1) The document discusses satellite communication uplink and downlink equations. The uplink equation considers parameters like uplink EIRP, antenna gains and losses to determine uplink performance. Downlink performance is determined similarly. 2) Noise figure is introduced as a way to quantify noise from devices. It is defined as the ratio between input/output signal-to-noise ratios. Noise temperature is also defined in terms of noise figure. 3) The overall system noise temperature is calculated by summing the individual noise temperature contributions from each device in the signal path, accounting for any gains or losses. This represents the total noise at the antenna.

1. SATELLITE
COMMUNICATION
LECTURE-7
THE UPLINK & DOWNLINK EQUATION
NOISE FIGURE, NOISE TEMPERATURE
OVERALL SYSTEM NOISE TEMPREATURE

2. LINK EQUATION FOR UPLINK
• Satellite link performance evaluation for an uplink includes additional considerations and
parameters.
• If we represent the uplink parameters by the subscript U, then the basic link equations are
𝐶
𝑁 𝑈
= 𝐸𝐼𝑅𝑃 𝑈 +
𝐺
𝑇 𝑈
- 𝐿 𝑓𝑠 𝑈
- 𝐿 𝑈 + 228.6
when, 𝐿 𝑓𝑠 𝑈
is the uplink free space path loss and 𝐿 𝑈 is the sum of other losses on the uplink.
• Uplink performance is often specified in terms of a power flux density requirement at the
satellite receiver antenna to produce a desired satellite output transmit power.

3. UPLINK
• The performance of the final power amplifier in the satellite, usually a nonlinear high power traveling
wave tube amplifier (TWTA) or solid state amplifier (SSPA), is the critical element in defining the flux
density requirement for the uplink.
Basic satellite transponder parameters
• The single carrier saturation flux density, 𝚿, is defined as the power flux density required
at the satellite receiving antenna to produce the maximum saturated output power for the
transponder, with single carrier operation.

4. UPLINK
The power flux density is of the form:
𝑝𝑓𝑑 𝑟=
𝑃𝑡 𝐺𝑡
4𝜋𝑟2=
𝑒𝑖𝑟𝑝
4𝜋𝑟2
where, r is the path length.
From the definitions of spreading loss, S, and free space path loss, 𝐿 𝑓𝑠,we have-
𝑝𝑓𝑑 𝑟=
𝑒𝑖𝑟𝑝
𝐿 𝑓𝑠 𝑆
𝑜𝑟, 𝑒𝑖𝑟𝑝 = 𝑝𝑓𝑑 𝑟 𝑙 𝑓𝑠 𝑆
Thus, the EIRP at the ground terminal that provides the single carrier saturation flux density, 𝚿, at the
satellite receiving antenna:
𝑒𝑖𝑟𝑝 𝑈
𝑆
= 𝚿 𝑙 𝑓𝑠 𝑆 𝑈

5. UPLINK
• The resulting link equation for the uplink, for single carrier saturated output operation, is
therefore, in dB,
𝐸𝐼𝑅𝑃 𝑈
𝑆
= 𝚿 + 𝐿 𝑓𝑠𝑈 + 𝐿 𝑈 + 𝑆 𝑈
where, other uplink losses, 𝐿 𝑈, have been included.
• Thus,
𝐶
𝑁 𝑈
for uplink can be written as:
𝐶
𝑁 𝑈
=
𝑒𝑖𝑟𝑝 𝑈
𝑆 𝑔 𝑟
𝑡 𝑠 𝑈
𝑙 𝑓𝑠𝑈 𝑙 𝑈 𝑘
=
𝑙 𝑓𝑠𝑈 𝑙 𝑈 𝑆 𝑈
𝑔 𝑟
𝑡 𝑠 𝑈
𝑙 𝑓𝑠𝑈 𝑙 𝑈 𝑘

6. UPLINK
𝐶
𝑁 𝑈
=
𝑆 𝑈
𝑔 𝑟
𝑡 𝑠 𝑈
𝑘
Or in dB, the uplink equation can be written as:
𝐶
𝑁 𝑈
= 𝚿 + 𝑆 𝑈 +
𝐺
𝑇 𝑈
+ 228.6
This result gives the uplink performance for single carrier saturated output power operation.
• It is important to note that the link performance is independent of link losses and path length, and
performance improves with increasing SU, i.e., with decreasing uplink operating frequency.

7. DOWNLINK
• The basic performance equations for the downlink can be represented as:
𝐶
𝑁 𝐷
=
𝑒𝑖𝑟𝑝 𝐷
𝑆 𝑔 𝑟
𝑡 𝑠 𝐷
𝑙 𝑓𝑠𝐷 𝑙 𝐷 𝑘
Or in dB, the downlink equation can be written as:
𝐶
𝑁 𝐷
= 𝐸𝐼𝑅𝑃 𝐷 +
𝐺
𝑇 𝐷
- 𝐿 𝑓𝑠 𝐷
- 𝐿 𝐷 + 228.6
The uplink, described earlier, uses the saturation flux density at the satellite receiver at a specified link
performance quantity. This is generally not the case for the downlink, since the received signal at the
ground terminal is an endpoint in the total link, and is not used to drive a high power amplifier.

8. NOISE FIGURE
• A convenient way of quantifying the noise produced by an amplifier or other device in the
communications signal path is the noise figure, 𝒏 𝒇.
• The noise figure is defined by considering the ratio of the desired signal power to noise power ratio at the
input of the device, to the signal power to noise power ratio at the output of the device.
• Considering a device with a gain, g, and an effective noise figure,𝑡 𝑒, as shown in Figure. The noise figure of the
device is then, from the definition, is given as
𝑛 𝑓 =
𝑝𝑖𝑛
𝑛𝑖𝑛
𝑝 𝑜𝑢𝑡
𝑛 𝑜𝑢𝑡
=
𝑝𝑖𝑛
𝑘𝑡 𝑜 𝑏
𝑔𝑝𝑖𝑛
𝑔𝑘(𝑡 𝑜 + 𝑡 𝑒)𝑏
where, 𝑡 𝑜 is the reference temperature, usually 290K and b is the bandwidth.

9. NOISE FIGURE AND NOISE FACTOR
Then, simplifying we get-
𝑛 𝑓 =
𝑡 𝑜 + 𝑡 𝑒
𝑡 𝑜
= 1 +
𝑡 𝑒
𝑡 𝑜
When expressed in dB, noise figure becomes-
𝑁𝐹 = 10𝑙𝑜𝑔 1 +
𝑡 𝑒
𝑡 𝑜
𝑑𝐵
The term 1 +
𝑡 𝑒
𝑡 𝑜
is referred to as the noise factor.

10. NOISE OUT
• The noise out, 𝑛 𝑜𝑢𝑡, of the device in terms of noise figure is given as:
𝑛 𝑜𝑢𝑡 = 𝑔𝑘 𝑡 𝑜 + 𝑡 𝑒 𝑏 = 𝑔𝑘𝑡 𝑜 1 +
𝑡 𝑒
𝑡 𝑜
𝑏
𝑛 𝑜𝑢𝑡 = 𝑛 𝑓 𝑔𝑘𝑡 𝑜 𝑏
𝑛 𝑜𝑢𝑡 = 𝑛 𝑓 𝑔𝑛𝑖𝑛
This result shows that the noise figure quantifies the noise introduced into the signal path by
the device, which is directly added to the noise already present at the device input.

11. NOISE TEMPERATURE
The effective noise temperature can be found from noise figure-
𝐴𝑠, 𝑛 𝑓 =
𝑡 𝑜 + 𝑡 𝑒
𝑡 𝑜
= 1 +
𝑡 𝑒
𝑡 𝑜
𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒, 𝑡 𝑒 = 𝑡 𝑜 𝑛 𝑓 − 1
𝑤ℎ𝑒𝑛 𝑒𝑥𝑝𝑟𝑒𝑠𝑠𝑒𝑑 𝑖𝑛 𝑑𝐵,
𝑡 𝑒 = 𝑡 𝑜 10
𝑁𝐹
10 − 1 𝑑𝐵
This result provides the equivalent noise temperature for a device with a noise figure of NF dB.

12. OVERALL SYSTEM NOISE TEMPERATURE
• The noise contributions of each device in the communications transmission path, including
sky noise, will combine to produce a total system noise temperature, which can be used
to evaluate the overall performance of the link.
• Consider a typical satellite receiver system with the components shown in Figure.

13. OVERALL SYSTEM NOISE TEMPERATURE
• All noise temperature contributions will be summed at the reference point, indicated by the
dot in Figure.
• We begin with the left most component, then move to the right, adding the noise temperature contribution
REFERRED TO THE REFERENCE POINT, keeping track of any amplifiers in the path. The sum of the noise
temperature contributions as referred to the reference point will be the system noise temperature, 𝑡 𝑠.
• The line loss noise contribution 290 𝑙 − 1 referred back to the reference point, passes
through the LNA amplifier, in the reverse direction. Therefore the line loss noise contribution
AT THE REFERENCE POINT will be
290 𝑙 − 1
𝑔 𝐿𝐴
• which accounts for the gain acting on the noise power; i.e., a power of
290 𝑙−1
𝑔 𝐿𝐴
at the input to the LNA is
equivalent to a power of 290 𝑙 − 1 at the output of the device.

14. OVERALL SYSTEM NOISE TEMPERATURE
• Continuing with the rest of the devices, proceeding in a similar manner to account for all
gains in the process, we get the total system noise, 𝑡 𝑠 , at the reference point is-
𝑡 𝑠 = 𝑡 𝐴 + 𝑡 𝐿𝐴 +
290 𝑙 − 1
𝑔 𝐿𝐴
+
𝑡 𝐷𝐶
1
𝑙
𝑔 𝐿𝐴
+
𝑡𝐼𝐹
𝑔 𝐷𝐶
1
𝑙
𝑔 𝐿𝐴
Thus, the system noise temperature in terms of noise figure is given as-
𝑁𝐹𝑠 = 10𝑙𝑜𝑔 1 +
𝑡 𝑠
290
The system noise temperature, 𝑡 𝑠 represents the noise present at the antenna terminals from all
the front-end devices.