 600 K. 7-7. Determine the noise density for Problem 7-6. 7-8. Determine the minimum C/N ratio required to achieve a P(e) of 10-5 for an 8-PSK receiver with a bandwidth equal tofN. 7-9. Determine the energy per bit-to-noise density ratio when the receiver input carrier power is -100 dBW, the receiver input noise temperature is 290 K, and a 60-Mbps transmission rate is used. 7-10. Determine the carrier-to-noise density ratio for a receiver with a -70-dBW input carrier power, an equivalent noise temperature of 180 K, and a bandwidth of 20 MHz. 7-11. Determine the minimum C/N ratio for an 8-PSK system when the transmission rate is 60 Mbps, the minimum energy of bit-to-noise density ratio is 15 dB, and the receiver bandwidth is equal to the minimum Nyquist frequency. 7-12. For an earth station receiver with an equivalent input temperature of 200 K, a noise bandwidth of 20 MHz, a receive antenna gain of 50 dB, and a carrier frequency of 12 GHz, determine the following: G/Te,No, and N. 7-13. For a satellite with an uplink Ei/No of 14 dB and a downlink Ei/No of 18 dB, determine the overall Ei/No ratio. 7-14. Complete the following link budget:

Uplink Parameters 1. Earth station transmitter output power at saturation, 1 kW 2. Earth station back-off loss, 3 dB 3. Earth station total branching and feeder losses, 3 dB 4. Earth station transmit antenna gain for a lO-m parabolic dish at 14 GHz 5. Free-space path loss for 14 GHz 6. Additional uplink losses due to the earth's atmosphere, 0.8 dB t: sateIilte transponc!ercTl1e, -4.0 dBK-~ 8. Transmission bit rate, 90 Mbps, 8-PSK

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Chap. 7

Satellite Communications

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Downlink Parameters 1. Satellite transmitter output power at saturation, lOW 2. Satellite transmit antenna gain for a 0.5-m parabolic dish at 12 GHz 3. Satellite modulation back-off loss, 0.8 dB 4. 5. 6. 7. 8. 9.

Free-space path loss for 12 GHz Additional downlink losses due to earth's atmosphere, 0.6 dB Earth station receive antenna gainJor a lO-m parabolic dish at 12 GHz Earth station equivalent noise temperature, 200 K Earth station branching and feeder losses, 0 dB Transmission bit rate, 90 Mbps, 8-PSK ~

Problems

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