Noise, Link Budgets and Performance Engineering

Introduction

A satellite link is not designed successfully merely because a transmitter produces sufficient power or an antenna provides high gain. The engineering question is whether the received signal has adequate quality after propagation loss, antenna losses, thermal noise, interference, nonlinear distortion, and time-varying impairments have been considered. Link-budget analysis provides the quantitative framework for answering this question.

This chapter develops the principal methods used to evaluate uplinks, downlinks, and complete end-to-end satellite links. The central performance quantities are equivalent isotropically radiated power (EIRP), antenna figure of merit (G/T), carrier-to-noise ratio (C/N), carrier-to-interference ratio (C/I), energy per bit to noise-density ratio (Eb/N0), link margin, outage probability, and availability.

All decibel calculations must use compatible reference quantities. Power gains and losses are expressed in dB, temperatures in kelvin, and bandwidths in hertz unless explicitly stated otherwise.

Learning Objectives

After completing this chapter, the reader should be able to:

1. Calculate EIRP, received carrier power, G/T, C/N, C/I, and Eb/N0.

2. Construct uplink, downlink, and end-to-end link budgets.

3. Distinguish thermal noise, interference, implementation loss, and propagation impairments.

4. Determine link margin and estimate outage probability and availability.

5. Interpret the effect of antenna size, transmit power, bandwidth, coding, modulation, and atmospheric attenuation.

6. Evaluate a practical satellite-link design and identify its dominant constraints.

1. The Link-Budget Model

A link budget is an accounting of gains and losses between a transmitter and receiver. In linear form, the received carrier power is

Pr = Pt Gt Gr / Ltotal,

where Pt is transmitter output power, Gt and Gr are transmit and receive antenna gains in the direction of propagation, and Ltotal is the product of all dimensionless losses. In decibel form,

Pr(dBW) = Pt(dBW) + Gt(dBi) + Gr(dBi) - Ltotal(dB).

For a free-space path,

Lfs(dB) = 92.45 + 20 log10(fGHz) + 20 log10(dkm),

where fGHz is frequency in GHz and dkm is path length in kilometres. This expression assumes free-space propagation and uses the speed of light consistently with the stated units.

The total loss may include free-space loss, atmospheric absorption, rain attenuation, polarization mismatch, pointing loss, feeder loss, scintillation allowance, and other implementation losses. These terms should not be added indiscriminately: a loss must represent a physically distinct mechanism and must correspond to the operating conditions being analysed.

1.1 EIRP

Equivalent isotropically radiated power is

EIRP(dBW) = Pt(dBW) + Gt(dBi) - Lt(dB),

where Lt is the loss between the transmitter output reference plane and the antenna aperture. EIRP is the power an ideal isotropic antenna would need to radiate to produce the same far-field power flux density.

EIRP is not the actual power radiated by a directional antenna. For example, a 20 dBW transmitter feeding a 40 dBi antenna with 2 dB feeder loss has an EIRP of 58 dBW, while the physical radiated power remains lower than the isotropic equivalent.

1.2 Received Power and Flux Density

If the satellite transmits EIRP toward a receiving earth station, the incident power flux density at distance d is

S = EIRP / (4 pi d²),

in W/m². The receiving antenna effective aperture is

Ae = Gr lambda² / (4 pi),

where Gr is the linear receive gain and lambda is wavelength. Therefore,

Pr = S Ae = EIRP Gr / Lfs,

when only free-space loss is included.

2. Noise and System Noise Temperature

Thermal noise power over bandwidth B is

N = k Ts B,

where k = 1.380649 x 10^-23 J/K is Boltzmann’s constant and Ts is the system noise temperature in kelvin. In dBW,

N(dBW) = -228.6 + 10 log10(Ts) + 10 log10(B),

where -228.6 dBW/K/Hz is 10 log10(k).

The system temperature depends on the receiver noise temperature, antenna noise temperature, feeder losses, and the physical environment. A passive loss before a low-noise amplifier is particularly harmful because it both attenuates the signal and adds noise.

For a receiver with equivalent input noise temperature Te and antenna noise temperature Ta, a basic model is

Ts = Ta + Te.

If a passive component with linear loss L and physical temperature T0 precedes a receiver of equivalent noise temperature Te, the input-referred temperature is

Ts = Ta + (L - 1)T0 + LTe,

assuming matched components and a consistent reference plane. This relation illustrates why front-end losses are more damaging than losses after the low-noise amplifier.

2.1 Noise Figure and Noise Temperature

At a reference temperature T0, commonly 290 K, noise factor F and equivalent noise temperature Te are related by

Te = (F - 1)T0,

where F is linear, not in dB. If noise figure is specified as NF(dB), then F = 10^(NF/10).

For cascaded stages, Friis’ formula is

Ftotal = F1 + (F2 - 1)/G1 + (F3 - 1)/(G1G2) + ...,

where Fi are linear noise factors and Gi are preceding linear power gains. This shows that the first active stage generally dominates receiver noise performance.

2.2 G/T

The receiving-antenna figure of merit is

G/T(dB/K) = Gr(dBi) - 10 log10(Ts).

A larger G/T indicates better ability to receive a weak signal. G/T is especially useful because it combines antenna gain and receiver noise temperature into one quantity. It is a property of the receiving system and reference plane, not of the received carrier alone.

3. Carrier-to-Noise Ratio

The carrier-to-noise ratio is

C/N = Pr/(kTsB).

Using EIRP and G/T,

C/N(dB) = EIRP(dBW) + G/T(dB/K) - Lpath(dB) + 228.6 - 10 log10(B).

This equation assumes that EIRP, G/T, and path loss refer to compatible polarization, frequency, direction, and reference planes. Lpath may include free-space and atmospheric losses but should not include losses already incorporated into EIRP or G/T.

A useful carrier-to-noise-density form is

C/N0(dB-Hz) = EIRP + G/T - Lpath + 228.6.

Since N = N0B,

C/N(dB) = C/N0(dB-Hz) - 10 log10(B).

C/N0 is valuable when comparing systems with different occupied bandwidths.

4. Energy per Bit and Modulation Performance

For a bit rate Rb,

Eb/N0 = C/(N0 Rb),

so that

Eb/N0(dB) = C/N0(dB-Hz) - 10 log10(Rb).

Equivalently,

Eb/N0(dB) = C/N(dB) + 10 log10(B/Rb).

The ratio B/Rb is the spectral-efficiency reciprocal when B is the noise-equivalent bandwidth. The required Eb/N0 depends on modulation, coding rate, target bit-error rate, packet-error rate, implementation loss, and receiver architecture. It is therefore incorrect to assign one universal Eb/N0 threshold to all digital links.

For a coded system, the required operating value is often written

(Eb/N0)operating = (Eb/N0)required + Limpl,

where Limpl represents implementation degradation in dB. The available link margin is

Margin(dB) = (Eb/N0)available - (Eb/N0)operating.

5. Uplink, Downlink, and End-to-End Performance

An uplink budget evaluates the earth-station transmitter to the satellite receiver. Its important receive parameter is the satellite receive G/T. A downlink budget evaluates the satellite transmitter to the earth-station receiver and uses the earth-station G/T.

The uplink and downlink do not generally have equal C/N. The complete bent-pipe link combines independent noise contributions. If uplink and downlink C/N values are C/Nu and C/Nd, then

1/(C/N)total = 1/(C/Nu) + 1/(C/Nd),

where the ratios on the right are linear. In dB, conversion to linear units is essential before applying this relation.

With interference included, the total effective ratio is

1/(C/(N+I)) = 1/(C/N) + 1/(C/I),

again using linear ratios. For several independent interference sources,

1/(C/I)total = sum [1/(C/I)i].

This reciprocal addition explains why a very strong link cannot compensate indefinitely for severe interference.

Worked Example 1: Downlink C/N

A satellite downlink has EIRP = 52 dBW, earth-station G/T = 24 dB/K, path loss = 207 dB, and receiver noise bandwidth B = 36 MHz. Then

C/N = 52 + 24 - 207 + 228.6 - 10 log10(36 x 10^6).

Since 10 log10(36 x 10^6) = 75.56 dB,

C/N = 52 + 24 - 207 + 228.6 - 75.56 = 22.04 dB.

If the required operating C/N is 14 dB, the clear-sky margin is 8.04 dB before other allowances are applied.

Worked Example 2: End-to-End Combination

Suppose the uplink has C/Nu = 18 dB and the downlink has C/Nd = 22 dB. Linear ratios are 63.10 and 158.49. Therefore,

1/(C/N)total = 1/63.10 + 1/158.49 = 0.02213,

and

(C/N)total = 45.19, or 16.55 dB.

The end-to-end value is lower than either individual value, as required by physical reasoning.

6. Interference Engineering

Interference may be co-channel, adjacent-channel, intermodulation, cross-polarization, terrestrial, or intentional. Unlike thermal noise, interference may be correlated with traffic, frequency reuse, beam geometry, or network configuration.

Important interference ratios include C/I, carrier-to-adjacent-channel interference, and carrier-to-intermodulation ratio. The total performance ratio with thermal noise and interference is C/(N+I), not the simple arithmetic sum of C/N and C/I.

Satellite transponder nonlinearities can generate intermodulation products when multiple carriers share a travelling-wave tube amplifier. Input back-off and output back-off reduce distortion but also reduce available EIRP. Frequency planning, polarization discrimination, guard bands, antenna sidelobe control, power control, and filtering are therefore link-budget decisions as well as spectrum-management decisions.

7. Propagation Impairments and Availability

Clear-sky link budgets are insufficient for high-availability systems. Rain attenuation is often the dominant impairment above approximately 10 GHz, particularly for low elevation angles and tropical climates. Other impairments include gaseous absorption, cloud attenuation, scintillation, depolarization, and tropospheric multipath.

A simple design representation is

Marginrequired = Aavailability + Limplementation + Lother,

where Aavailability is the attenuation exceeded only for the allowed fraction of time. This is a design allowance, not a universal constant.

If attenuation A is modelled as a random variable with cumulative distribution function F_A(a), outage probability for a margin M is

Pout = P(A > M) = 1 - F_A(M).

Availability is

Availability = 1 - Pout,

when outage is defined solely by attenuation exceeding the available margin. Real service availability may also include equipment failures, power interruptions, satellite outages, and operational downtime.

For a Gaussian approximation to a performance variable X with mean mu and standard deviation sigma, the probability of falling below threshold x0 is

P(X < x0) = Phi((x0 - mu)/sigma),

where Phi is the standard normal cumulative distribution. Rain attenuation itself is often non-Gaussian, so empirical distributions or recognized propagation models are preferred for engineering design.

Availability and Diversity

Site diversity uses geographically separated gateways so that intense rain at one site is less likely to affect the other simultaneously. Uplink power control can compensate for moderate attenuation, but it cannot compensate without limit because of amplifier saturation, interference constraints, and finite power. Adaptive coding and modulation reduce the required Eb/N0 during fades, trading throughput for availability.

8. A Systematic Link-Budget Procedure

A defensible link budget follows these steps:

1. Define the service: frequency, orbit, coverage, modulation, coding, bit rate, bandwidth, and target availability.

2. Establish reference planes for transmitter power, antenna gain, receiver input, and system temperature.

3. Calculate EIRP for each transmitting terminal.

4. Calculate free-space and propagation losses for the actual frequency, slant range, and elevation angle.

5. Determine receiver G/T, including antenna noise and front-end losses.

6. Calculate C/N0, C/N, and Eb/N0 for uplink and downlink segments.

7. Combine independent noise and interference contributions in linear units.

8. Subtract implementation losses and determine margin.

9. Allocate fade margin according to propagation statistics and required availability.

10. Perform sensitivity analysis by varying power, antenna gain, temperature, bandwidth, elevation, and rain attenuation.

The budget should state whether values are clear-sky, worst-case, annual-percentile, or instantaneous. It should also identify all assumptions and avoid double-counting losses.

9. Detailed Applied Case: Illustrative Ku-Band VSAT Service

Background

Consider an illustrative geostationary Ku-band VSAT system serving remote industrial sites. The service requires 4 Mbit/s forward data, QPSK with coding, and 99.9% annual link availability. The gateway transmits through a high-gain antenna, while remote terminals use smaller antennas.

Problem

The clear-sky design must provide adequate end-to-end Eb/N0, while rain attenuation at the remote sites may consume the available margin. The engineer must decide whether to increase gateway power, enlarge remote antennas, reduce coding rate, or introduce adaptive coding and modulation.

Analysis

Assume the calculated clear-sky values are:

• Uplink C/N = 20 dB.
• Downlink C/N = 16 dB.
• C/I = 25 dB.
• Required end-to-end operating C/N after implementation allowance = 11 dB.

First combine uplink and downlink noise. The linear uplink and downlink ratios are 100 and 39.81. Thus,

1/(C/N)noise = 1/100 + 1/39.81 = 0.03512,

so the combined C/N is 28.48, or 14.55 dB. Combining this with C/I = 25 dB gives

1/(C/(N+I)) = 1/28.48 + 1/316.23 = 0.03868,

which gives C/(N+I) = 25.85, or 14.12 dB. The clear-sky margin relative to the 11 dB operating requirement is therefore 3.12 dB.

Approach and Solution

A 3.12 dB margin may be insufficient for the required availability if the annual attenuation distribution frequently exceeds this value. The design team evaluates three measures:

1. Increase remote antenna gain by 2 dB, improving downlink C/N and reducing the terminal’s susceptibility to rain fade.

2. Apply adaptive coding and modulation so that the terminal changes to a mode requiring 2 dB less Eb/N0 during moderate fades.

3. Use uplink power control within the satellite transponder’s power and interference limits.

The preferred solution is a coordinated combination rather than unlimited power increase. Antenna improvement provides a permanent gain, adaptive coding preserves connectivity at reduced throughput, and power control compensates for short-term attenuation. A propagation study using local rain statistics is then required to verify the 99.9% target.

Outcome

The final design is accepted only after the attenuation exceeded for 0.1% of the year is shown to be below the combined available margin in the selected operating mode. The link budget is maintained in several modes rather than as a single nominal row.

Learning Points

The dominant design variable is not always transmitter power. A modest antenna improvement, appropriate coding adaptation, and accurate local propagation statistics may provide better availability and lower interference than a large fixed-power increase. End-to-end performance must be calculated using reciprocal linear combinations, and interference must be included explicitly.

10. Design Trade-offs and Limitations

Increasing transmit power improves C/N only logarithmically: a 3 dB power increase doubles linear power and increases the ratio by 3 dB. Increasing antenna diameter can improve gain, but it increases cost, pointing sensitivity, structural loading, and installation requirements. Reducing bandwidth lowers thermal noise but may constrain symbol rate and spectral efficiency. Lowering system temperature is particularly valuable at the receiver, although cryogenic solutions are generally impractical for ordinary user terminals.

A link budget is a model, not a measurement. Errors arise from uncertain antenna patterns, inaccurate rain statistics, misaligned reference planes, unmodelled interference, equipment ageing, and optimistic implementation assumptions. Commissioning measurements of EIRP, G/T, spectrum, and performance under representative weather should therefore validate the analytical budget.

11. Governance, Regulation, and Responsible Engineering

Satellite links operate within national licensing regimes and international frequency coordination processes. Engineers must respect power-flux-density limits, emission masks, orbital coordination agreements, and interference-protection requirements. Deliberate interference, unauthorised transmission, and misleading availability claims are serious technical and regulatory failures.

Automated systems using AI may assist with anomaly detection, propagation prediction, power control, and adaptive resource allocation. However, training data may be geographically biased, predictions may fail during unusual weather, and automated power changes may create interference. Human oversight, explainable alarms, conservative bounds, audit logs, and regulatory compliance remain necessary.

12. Contemporary Developments and Best Practices

Modern high-throughput satellites use multibeam frequency reuse, digital channelizers, beam hopping, flexible payloads, and adaptive coding and modulation. These developments improve capacity but make interference, gateway diversity, and resource scheduling more coupled. Electronically steered antennas enable rapid beam control but require careful calibration and sidelobe management.

Best practices include maintaining separate clear-sky and fade-condition budgets, using linear units for reciprocal combinations, documenting reference planes, including implementation loss explicitly, validating antenna and G/T measurements, applying realistic propagation statistics, and performing Monte Carlo or time-series simulations for availability. Sensitivity analysis should identify whether power, antenna gain, noise temperature, interference, or propagation is the most cost-effective improvement.

Chapter Summary

Link-budget engineering converts a satellite communication requirement into measurable power, noise, interference, and availability quantities. EIRP combines transmitter power and transmit antenna gain; G/T combines receive antenna gain and system noise temperature. Free-space and atmospheric losses determine received carrier power, while Boltzmann’s relation determines thermal noise. C/N0, C/N, and Eb/N0 connect the physical link to bandwidth, bit rate, modulation, coding, and error performance.

Uplink and downlink noise ratios combine through reciprocal linear addition, as do thermal noise and interference. Link margin is the difference between available and required performance, while outage probability depends on the statistical distribution of propagation impairments and other failure mechanisms. High-quality designs distinguish clear-sky performance from availability performance, avoid double-counting losses, validate assumptions through measurement, and balance power, antenna size, coding, bandwidth, interference, cost, and regulation.

Key Terms

EIRP: Equivalent isotropically radiated power of a transmitting system.

G/T: Receiver figure of merit equal to antenna gain divided by system noise temperature.

System noise temperature: Equivalent input temperature representing antenna and receiver noise.

Noise figure: Degradation of signal-to-noise ratio introduced by a receiver.

Free-space path loss: Ideal propagation loss caused by spherical spreading.

C/N: Carrier-to-noise power ratio in a specified bandwidth.

C/N0: Carrier-to-noise-density ratio, independent of receiver bandwidth.

C/I: Carrier-to-interference ratio.

Eb/N0: Energy per bit divided by noise spectral density.

Implementation loss: Practical degradation relative to an ideal modem or coding result.

Link margin: Available performance above the required operating threshold.

Uplink: Transmission from an earth station to a satellite.

Downlink: Transmission from a satellite to an earth station.

Rain attenuation: Signal loss caused by absorption and scattering in precipitation.

Outage probability: Probability that performance falls below a specified threshold.

Availability: Fraction of time a service meets its performance requirement.

Site diversity: Use of geographically separated sites to reduce common propagation outages.

Power control: Dynamic adjustment of transmit power to compensate for channel variation.

Adaptive coding and modulation: Dynamic selection of coding and modulation according to link conditions.

Intermodulation: Unwanted spectral products generated by nonlinear devices.

Review Questions

Short Answer Questions

1. Define EIRP and distinguish it from physical radiated power.

2. Why is G/T an important receiver performance metric?

3. State the relationship between C/N0, C/N, and receiver bandwidth.

4. Why must C/N and C/I be combined using linear ratios?

5. What is meant by link margin?

Long Answer Questions

1. Derive the decibel expression for C/N using EIRP, G/T, path loss, Boltzmann’s constant, and bandwidth.

2. Explain the construction of an uplink and downlink budget, including reference planes and propagation losses.

3. Discuss the relationship between noise figure, equivalent noise temperature, and cascaded receiver stages.

4. Explain how rain attenuation, adaptive coding, power control, and site diversity influence availability.

5. Critically evaluate the trade-offs among transmit power, antenna diameter, bandwidth, receiver temperature, and interference protection.

Analytical / Application Questions

1. A link has EIRP = 48 dBW, G/T = 21 dB/K, path loss = 205 dB, and bandwidth = 10 MHz. Calculate C/N and determine the margin if the required value is 12 dB.

2. An uplink C/N is 17 dB and a downlink C/N is 19 dB. Calculate the combined end-to-end C/N in dB.

3. A system has available Eb/N0 of 9 dB and requires 6.5 dB, including implementation loss. Determine its clear-sky margin and explain what additional information is required to assess availability.

Multiple Choice Questions with Answers

Question 1

A transmitter has 20 dBW output power, a 40 dBi antenna, and 2 dB feeder loss. What is its EIRP?

A. 18 dBW

B. 58 dBW

C. 62 dBW

D. 800 dBW

Correct Answer: B. 58 dBW

Question 2

Which quantity combines receive antenna gain and system noise temperature?

A. EIRP

B. C/I

C. G/T

D. Eb/N0

Correct Answer: C. G/T

Question 3

What is the approximate thermal noise power for Ts = 500 K and B = 1 MHz?

A. -178.6 dBW

B. -141.6 dBW

C. -108.6 dBW

D. -82.6 dBW

Correct Answer: B. -141.6 dBW

Question 4

If C/N0 is 80 dB-Hz and the bit rate is 1 Mbit/s, what is Eb/N0?

A. 20 dB

B. 60 dB

C. 80 dB

D. 140 dB

Correct Answer: A. 20 dB

Question 5

An uplink C/N is 20 dB and a downlink C/N is 20 dB. What is the combined C/N?

A. 10 dB

B. 17 dB

C. 20 dB

D. 40 dB

Correct Answer: B. 17 dB

Question 6

Which impairment is commonly especially important for Ku-band and higher-frequency links?

A. Rain attenuation

B. Earth rotation

C. Solar illumination only

D. Battery capacity

Correct Answer: A. Rain attenuation

Question 7

If available Eb/N0 is 11 dB and required operating Eb/N0 is 8 dB, the link margin is:

A. -3 dB

B. 3 dB

C. 8 dB

D. 19 dB

Correct Answer: B. 3 dB

Question 8

What does C/(N+I) represent?

A. Carrier relative to thermal noise and interference together

B. Carrier relative only to antenna gain

C. Noise relative to bandwidth

D. Interference relative to transmitter power

Correct Answer: A. Carrier relative to thermal noise and interference together

Question 9

A 3 dB increase in transmitted power ideally produces what change in carrier-to-noise ratio?

A. 0.5 dB

B. 1 dB

C. 3 dB

D. 10 dB

Correct Answer: C. 3 dB

Question 10

Availability, when outage is defined by threshold exceedance, is equal to:

A. Pout

B. 1 + Pout

C. 1 - Pout

D. Pout/2

Correct Answer: C. 1 - Pout