NTIA Report 97-341 

Link Analysis for the LRPT Digital 

Weather Satellite System 

Roger A. Dalke 

Robert J. Achatz 

Christopher L. Holloway 

George A. Hufford 

Edmund A. Quincy 

U.S. DEPARTMENT OF COMMERCE 

William M. Daley, Secretary 

Larry Irving, Assistant Secretary 

for Communications and Information 

September 1997 

iii

CONTENTS 

Page 

ABSTRACT.....................................................................................................................................1 

1. INTRODUCTION .....................................................................................................................1 

2. SPACE-TO-EARTH LINK ANALYSIS ..................................................................................2 

 2.1 Equations for Received Power and Noise Power ................................................................2 

 2.2 Earth Station Receiving Systems.........................................................................................3 

 2.3 Satellite Location .................................................................................................................4 

 2.4 Directional and Path Length Variations Due to Troposphere..............................................4 

 2.5 System Noise Temperature..................................................................................................6 

3. PROPAGATION EFFECTS......................................................................................................7 

 3.1 Tropospheric Effects............................................................................................................7 

 3.2 Ionospheric Effects ..............................................................................................................8 

4. EFFECTS OF RADIO NOISE ON THE WEATHER SATELLITE SYSTEM .....................13 

 

 4.1 The Radio Noise Environment...........................................................................................13 

 4.2 Modification of Noise Power for Proposed Receiving Antennas......................................19 

 4.3 Receiving System Noise and Carrier-to-Noise Ratio ........................................................19 

 4.4 Issues Pertaining to Man-made Noise Statistics ................................................................20 

5. CARRIER-TO-NOISE RATIO REQUIREMENTS FOR LRPT LINK .................................22 

 

 5.1 Signal Design Description .................................................................................................22 

 5.2 Required Carrier-to-Noise Ratios ......................................................................................24 

 5.3 Other Signal Design Considerations..................................................................................26 
iv 

CONTENTS (Cont’d) 

Page 

6. SUMMARY AND CONCLUSIONS ......................................................................................30 

7. REFERENCES ........................................................................................................................33 

APPENDIX A: LINK BUDGET...................................................................................................37 

APPENDIX B: REFERENCE EQUATIONS USED IN SECTION 5..........................................51 
LINK ANALYSIS FOR THE LRPT DIGITAL WEATHER SATELLITE SYSTEM 

R. Dalke, R. Achatz, C. Holloway, G. Hufford, and E. Quincy∗

The National Oceanic and Atmospheric Administration, the European Space Agency, 

and the European Organization for the Exploitation of Meteorological Satellites are 

designing a weather satellite system that will broadcast digital weather images at 

VHF. As a part of that effort, the Institute for Telecommunication Sciences has 

analyzed the VHF digital communications link. The results of the link analysis are 

described in this report. This analysis is based on published literature and models that 

describe propagation effects such as ionospheric scintillation and man-made noise, 

and are applicable to VHF digital communications. The analysis includes the 

estimation of the required link margins for coded binary and quaternary phase-shift 

modulation methods. 

Key words: VHF satellite communications; VHF digital communications; man-made noise; 

ionospheric scintillation; meteorological satellites; weather satellite images; low rate 

picture transmission (LRPT); automatic picture transmission (APT); television infrared 

observation satellite (TIROS) 

1. INTRODUCTION 

In 1963, the United States launched polar orbiting weather satellites that transmit images of the earth 

using an FM broadcast at radio frequencies between 137 and 138 MHz. This broadcast system is 

called the automatic picture transmission (APT) system and was used originally by U.S. weather 

offices. Plans for building relatively simple, low-cost ground receiving stations were widely 

distributed to meteorological services worldwide. Since that time, activity and interest in receiving 

the direct readout images has increased significantly. Currently, there are plans to upgrade the APT 

system to digital technology, which is referred to as the low rate picture transmission (LRPT). Design 

decisions will require a detailed analysis of VHF propagation effects, noise environment, receiving 

site environment, and their effects on received picture quality. 

This report details a study of the VHF satellite-to-ground propagation channel and its effects on the 

proposed LRPT digital broadcast system. Technical specifications used in this study (e.g., 

transmitter, bandwidth, modulation, and receivers) are based on both the existing APT system and 

the proposed LRPT system. The link analysis was divided into scenarios based on the type of earth 

station receiving system (low-end, high-end) and the satellite receiver path geometry that would give 

the maximum received signal strength (satellite at zenith) and the minimum signal strength with the 

satellite in view (minimum specified elevation). In addition, four different man-made noise 

environments were addressed. The specifications for these different cases and the analysis of the 

satellite-to-earth link are detailed in the report. 

 

∗

 The authors are with the Institute for Telecommunication Sciences, National Telecommunications 

and Information Administration, U.S. Department of Commerce, Boulder, CO 80303 
2

The analysis of the space-to-earth link requires consideration of the link path geometry and the 

effects of the ionosphere and troposphere on the radio signal. At the frequency of interest (137 

MHZ), the signal will easily penetrate the ionosphere, however, one must consider the deleterious 

effects of ionospheric scintillation. In general, scintillation is not an important factor at midlatitudes. 

Scintillation can be significant, however, when the radio link path traverses sections of the 

ionosphere above the magnetic equatorial and polar regions of the earth where fades exceeding 10 dB 

can be experienced. At the frequency of interest, the troposphere has little effect on the signal. The 

effects of both the ionosphere and the troposphere are discussed in this report. 

Knowledge of the level of external radio noise at the receiver is essential for system design. Radio 

noise originates from both natural and man-made sources. Natural radio noise considered in this 

analysis is primarily due to heavenly bodies (e.g., sun, planets, and stars). In populated areas at 137 

MHZ, noise originating from human activities typically dominates the natural radio noise 

background. In this Study, we considered both sources of noise and their effects on the link 

requirements. 

In Section 2 we define the radio link geometry and relevant link equations. We also identify and 

characterize two representative combinations of earth station (E/S) equipment that are used in the 

link calculations. Section 3 focuses on the propagation effects introduced by the ionosphere and 

troposphere that affect link budget calculations and overall system performance. The noise 

environment for this system is analyzed in Section 4, where we calculate predicted noise levels based 

on published noise measurements in four different man-made noise environments. Based on these 

results, the received carrier-to-noise ratio (CNR) for each noise environment and E/S receiver system 

is tabulated. We also have reviewed proposed digital modulation schemes and their performance in 

terms of CNR required to achieve specified bit-error-ratios (see Section 5). The results of the link 

budget calculations are tabulated in Appendix A. Here we provide tables detailing the link 

calculation and the resulting link margin based on the required CNR for two modulation schemes. 

The cumulative distribution (time availability) of the CNR for 5-W and 15-W transmitters, the lowend and high-end receiving system, and the four noise environments are also given in Appendix A 

2. SPACE-TO-EARTH LINK ANALYSIS 

In this section we introduce the link equations needed to calculate the CNR ratio. We also specify the 

receiver and antenna characteristics for the low-end and high-end receiving systems evaluated in this 

report. 

2.1 Equations for Received Power and Noise Power 

The received power at the output terminals of the receiving antenna is given by [1]: 

Pr = EIRP + Gr – Lfs – A (dBW) (1) 
3

where EIRP is the effective isotropic radiated power, the product of the transmitter antenna gain, and 

the effective (including system losses) transmitter power; Gr, is the receiver gain; and Lfs is the free 

space or basic transmission loss: 

Lfs = 32.45 + 20logFMHzRkm (dB) , (2) 

where Rkm is the path distance (in km) and FMHz is the frequency (in MHz). A represents path 

attenuation resulting from propagation in a lossy medium. The effects of propagation in the 

troposphere and ionosphere (including ionospheric scintillation) are discussed in Section 3 of this 

report. 

The CNR is given simply as the ratio of the received signal at the terminals of the receiving antenna 

to the system noise power referenced to the same point in the receiving system: 

CNR = Pr – 10log(kb) – 10log (Tsys) (dB) , (3) 

where k is Boltzmann's constant (1.380662 x 10-23 J/K), b is the noise equivalent bandwidth of the 

receiver (72 kHz for the proposed LRPT), and Tsys is the system noise temperature and is defined in 

Equation (6) below. 

In the link calculations that follow, we have assumed two values for the transmitter output power: 

5 W and 15 W. Losses for the transmitting satellite system are assumed to be 2.2 dB [2] (this 

includes antenna circuit losses, polarization mismatch, transmission line losses, etc.) 

2.2 Earth Station Receiving Systems 

For the purposes of this study, two archetypal E/S receivers are defined; a low-end system and a 

high-end system. The high-end system consists of a high-gain tracking antenna combined with a high 

quality receiver having a noise figure of 1 dB. The low-end system consists of an “omnidirectional” 

antenna combined with an average quality receiver having a noise figure of 6 dB. 

The typical high-end antenna is a crossed Yagi-Uda with a gain of about 10 dB as described by 

Summers [3]. For the purposes of the link calculations, we have approximated the directive gain for 

this antenna by using a published antenna pattern for a Yagi-Uda antenna with roughly the same 

features (e.g., number and size of elements) [4]. The pattern is shown in Figure 1. To approximate a 

crossed Yagi-Uda, we assumed that the pattern was rotationally symmetric. The resulting gain is 

somewhat higher than 10 dB, but should provide a reasonable approximation for the purposes of 

noise calculations. Since the high-end system tracks the satellite, the receiver gain (Gr) does not 

depend on the satellite elevation (here Gr = 10 dB). 
4

The typical “omnidirectional” antenna is a half wavelength VHF Volute. The pattern is shown in 

Figure 2 [2]. The Volute antenna is not steerable; hence, the low-end system receiver gain varies with 

elevation angle as shown in Figure 2. For each system (high/low-end receivers), link calculations 

were made for the greatest and the least free space path loss with the satellite within the specified 

viewing elevation angles. The greatest path loss occurs at the lowest elevation angle for which the 

system is required to achieve the specified link margin: 5° for the high-end system and 13° for the 

low-end system. The least path loss occurs at zenith. 

2.3 Satellite Location 

Effective radiated isotropic power is a function of the transmitting antenna gain Gt and the satellite 

look angle α. The satellite look angle α is defined in Figure 3 and is determined by the following 

expression: 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = −

s

e

r

r cos(EL) sin 1 α , (4) 

where 

r r Altitude s = e + , (5) 

where re is the radius of the earth (6370 km) and A is the altitude of the satellite (824 km). For the 

three elevation angles of interest (90°, 13°, and 5°), the corresponding look angles are 0°, 60°, and 

62°, respectively. The gain of the satellite antenna as a function of look angle is determined from the 

transmitting antenna pattern shown in Figure 3 [5]. The gains for the three look angles of interest are 

3.7, 0, and -0.3 dB, respectively (Figure 4). 

The distance to the satellite as a function of elevation angle is given by: 

2

1

2 2 )] 2 [ 2 cos( α

π R = rs + re − re rs − EL − (6) 

which, for the elevation angles of interest is 824, 2207, and 2833 km respectively. 

2.4 Directional and Path Length Variations Due to the Troposphere 

The ray path through the troposphere is curved due to refraction. Because of the curvature of the 

path, the direction to the satellite is different from the geometric direction. This change in the path 

direction changes both the satellite look angle and distance to the satellite. Based on expressions 
5

Figure 1. Pattern for a six-element Yagi-Uda antenna. 

Figure 2. Volute antenna pattern. 
6

Figure 3. Space-to-earth path geometry. 

given in [6] and an operating frequency of 137 MHz, the largest change in elevation angle is less than 

one tenth of a degree and the largest change in path length is 28 m (both occur at an elevation angle 

of 5°), hence, the troposphere has a negligible effect on the received signal power. 

2.5 System Noise Temperature 

The total system noise temperature has contributions from the antenna, antenna circuit and 

transmission line, and the receiver. The following expression for the system noise temperature is 

Figure 4. Satellite transmitter antenna pattern. 
7

referenced to the receiving antenna terminals: 

Tsys = Ta + L − T0 +LTr ( 1)

 (7) 

(10 1) 10 = 0 −

NF

Tr T

where L represents E/S losses (e.g., antenna circuit, polarization mismatch, and transmission line 

losses), T0 is the ambient temperature (290 K), NF is the noise figure of the receiver, and Ta is the 

antenna temperature. The antenna temperature is due to both natural and man-made noise sources 

which are analyzed in detail in Section 4. The temperature of the low-end earth station receiver is 

865 K and the high-end earth station is 75 K. For the purposes of this analysis, the earth station losses 

were assumed to be 2 dB (receiver implementation losses not including demodulation losses) [7]. 

3. PROPAGATION EFFECTS 

The transmitted power arrives at the receiver at greatly reduced levels, primarily because of the 

spherical spreading of the radio wave. This “free space loss” for the space-to-earth propagation path 

will equal about 135 dB. In addition, however, the radio wave must travel through the atmosphere 

and then possibly through obstacles on the ground. In some circumstances, this can lead to further 

losses of tens of decibels. Many of these circumstances are easily avoidable and should not be 

designed against. It seems folly, for example, to attempt reception where there is no clear view of the 

sky, at street level in a downtown urban area, or at the bottom of a deep canyon. Other circumstances, however, require some planning if they are to be avoided. Tropospheric and ionospheric 

effects are discussed below. 

3.1 Tropospheric Effects 

The lowest 10 km or so of the atmosphere is the troposphere. Its major constituents are the gases 

nitrogen, oxygen, and water vapor. These combine to give it an index of refraction n. At standard 

conditions, this index has a value of about 1.000300, and it always differs only slightly from unity. 

For this reason, one usually resorts to discussions of the refractivity N = n–1 and measures that 

quantity in parts per million or, as the engineers prefer to say, N-units. In a standard atmosphere, 

then, the refractivity has a sea level value of about 300 N-units and decreases exponentially with altitude, having a scale height of about 7.5 km. Although the numbers involved here are small, they 

sometimes have important consequences. For example, since the refractivity decreases with height, 

radio waves tend to bend down towards the ground. On terrestrial paths, this extends the horizon, a 

fact that can be accounted for by pretending (under the standard conditions given above) that the 

earth’s radius is 4/3 its actual value. On satellite paths, however, the waves will leave the atmosphere 

before they have suffered much bending. A ray leaving the earth at an elevation angle of 5° will, 

when it exits the troposphere, have changed its direction by about 2 mrad (0.1°). 
8

In general, the refractivity is a function of pressure, temperature, and humidity, and therefore a 

function of the weather (see e.g., [8, 9, 10]). When the atmosphere is well mixed (as is the normal 

condition and especially so during storms) the refractivity is a well-behaved function of position and 

will resemble the “standard” atmosphere described above. But a stable atmosphere often means 

trouble because, the refractivity is horizontally stratified and can vary with height in quite abnormal 

ways. The most severe possibility occurs when an atmospheric duct forms, in which radio waves 

bend downwards and are “trapped” close to the earth’s surface so that they may travel a considerable 

distance. The occurrence of these ducts often is related to the “inversion layers” so frequently 

lamented. 

Actually, however, a ray will “penetrate” such ducts even at fairly small angles of elevation. The rule 

of thumb is that rays steeper than 30 will be unaffected by any stratified atmosphere. Thus, satellite 

reception, even at 5° above the horizon, should be unaffected. 

On the other hand, there may be instances of unintended reception. A satellite may be below the 

horizon while its signal is carried by a duct directly to the receiver. If this is an unwanted signal from 

a separate service, it may become deleterious interference. In the case of reception of the desired 

satellite, the signal may be received unexpectedly (i.e., early), fadeout, and after a wait, reappear and 

behave as expected. 

Molecular absorption (by oxygen or water vapor) and rain attenuation is, at these frequencies, too 

small to measure. Even obstacle losses (when, say, a building or a tree canopy intersects the radio 

path) and penetration losses (when the receiver is inside a building) might be only a few decibels, 

depending on the exact geometry. While avoiding such losses will certainly improve the system’s 

efficiency, there may be situations where they cannot be avoided and where the losses will still be 

tolerable. 

Another situation that one should try to avoid is that in which “multipath” might degrade reception. 

Reflections from buildings or scattering from trees can introduce additional radio paths that might 

interfere destructively with the direct path. A building behind the receiver is particularly 

troublesome. Proposed bandwidths are small enough that fading will not be frequency selective, but 

the remaining flat fading can easily exceed 10 dB. Because the satellite moves, the fading will be 

dynamic. If such behavior is unavoidable, perhaps space diversity will be useful. 

3.2 Ionospheric Effects 

The ionosphere is that part of the atmosphere that exists from perhaps 70-1000 km above the earth. 

The air here is very tenuous and the sun’s rays strip electrons from the molecules forming a plasma 

of positively charged ions and negatively charged free electrons. It is these free electrons that interact 

with radio waves and can cause deviations from free-space transmission. One speaks of an “effective 

refractivity” having the form (at high frequencies) N= -40.3 Ne/f2

, where Ne is the electron density
9

and f the radio frequency in Hz. At 137 MHz and the densest part of the ionosphere (the F-layer with. 

Ne=1.6x1012/m3

), N has the value -0.003. Not only is this negative (so that the phase velocity is 

greater than it is in free space) but its magnitude is much larger than the refractivity of the troposphere. 

Thus, the frequency of 137 MHz is high enough that the waves will easily penetrate the ionosphere, 

but not high enough that this penetration will be unaffected. But there are times when the free 

electrons form into generally irregular clouds and blobs. This makes the effective index of refraction 

similarly irregular so that a kind of diffractive screen forms and the received signal level may deviate 

from the assumed free-space level. The irregularities change with time so that the received signal 

changes with time and one says that it “scintillates.” The central value is still the computed freespace value, and deviations (at 137 MHz) might be 10 dB or more. Of course, 10 dB more signal will 

not be a problem, but the loss of 10 dB will usually be disastrous. The temporal variation is that of a 

stochastic process with frequency components beginning to disappear at about 1 Hz. Fadeouts 

exceeding 3 dB have an average duration of maybe 1 s. 

These effects are largely dependent on the earth's magnetic field. They appear mostly within about 

30° of the magnetic poles or 20° of the geomagnetic equator. Midlatitudes usually are free of any 

significant effects. Figure 5 delineates the areas of possible concern (except for the rare occurrence of 

a fierce magnetic storm). In addition, there are strong yearly, seasonal, and diurnal variations. In the 

equatorial region, scintillation appears almost entirely at night between, say, between 1000 and 0500 

hours. It is twice as strong during equinoctial periods as during the solstices. It is highly dependent 

on solar activity, showing much greater effects during sunspot maxima as during sunspot minima. In 

the auroral regions, there are two important parts of the ionosphere: the “polar cap” and the “auroral 

oval.” The polar cap appears directly over the magnetic pole and is almost always there. 

Figure 5. Regions of the world where ionospheric scintillation might be significant (shaded areas). 
10

Only during the summer (when the sun shines all night long) does scintillation tend to disappear. At 

all other times, it seems to be independent of the hour and of solar activity. The auroral oval is a ring 

about 20° or 25° away from the pole. This is the ring that receives a rain of particles from the sun and 

responds with the awesome auroral displays. The resulting radio scintillation is strongest at night and 

depends strongly on sunspot number. 

To illustrate what might happen, Figures 6 through 10 show the average standard deviations σx of 

received signal levels from simulated weather satellite (TIROS) passes. Receiver sites were selected 

for their relation to the phenomena, while the satellite was placed at the point (in any one pass) is 

nearest to the receiver. The orbits are sun synchronous so that their ascending nodes (for example) 

occur always at the same local time. However, the longitudes of these nodes may appear anywhere 

along the equator, and for our purposes were assumed to be random and uniformly distributed. The 

short segments in the figures show the consequent scintillation indices at the times the two satellites 

passed over the receiver. Three sunspot numbers were used: 150, a near maximum; 50, an average 

number; and 10, a near minimum. At Washington (Figure 7), however, the scintillation was not only 

very small; it was independent of sunspot number. The three northern cities (Figures 8-10) exhibited 

varying degrees of alarming results. While the standard deviations are rarely larger than 4 dB, they 

can have sensible values at any time. 

Figure 6. Average scintillation indices near Abidjan, Ivory Coast at 5° N, 4° W, during passes of 

TIROS as planned. The curves are drawn for three sunspot numbers. 
11
12
13

We should note here that in order to construct the results of the figures of this section, we were 

forced to use one of the original models for ionospheric scintillation. The model was suggested in 

1973 by Fremouw and Rino [11] and implemented by Pope [12] in 1974. The latest version [13] of 

this same model will presumably give similar but distinctly different values. It is now becoming 

available for use, and in Figure 11 we compare the two versions, showing how they predict the 

average scintillation throughout one day at the equatorial site of Abidjan, Ivory Coast. Note in 

particular that the new version has limited the values when they approach conditions corresponding 

to Rayleigh fading. Note, too, the values obtained using the older version differ from values in Figure 

5. Parameters for the receiver are the same but the transmitter on the satellite is at a different 

location. 

To escape the harmful effects of scintillation one might propose a form of diversity reception. 

Unfortunately, the fields vary only slowly with time, space, frequency, or polarization. There is little 

“diversity action” and such proposals do not seem useful. Space diversity might serve, but the 

receiving antennas would need to be separated by 100 or 200 m. 

The best way to avoid these effects seems to be to choose proper times of attempted reception. This 

is a fairly straightforward process in the equatorial regions where one could avoid the hours close to 

midnight. For the case under study, that means that the ascending and descending nodes should be 

carefully chosen. The present choices for APT, for example, are excellent ones. 

4. EFFECTS OF RADIO NOISE ON THE WEATHER SATELLITE SYSTEM 

The performance of a radio system is dependent on the received signal strength and the natural and 

man-made radio noise processes. In general, there are a number of noise processes to consider: the 

noise internally generated by the receiving system; natural noise (e.g., atmospheric, solar, and 

galactic); unintentionally radiated man-made noise; and intentionally radiated noise (e.g., 

interference). Typically, the noise processes depend on frequency, time, and location. Statistics 

related to a variety of natural and man-made sources have been compiled and published [e.g., 4.2, 

4.3]. In this section, we review those noise sources that affect the broadcast of weather images at 137 

MHZ and estimate (based on published statistics) the system noise temperature and the CNR for the 

high-end and low-end system receiving systems. 

4.1 The Radio Noise Environment 

Environmental noise is in general a nonstationary random process. Noise measurements are made 

over periods of time for which the process is stationary enough to obtain the required statistics (such 

as the rms voltage). Measured noise data commonly are given in terms of the external antenna noise 

figure Fa: 

kT b

P

T

T

F a n

a

0

10

0

10 = 10log = 10log , (8) 
14

 Figure 11. A comparison of two versions of our ionospheric scintillation model 

near Abidjan, Ivory Coast. The newer version is given by the 

dashed line, the older version is given by the solid line. 

where pn is the available noise power. Published statistics [14, 15, and 16] based on measurements 

provide information on the distribution of Fa (time and location variability) for natural and manmade noise environments. 

The overall background natural radio noise from 1 Hz to 1 THz is shown in Figure 12 [14]. Note that 

around 137 MHZ, the important sources of natural radio noise are the sun and galactic noise. Figure 

13 (a corrected figure from CCIR Report 670 [15]) shows the same results over a smaller frequency 

range (100 MHZ to 100 GHz). Here, the estimated median business-area man-made noise has been 

included. It is clear that in the frequency range of interest, man-made noise has a significant 

influence on the radio link. 

The effects of the sun and galaxy can be estimated using the published statistics. As shown in the 

figures, the sun is a strong radio noise source. Since the sun has a diameter of about 1⁄2° and the 

receiving antennas have a relatively wide beamwidth, it is expected that the effect of the sun for the 

most part will not be important. This is particularly true for a Yagi-Uda receiving antenna since the 

sun will not always be within the main beam. The relationship between the noise temperature of the 

sun and the receiving antenna is given by the following expression: 

2

) 1440 ( ) ( ) ( 4

π

π sun

sources

ant T P d DT D T = Ω Ω Ω = ∫ , (9) 

where D is the receiving antenna directivity and P is the antenna pattern. When a quiet sun
15

Figure 12. Natural radio noise, 1 Hz to 1 THz [14]. 

(T ≈ 1.5×106

 K) is in view, the temperature of the Volute antenna is approximately 17 K and the 

temperature of the Yagi-Uda antenna is approximately 71 K. Figure 12, shows that the noise figure 

for a disturbed sun is roughly 30 dB greater than that for a quiet sun. It is expected that such extreme 

noise levels are sporadic and should not drive the system design process. These data indicate that a 

quiet sun will not have a significant effect on the radio link when compared to other environmental 

noise sources. 

In Figure 13, there are two curves associated with galactic noise. The lower curve B is for an 

omnidirectional antenna, while the upper curve C is for an infinitely narrow beam aimed toward the 

galactic center. Maximum galactic noise for the weather satellite system should occur when the YagiUda antenna is directed toward the galactic center. This maximum can be estimated using published 

radio sky data. CCIR Report 720-2 [16] provides maps of the brightness temperature of the radio sky 

at 408 MHz and an approximate expression for the frequency dependence of the noise. To obtain a 

more realistic value, published radio sky brightness temperatures at 150 MHz [17] were used to
16

 Figure 13. Fa versus frequency (100 MHZ to 100 GHz) [14]. 

 A. Estimated median business area man-made noise 

 B. Galactic noise 

 C. Galactic noise (galactic center - infinitely narrow beamwidth) 

 D. Quiet sun (1⁄2 degree beamwidth directed at sun) 

 E. Sky noise due to oxygen and water vapor 

 F. Cosmic background 2.7 K 

estimate the noise power when the galactic center is in view. Based on this data, it was found that the 

antenna temperature due to the galactic center is less than 600 K. We concluded that the galactic 

noise represented by curve C (560 K) should provide a reasonable estimate of the overall galactic 

noise power for this system. 

The most significant single source of environmental noise is the contribution due to man-made 

sources. Figure 14 (from CCIR Report 258-5 [18]) gives a more detailed picture of man-made noise 

levels. In this figure, the median noise as a function of frequency, for four different environments 

(Table 1) is plotted along with galactic noise. As indicated previously, the noise figure is 

nonstationary and Fam represents the hourly median value. 

The statistical distribution used in the following calculations is a composite Gaussian model that 

accounts for skewness. CCIR Report 258 provides upper (Du) and lower (Dl) decile values for this 

distribution as a function of frequency and environment. Spaulding and Stewart [19] have analyzed 

the data used to obtain Du and Dl for man-made noise and have found that it is appropriate to use Du

= 9.7 dB and Dl = 7 dB, independent of environmental category and frequency. This approach was 

used in the following calculations. The contribution due to galactic noise also is included in the 

cumulative distribution calculations. The galactic noise distribution was assumed to be Gaussian with 

Du = Dl = 2 dB [19]. 

Examples of the calculated cumulative distributions of Fa for the sum of galactic and business, 

residential, rural, and quiet rural noise environments are shown in Figure 15. This figure gives the
17

Figure 14. Median values of man-made and galactic noise. 

probability (percent of an hour in this case) that Fa is exceeded. Note that the influence of galactic 

noise becomes more important for the larger probabilities. 

Location variability is another important consideration. CCIR Report 258 gives the standard 

deviation of the median value with respect to location for the business, residential, and rural 

environments. As may be expected, location variability for the business environment is much larger 

than either the residential or rural environment. Location variability for the quiet rural environment 

should be small. The increased noise levels that may be expected for greater (than 50%) coverage are 

given in Table 2 (these quantities are added to Fa in Figure 15). 

Table 1. CCIR Report 258 Definitions of Man-made Noise Environments 

Environment Characteristics 

Business Areas where predominant usage is for any type of 

business 

Residential Areas used predominantly for single or multiple family 

dwellings (at least 5 single family units per hectare); no 

large or busy highways 

Rural Areas where dwelling density is no more than 1 every 

2 ha 

Quiet Rural No definition given 
18

Figure 15. Distribution of Fa for man-made and galactic noise. 

The measurements for the quiet rural noise environment are valid below 30 MHz as shown in Figure 

14. In the calculations that follow, the curve is continued (slope of 28.6) to 137 MHz and the 

standard deviation recommended by Spaulding [19] is used to obtain the cumulative distribution 

shown in Figure 15. For exceedence levels of greater than 10%, the noise level in the so called quiet 

rural environment is due largely to galactic noise. 

Table 2. Increased Noise Due to Location Variability 

% locations Business σ = 8.0 

∆FadB 

Residential σ = 2.7 

∆FadB 

Rural σ = 3.2 

∆FadB 

99 18.6 6.3 7.5 

95 13.2 4.5 5.3 

90 10.3 3.5 4.1 

80 6.7 2.3 2.7 

70 4.2 1.4 1.7 

60 2.0 0.7 0.8 
19

4.2 Modification of Noise Power for Proposed Receiving Antennas 

Measurements of the man-made noise described above were made with a receiving antenna 

consisting of a short monopole above a perfectly conducting ground plane. Assuming that man-made 

noise is omnidirectional with respect to azimuth and arrives between 0° and 10° elevation, we 

estimated the gain in noise power (relative to the monopole) for the Volute and Yagi-Uda antennas 

described in Section 2 of this report. For the Volute antenna, the gain (for elevation angles of noise 

arrival) is roughly the same as for a short monopole antenna; hence, received noise power should be 

about the same as given in the previous section (e.g., Figure 15) irrespective of satellite elevation. 

Since the Yagi-Uda antenna has a higher gain, the received noise power is significantly different than 

for the monopole antenna, and hence, will vary with elevation. Assuming the noise power arrives 

equally from all directions at elevations of less than 10°, and the antenna pattern is symmetric 

(crossed Yagi). The calculated relative antenna temperature for the Yagi-Uda and a monopole 

antennas over a perfect conductor is shown in Figure 16. Since the ground temperature is much 

smaller than the man-made noise temperature, it was not included in the calculation. For the purposes 

of this analysis, we were interested primarily in the relative gain for elevation angles of 90° and 5°. 

In terms of the link budget calculation, when the main beam elevation angle is at 90°, 5 dB should be 

subtracted from the noise; when the main beam elevation angle is at 5°, 5 dB should be added to the 

noise. 

4.3 Receiving System Noise and Carrier-to-Noise Ratio 

Using the information provided above, we estimated the noise power for man-made and galactic 

radio noise environments. Calculated values presented in this section are based on a time availability 

of 

Figure 16. Variation of received noise as a function of elevation angle. 
20

99.8% of the average year as required for the weather satellite system. Table 3 gives the noise figure 

(and temperature) exceeded 0.2% of the time for 50% of the locations. For coverage of more than 

50% of locations, the appropriate ∆Fa from Table 2 should be added. 

The system noise power for the high-end system (receiver noise figure of 1 dB) and the low-end 

system (receiver noise figure of 6 dB) are given in Section 2 of this report. Note that the low-end 

receiver contributes about 1,500 K to the system temperature. For practical considerations (i.e., 

changes in noise power of more than a few tenths of a dB), the receiver noise figure only matters 

when the Yagi-Uda antenna is in a quiet rural environment and at elevations of around 90°. In this 

case, the temperature increases to 4,041 K (or a 2-dB increase in the system noise figure). It should 

be noted that an observation elevation of 90° is a relatively infrequent occurrence. Based on the 

required time availability, there is no practical distinction between the high-end receiver and the lowend receiver, particularly if greater than 50% location availability is desired. 

Table 4 gives the calculated CNR exceeded for the two receiving antennas (for areas unaffected by 

ionospheric scintillation) for 50% of the locations 99.8% of the time. The bandwidth is 72 kHz and 

the receiver noise figure is 6 dB, which as indicated above has little effect on CNR. Details of the 

link calculation used to obtain the results shown in Table 4 are provided in Appendix A. Table 4 

includes results for the CNR exceeded 90% of the time. Plots of the cumulative distributions (% of 

time that a given CNR is exceeded) for the various cases shown in Table 4 also are given in 

Appendix A 

4.5 Issues Pertaining to Man-made Noise Statistics 

The man-made noise statistics presented are largely based on measurements that were made more 

than twenty years ago in North America [20]. Since that time, the number of cars has increased; 

however, there have been improvements in the suppression of noise from automobile ignition 

systems (a major contributor to man-made noise in urban areas) and one may predict that noise levels 

Table 3. Noise Figure/Temperature for the System Receiving Antennas 

Volute Antenna Yagi-Uda Antenna 

90° Elevation 

Yagi-Uda Antenna 

5° Elevation Environment 

FadB TaK FadB TaK FadB TaK 

 Business 39.4 2.5x106 34.9 9.0x105 44.4 8.0x106

 Residential 35.1 9.4x 105 30.1 3.0x105 40.1 3.0x106

 Rural 29.8 2.8x105 24.8 8.8x104 34.8 8.8x105

 Quiet Rural 14.3 7.8x103 9.3 2.5x103 18.3 2.0x104
21

in business and residential environments has decreased. In a 1995 paper, Spaulding [14] reviewed 

more recent measurements and trend analysis presented by various researchers. In this paper, he 

discusses the likelihood that noise levels have dropped by 10-20 dB and concludes that “at 100 MHz 

in the 1970’s time-frame, Fa was on the order of 20 dB but now is probably approximately 20 dB 

less.” This conclusion, however is not based on a comprehensive set of noise measurements as would 

be necessary to update the previous survey described in reference [20]. 

While the improvements in automobile ignition systems have affected the noise levels in business 

and residential environments, the contribution due to power transmission and distribution lines, 

where the noise contribution at 100 MHz is due to gap discharge and corona, has probably not 

decreased with time. Figure 17 shows Fa under and a 1/4 mile from a 115-kV line in rural Wyoming. 

Note that the noise measured a 1/4 mile from the power line parallels that predicted for a rural 

environment. If power and distribution lines are the primary noise source in rural environments, rural 

man-made noise is not expected to have decreased. Also, one would not expect noise in an urban 

environment to be less (than rural), as would be the case with a 20-dB reduction in Fa. 

The results presented in this section are applicable to North America; the validity of extension to 

other parts of the world cannot be determined precisely. CCIR Report 258 describes VHF 

measurements made in business and residential areas of the United Kingdom where the noise powers 

were found to be some 10 dB below the results in Figure 4.3. The differences are attributed to 

differences in patterns of utilization of electrical and mechanical appliances, regulations of 

interference, etc. The report also states that due to such differences, the noise statistics should be used 

with caution. It is interesting to note that if an overall 10-dB reduction in urban noise can be justified, 

the man-made noise environments near 100 MHz would be bounded by what are now classified as 

rural (worst) and quiet rural (best) environments. 

In summary, it is likely that there are business (and/or residential) environments with noise levels 10 

dB or more below accepted published values. Although applying a 10-dB reduction to published 

Table 4. CNR (dB) for the Volute and Yagi-Uda Antennas at Maximum (90°) and Minimum 

(13° and 5°, respectively) Elevation Angles 

5-W Transmitter 5-W Transmitter 

Environment Volute Yagi-Uda Volute Yagi-Uda 

90° 13° 90° 5° 90° 13° 90° 5° 

Business -5.8 -20.8 5.7 -18.7 -1.0 -16.1 10.5 -14.0

Residential -1.5 -16.5 10.0 -14.4 3.3 -11.8 14.8 -9.7

Rural 3.8 -11.2 15.3 -9.1 8.6 -6.5 20.0 -4.4

Quiet Rural 18.6 3.5 30.3 6.3 23.3 8.3 35.1 11.1
22

Figure 17. Power line noise measurements near a 115-kV line in rural Wyoming [20]. 

man-made noise statistics for business/residential environments may appear to be reasonable, the 

validity of doing so as a general rule is untested at the present time. 

5. CARRIER-TO-NOISE RATIO REQUIREMENTS FOR LRPT LINK 

This section describes how CNR requirements vary for different signal designs. Signal design in this 

context refers to the link modulation, demodulation, and error-correction coding. First, the signal 

designs are described; next calculations for the required CNR for each signal design are presented; 

and finally, signal design factors other than required CNR that may impact LRPT link performance 

are discussed. Appendix B gives equations used for computations contained in this section. 

5.1 Signal Design Description 

The signal design includes modulation, demodulation, and error correction. In this subsection, signal 

designs that were analyzed are described. 
23

5.1.1 Modulation/Demodulation 

Binary phase-shift keying (BPSK) and quadrature phase-shift keying (QPSK) modulation are 

considered in this report. Without differential source encoding, BPSK and QPSK demodulation 

require coherent detection and a method such as unique word insertion to resolve phase ambiguities 

at the receiver. If differential source encoding is used, phase ambiguities are resolved without unique 

word insertion; however performance is degraded. Examples of binary and quadrature differentialencoding algorithms are available in [21, 22]. 

Differentially encoded BPSK or QPSK can be detected coherently or differentially. If they are 

detected coherently, they are called differentially encoded binary phase-shift keying (DEBPSK) or 

differentially encoded quadrature phase-shift keying (DEQPSK) demodulation. The coherently 

detected symbols are sampled, mapped into bits, and differentially decoded. 

Differential BPSK (DBPSK) and differential QPSK (DQPSK) demodulation use differential 

detection. DBPSK detection is accomplished by multiplying the current symbol by the previous 

symbol. DQPSK detection is accomplished by multiplying the current symbol by the previous 

symbol in both I and Q channels. The differentially detected symbols are sampled and mapped into 

bits. There is no need to differentially decode the bits. 

5.1.2 Error-Correction Coding 

The Reed Solomon (RS), convolutional (CV), and concatenated (CC) coding error-correction 

methods [22] used in this study are derived from [23, 24]. Key parameters for the codes are rate and 

distance. The rate is the ratio of the number of codeword symbols n to information symbols k. The 

distance is a measure of the difference between codewords. 

RS (n = 255, k = 223) code has a 7/8 rate and 32 symbol distance and is used in all proposed signal 

designs [25, 26]. The 32 redundancy symbols allow correction of up to 16 of the 255 codeword 

symbols. A symbol for the RS (255, 223) code is 8 bits or 1 byte long. The 223 information bytes 

transmitted can be used “as is” or may be corrected by using the 32 redundancy bytes. RS codes are 

known for their error-burst-correction capabilities and require codeword synchronization. 

CC coding uses an inner CV code with a outer RS code [27, 28, 29, 30]. The performance of a CC 

can be calculated by computing the probability of error at the output of the CV decoder and then 

using this result as the input probability of error to the RS decoder. 

The (k = 1, n = 2, K = 7) CV code generates 2 coded bits from one information bit for a code rate of~ 

with a minimum free distance of 10. The K is the code’s constraint length and for the (1, 2, 7) CV 

code represents the number of shift register bits used to generate the code. The Viterbi algorithm 

decodes the CV -encoded bits. 
24

An RS interleaver usually is placed between the CV decoder and the RS decoder to minimize the 

effect of error bursts produced by the CV decoder on the RS decoder. Error burst length for the (1, 2, 

7) CV code is defined as a string of bits that starts and stops with a gap of at least six correct bits. 

The error bursts are caused by insufficient received CNR and node synchronization. Node 

synchronization occurs when the beginning of the convolution encoder n-tuples is known. If the 

beginning is not known, the node is not synchronized and BER approaches 0.5. The process of node 

synchronization may take hundreds of symbols. 

5.1.3 Signal Designs 

Table 5 lists the signal designs that are capable of providing the specified data rate with the same 

99% bandwidth. QPSK schemes have CC coding while BPSK schemes use only RS coding. 

Table 5. Possible Signal Designs for the LRPT Link 

Modulation Coding 

BPSK RS 

DEBPSK RS 

DBPSK RS 

QPSK CC 

DEQPSK CC 

DQPSK CC 

5.2 Required Carrier-to-Noise Ratios 

The required CNR is the symbol energy-to-noise ratio (Es/No) plus the modulation and demodulation 

losses for a given signal design: 

CNRrequired Es No Lm / d = / + (10) 

Link margins are computed by subtracting the required CNR from the received CNR (link margins 

are given in Appendix A). 

The LRPT link requires a data rate of 72 kbps at the input to the RS decoder. This data rate includes 

all packet overhead. A BER of 10-6 is assumed to be sufficient for the image compression algorithm 

to deliver the necessary image quality. Rectangular pulse shaping is assumed. Results are valid for 

Gaussian noise only. 
25

5.2.1 Modulation and Demodulation Losses 

To determine the required CNR, the modulation and demodulation losses must be estimated. These 

losses include imperfections in 1) transmitter and receiver filtering, 2) carrier recovery, 3) clock 

recovery, 4) I/Q amplitude balance, 5) I/Q time symmetry, 6) oscillator phase noise, and 7) power 

amplifier linearities. For this study, modulation and demodulation losses were estimated to be 2.0 dB 

for BPSK signal designs [31] and 3.0 dB for QPSK signal designs [32]. 

5.2.2 Symbol Energy-to-Noise Ratio 

All signal designs include RS coding. Figure 18 shows the output bit error rate of the RS code as a 

function of input BER. The input bits are assumed to be degraded by an additive white Gaussian 

noise (AWGN) channel. 

In Figure 18, a BER of 0.0025 is needed at the input of the RS decoder to produce a BER of 10-6 at 

the output of the RS decoder. Figure 19 shows the BER performance for all BPSK demodulators. 

The required Es/No is determined by the intersection of each curve with the 0.0025 BER point. 

BPSK, DEBPSK, and DBPSK require an Es/No of 5.8, 6.5, and 7.2 dB, respectively. 

For QPSK modulation, we determined the Es/No required for the CV decoder to maintain a BER of 

0.0025 at the input of the RS decoder. Figure 20 shows the performance of QPSK with a (1, 2, 7) CV 

code. Figure 21 shows the performance of DQPSK with a (1, 2, 7) CV code. A Viterbi algorithm 

path memory length of32 and no quantization of the input samples was assumed. 

The required Es/No for QPSK + CC and DEQPSK + CC can be read directly from Figure 20. QPSK 

+ CC needs 2.6 dB to produce a BER of 0.0025 at the input of the RS decoder. DEQPSK + CC needs 

2.8 dB to produce a BER of 0.00125 at the output of the CV decoder. The BER of DEQPSK is 

doubled to 0.0025 by the differential decoder prior to the input of the RS decoder. Figure 21 shows 

that the required Es/No for DQPSK + CC is 5.2 dB. 

5.2.3 Results 

Table 6 summarizes the Es/No, coding gain, and required CNR needed for each signal design. The 

coding gain is the difference between 10.5 dB (the Es/No needed for uncoded BPSK and BER of 

10-6) and the Es/No needed for that signal design. The highlighted rows indicate the two signal 

designs used for link margin computations. 
26
27
28

5.3 Other Signal Design Considerations 

Other demodulation issues, including 1) carrier recovery, 2) symbol timing, 3) non-Gaussian noise, 

and 4) ionospheric scintillation are discussed in this section. 

5.3.1 Carrier Recovery 

Carrier frequency tracking is required for all of the signal designs since a Doppler shift due to the 

satellite’s movement causes the center frequency to shift. BPSK, DEBPSK, QPSK, and DEQPSK are 

coherent detection methods that require carrier phase tracking also. Phase jitter caused by imperfect 

carrier phase tracking increases the BER [33]. Additional energy, included in the demodulator losses, 

is needed to overcome excessive phase jitter. 

All of the signal designs are assumed to be transmitted as double sideband suppressed carrier channel 

waveforms. A nonlinearity followed by a narrowband filter (or phase-locked loop) is often used to 

generate a harmonic of the carrier frequency for carrier recovery. BPSK requires a second order 

nonlinearity while QPSK requires a fourth order nonlinearity [34]. Figure 22 shows the rms phase 

jitter in radians as a function of input Es/No. 

Figure 22 shows that QPSK phase jitter is greater than BPSK for a fixed narrowband filter bandwidth 

B. Table 7 shows the required Es/No for each demodulator and its associated rms phase jitter. Phase 

jitter for QPSK signal designs is an order of magnitude larger than BPSK signal designs. 

5.3.2 Symbol Timing 

Symbol-timing recovery is required for all the signal designs. Timing jitter caused by imperfect 

symbol timing recovery increases the BER [33]. Additional energy, included in the demodulator 

losses, is needed to overcome excessive timing jitter. 

Table 6. Signal Design Results (BER 10-6, 72 kbps, shading represents designs used in Appendix A) 

Signal Design Es/No (dB) Required CNR (dB) Coding Gain (dB) 

BPSK + RS 5.8 7.8 4.7 

DEBPSK + RS 6.5 8.5 4.0 

DBPSK + RS 7.2 9.2 3.3 

QPSK + CC 2.6 5.6 7.9 

DEQPSK + CC 2.8 5.8 7.7 

DQPSK + CC 5.2 8.2 5.3 
29

 Figure 22. Carrier phase recovery for BPSK (lower curve), and 

QPSK (upper curve) when BT = 0.01. 

Symbol timing recovery commonly is implemented with a delay and multiply circuit followed by a 

narrowband filter, with bandwidth B, tuned to the symbol rate. In QPSK signal designs the delay and 

multiply circuit is performed in I and Q channels, which are then combined to form the timing 

waveform [35]. Figure 23 shows the rms timing jitter in radians as a function of input Es/No. 

Table 8 shows the Es/No for each signal design and its associated rms timing jitter. The table shows 

that QPSK symbol timing recovery performance is similar to BPSK. 

 Table 7. Signal Design RMS Phase Jitter for BT = 0.01 (shading represents designs used in 

Appendix A) 

Signal Design Es/No (dB) RMS Phase Jitter 

(radians) 

BPSK + RS 5.8 0.040 

DEBPSK + RS 6.5 0.035 

QPSK + CC 2.6 0.30 

DEQPSK + CC 2.8 0.30 
30

Figure 23. Symbol timing recovery for BPSK and QPSK when BT = 0.01. 

5.3.3 Non-Gaussian Noise 

All calculations in this section assume additive white Gaussian noise. It should be noted that manmade noise is typically non-Gaussian. Simulation is required to assess the impact of man-made noise 

on these signal designs. 

5.3.4 Ionospheric Scintillation 

Ionospheric scintillation causes the received signal power to vary over time. Interleavers are used to 

decrease the probability that adjacent symbols experience the same power fade. The performance of 

CV codes operating in a Rician-fading channel with and without interleaving has been well 

documented [36, 37]. However, interleaving is optimal when BdTI = 0.01, where Bd is a measure of 

the channel’s fading rate, T is the symbol period, and I is the interleaving depth. Improvement in 

performance is possible with BdTI < 0.01. Relaxing this constraint decreases interleaver memory and 

delay. Simulation is required to assess the impact of interleaving on these signal designs. 

6. SUMMARY AND CONCLUSIONS 

For the purposes of this study, two archetypal E/S receivers were defined: a low-end system and a 

high-end system. The high-end system consists of a high-gain-tracking antenna combined with a 

high-quality receiver having a noise figure of 1 dB. The low-end system consists of an 

“omnidirectional” antenna combined with an average quality receiver having a noise figure of 6 dB. 
31

Table 8. Signal Design RMS Timing Jitter for BT = 0.01 (shading represents designs used in 

Appendix A) 

Signal Design Detection Es/No (dB) RMS Timing Jitter 

(radians) 

BPSK + RS 5.8 0.09 

DEBPSK + RS 6.5 0.08 

DBPSK + RS 7.2 0.07 

QPSK + CC 2.6 0.12 

DEQPSK + CC 2.8 0.12 

DQPSK + CC 5.2 0.09 

The typical high-end antenna is a crossed Yagi-Uda with a gain of about 10 dB. Both antennas are 

circularly polarized. Propagation studies at 137 MHz conducted by ITS conclude that scintillation 

effects may be detrimental in the equatorial and high-latitude regions. In the equatorial regions, 

scintillation occurs typically in the late night to early morning hours. In the high-latitude regions, 

scintillation is independent of time except near the polar extremities where scintillation is strongest at 

night. Midlatitude regions, including the United States, should not be affected significantly except 

possibly during fierce magnetic storms. 

The normalized variation in received signal power (scintillation index) was calculated from the 

Ionospheric Scintillation Model developed for the U.S. Air Force by Fremouw and Rino [11]. Our 

analysis shows that scintillation fading of 10 dB or more can occur during peak solar activity in the 

high latitudes or in the vicinity of the magnetic equator. It is expected that such occurrences are 

somewhat rare over the 11-year solar cycle. Fades exceeding 3 dB have an average duration of 1 s. 

Link margin calculations for the results presented are based on the 1990 CCIR Report “Man-made 

radio noise” (Report 258-5) that is based on work by Spaulding and Stewart over 20 years ago [19]. 

More recently, Spaulding estimated that man-made noise at 100 MHz in business environments had 

decreased 10-20 dB from the 20-dB level in the 1970’s [14]. We are recommending that 

measurements be made in the representative environments to determine if noise levels have in fact 

changed significantly. 

A variety of modems and channel-coding techniques (“signal designs”) were analyzed to determine 

the CNR ratio necessary to meet the required 10-6 BER for LRPT image transmission at 72 kbps. The 

modems analyzed were 2 and 4-ary phase-shift keyed with and without differential detection or
32

decoding. These modems were combined in the analysis with Reed Solomon or concatenated coding. 

All performance calculations and link margins are for additive white Gaussian noise without 

multipath. The effects of non-Gaussian man-made noise should be investigated. 

Tables 9 and 10 give the link margins as a function of noise environment, time availability (99.8% 

and 99%), maximum (13° elevation) and minimum (90° elevation) propagation path length, and two 

modulation/coding schemes. Shaded areas indicate that the minimum 1-dB link margin is satisfied. 

These tables show that increasing the transmitter power from 5 W to 15 W does not have a 

significant effect on coverage. We also determined that if time availability requirements are relaxed, 

coverage is increased significantly. 

Table 9. Link Margins in dB for Low-End System, 99.8% Time Availability and 5-W Transmitter 

(Dark shading meets 1-dB margin with 5-W transmitter. Light shading extends coverage 

for a 15-W transmitter.) 

13° Elevation 90° Elevation 

DEBPSK+RS DEQPSK+CC DEBPSK+RS DEQPSK+CC 

Business -29 -26 -14 -12 

Residential -25 -22 -10 -7 

Rural -19 -17 -5 -2 

Quiet Rural -5 -2 +10 +13 

Table 10. Link Margins in dB for Low-End System, 90% Time Availability and 5-W Transmitter 

(Dark shading meets 1-dB margin with 5-W transmitter. Light shading extends coverage 

for a 15-W transmitter.) 

13° Elevation 90° Elevation 

DEBPSK+RS DEQPSK+CC DEBPSK+RS DEQPSK+CC 

Business -17 -15 -2 +1 

Residential -13 -10 +2 +5 

Rural -8 -5 +7 +10 

Quiet Rural +1 +3 +16 +18 
33

7. REFERENCES 

[1] T. Pratt and C.W. Bostian, Ch. 4 of Satellite Communications. New York, NY: John Wiley & 

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[3] R.J. Summers, “Educator's guide for building and operating environmental satellite receiving 

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34

[15] Recommendations and Reports of the CCIR, '”Worldwide minimum external noise levels, 0.1 

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[19] A.D. Spaulding and F.G. Stewart, “An updated noise model for use in IONCAP,” NTIA 

Report 87-212, Jan. 1987. 

[20] A.D. Spaulding and R.T. Disney, “Man-made noise: Part I,” Office of Telecommunications 

Report 74-38, Jun. 1974. 

[21] K. Feher, Digital Communications, Englewood Cliffs, NJ: Prentice Hall, pp. 138-140 and 

169-171, 1981. 

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[23] Consultive Committee for Space Data Systems, “Telemetry: Summary of concept and 

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35

[29] K.Y. Liu, “Recent results on the use of concatenated Reed Solomon/Viterbi channel coding 

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Administration, Goddard Space Flight Center, Code 970.1, Oct. 4, 1991. 

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37 

APPENDIX A: LINK BUDGET 

This appendix contains data from link calculations for both the low-end and high-end receiving 

systems. The receiving systems are defined by the receiver noise figures and antennas described in 

Section 2 of this report. The transmitter and receiver losses are assumed to include antenna circuit 

losses, polarization mismatch, and transmission line losses. Modulator/demodulator losses are given 

in Section 5 and are included in the required CNR. 

Tables A-1 through A-4 give the link budget data for various noise environments and receiving 

systems. The first column of numbers in the link budget corresponds to a 5-W spacecraft (S/C) 

transmitter and the second column corresponds to a 15-W S/C transmitter. The antenna temperature 

and system temperature correspond to the definitions given in Section 2 of this report. 

Figures A-1 through A-8 give the cumulative distributions (with respect to time) of the received CNR 

for high-end and low-end systems in various noise environments. The threshold levels required for 

both DEBPSK and DEQPSK modulation are included in the figures. In each figure, there are four 

curves corresponding to two elevation angles and two transmitter powers Pt. The upper two curves 

are for an elevation of 90° (15-W and 5-W transmitter power) and the lower two curves are for an 

elevation of 5° and the same two transmitter power levels. 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 

51 

APPENDIX B: REFERENCE EQUATIONS USED IN SECTION 5 

B.1 BPSK Probability of Error 

The following equations are from [1] and are used for calculating bit error probabilities Pb, where Rd

is the symbol energy-to-noise ratio. 

● BPSK [eq. 5-47, ref. 1] 

( ) 2

1

b Rd P = erfc

● DEBPSK [eq. 5-114, ref. 1] 

( ) 2

1 ( ) 2

b d Rd P = erfc R − erfc

● DBPSK [eq. 5-125, ref. 1] 

exp( ) 2

1 Pb = −Rd

B.2 QPSK Probability of Error 

The following CV code equation is from [2]. For the (1, 2, 7) CV code, N = 20, dfree = 10, and β is an 

array having values 36, 211, 1,404, 11,633, 76,628, and 469,991 for elements 10, 12, 14, 16, 18, and 

20 respectively. 

( ) P d P2 d

N

d d free

b ∑ β =

<

● P2(d) for QPSK and DEQPSK 

) ( ) 2 ( 2

1 ( ) 2 Q R d R d P d erfc d

d = =

● P2(d) for DQPSK 

))] 4 2[ ( 2 sin( 3

4 ))] 4 2

[ ( sin( 3

2 ( ) 2

π π P d = erfc Rd d = Q Rd d
52 

B.3 Carrier Recovery 

The carrier recovery equations are from [3]. In the following equations, R is the input signal-to-noise 

ratio, BN is the narrowband filter bandwidth, T is the symbol period, σφ is the rms phase jitter in 

radians, φ is the instantaneous phase, φˆ is the average phase, and E {•} is the expectation operator. 

{ } 2 2

σ φ φˆ φ = E −

● BPSK 

] 4

1

2

1 [ 2

2

R R

σ φ = BNT +

● QPSK 

] 1 2.531 1 21.094 1 24.469 1 [0.1125 1.4625 2 3 4

2

R R R R

σ φ = BNT + + + +

B.4 Symbol Timing Recovery 

The symbol timing recovery equations are from [4]. In the following equations, T is the symbol 

period, τ is the instantaneous delay, τˆ is the average delay, ξ is the relative delay error, πσ ξ is the 

rms timing jitter in radians, Rs is the symbol rate, and BN is the narrowband filter bandwidth. The 

relative delay error is expressed as: 

T

(τ τˆ) ξ − =

and the variance can be expressed as 

s s

s

N

E R

E

N B N

4

) 2 (1

( )

0

0

2

2

+

=

π

πσ ξ

B.5 Reed Solomon Code 

The RS code equations were derived from results in [2]. N is the number of symbols in the codeword, 

p is the probability of input bit error, m is the number of bits per symbol, t is the number of 

correctable symbol errors, and Pb is the output bit error rate. 

i N i

N

i

N

i t

b mp mp N

i P −

= +

⎟ − ⎠

⎞ ⎜

⎝

⎛ = ∑ ( ) (1 )

1 2
53 

B.6 References 

[1] W.C. Lindsey and M.K. Simon, Telecommunication System Engineering, Englewood Cliffs, 

NJ: Prentice Hall, 1973. 

[2] J.G. Proakis, Digital Communications 3rd Edition, New York, NY: McGraw Hill, pp. 464-

466 and 470-511. 

[3] L.E. Franks, “Carrier and bit synchronization in data communications - A tutorial review,” 

IEEE Transactions on Communications, vol. COM-28, no. 8, pp. 1107-21, 1980. 

[4] L.C. Palmer, S.A Rhodes, and S.H. Lebowitz, “Synchronization for QPSK transmission via 

communication satellites,” IEEE Trans. Comm., vol. COM-28, no. 10, pp. 1302-1314, 1980.