Link-budget analysis allows you to specify the performance of receivers and transmitters, and ensure there is sufficient margin between the received and required carrier powers to deliver the required link performance.
With so many applications exploiting space technology, a question I often get asked is how to plan and design the RF up and down-links between satellites and ground stations. In this post, I want to introduce the fundamentals of satellite-communication links, how to predict their performance, how to specify the performance of receivers and transmitters, and how to ensure there is sufficient margin between the received and required carrier powers to deliver the required link performance, i.e., Eb/N0, SNR, or C/N0.
In terms of spectrum management, the choice of carrier frequency is dictated by the required service, e.g., TT&C, Earth exploration, deep space, or payload communications; the transmission direction, i.e., Earth-to-space or space-to-Earth; ITU regulations such as the maximum permitted power-flux density, CCSDS requirements, the information bit rate or bandwidth, spectral congestion; the capability, coverage and price of ground-station support; and the availability of licenses. I have worked on a number of projects where the choice of carrier frequency was based primarily on cost!
Coding, baseband filtering and modulation formats impact the maximum occupied bandwidth and these are selected to fit within the assigned frequency range. As an example, a TT&C transmitter with a data rate of 32 kbps will nominally require information bandwidths of 64 or 32 kHz when modulating a carrier using BPSK or QPSK respectively.
Figure 1 shows a typical link between a transmitter and a receiver, e.g. between a spacecraft and a ground station, i.e. a downlink, or between a mobile user and a satellite, i.e. an uplink. The transmitter output is radiated using an antenna and a receiving antenna captures the carrier power from the incoming electromagnetic wave and feeds this to an LNA.
Figure 1 Configuration of a satellite link.
A transmitter feeds an antenna, with gain GT outputting a total power, PT in W, towards a receiver. If this is radiated isotropically, i.e., uniformly in all directions, then the power flux density in W/m2 received at a distance r metres from the source is: PT/4𝝅r2. In practice, a directional antenna is used to maximise the transmitted power along a particular direction of interest, known as the boresight, resulting in an antenna gain and a received power flux density of:
The performance of the transmit equipment is measured by its Effective Isotropic Radiated Power (EIRP) in W, defined as PTGT. On its way, the radiated power encounters free-space loss, comprising atmospheric and rain attenuation, de-pointing and polarisation effects, as well as insertion, matching and noise-figure losses in the transmitting and receiving equipment.
A receiver consists of its antenna with gain GR in the direction of the transmitter, connected by a feeder to an LNA. Given the power flux density, Ƒ, at the receiving antenna with an effective aperture area, Aeff, the received power in W is:
The above equation can be re-written as:
which is known as the Friis transmission formula, comprising the EIRP, the antenna gains, and the path loss. For given values of wavelength (or frequency) and distance, the received signal power, PR, can be increased using three methods:
The Friis transmission formula can be expressed in dB as:
At the receiver input, the power of the modulated carrier is, C, and all sources of noise in the link contribute to the system noise temperature, T. This conditions the noise power spectral density, N0, at the receiver input, enabling the calculation of the link performance, C/N0. The performance of the receive equipment is measured by its figure-of-merit, G/T, where G represents the overall gain of the receive equipment.
In a space-communication link, the receiver has to cope with extremely weak carrier inputs because of transmission over long distances and physical size and mass limits of spacecraft antennae. Noise power at the receiver must be minimised to maximise performance and is calculated using, kTB, where k is Boltzmann’s constant, T the system noise temperature and B the noise bandwidth. Let’s look at some examples:
Example 1: Uplink Received Power
Consider a transmitting antenna of an Earth station equipped with an antenna of diameter 4 m, fed with a power PT of 100 W at a frequency of 10 GHz. It radiates power towards a GEO satellite, 42,000 km from the station, on the axis of the receive antenna with an effective aperture area of 1 m2:
The EIRP of the transmitting Earth Station is PTGT = 20 dBW + 50.2 dBi = 70.2 dBW
The power flux density at the receiver is PTGT / 4𝝅r2 = -93 dBW/m2
The free-space loss over 42,000 km at 10 GHz is (4𝝅r / λ)2 = 204.9 dB
The gain of the satellite receiving antenna, GR = (4𝝅Aeff / λ) 2 = 41.4 dB
The received, carrier power is EIRP – free-space attenuation + gain of receiving antenna = 70.2 – 204.9 + 41.4 = -98.2 dBW, which is equivalent to 150.1 pW or 245 µV peak-to-peak for a 50 Ω input.
If we assume an Eb/N0 of 10.5 dB, a feeder attenuation of 3 dB, polarisation and de-modulation losses of 1.5 and 2.5 dB respectively, the required and received C/N0 are 53 dB and 101.2 dB respectively, resulting in a healthy link margin of 48.2 dB.
In terms of correctly specifying the receiver, its input sensitivity needs to be reconciled with the received, carrier power to ensure it can function and deliver the required performance. The minimum required sensitivity can be calculated from the minimal noise power based on the receiver’s noise figure and kTB. The resulting link margin is obtained by subtracting the required C/N0 from the received C/N0, with the former derived from a target Eb/N0 or BER. All receivers have a dynamic range, which is the ratio of maximum to minimum signal strength over which they are designed to operate.
For uplinks, ground-station providers typically specify its transmit power, EIRP, the frequency range and antenna polarisation to assist RF planning and analyses.
Example 2: Downlink Received Power
Consider a transmitting antenna of a LEO satellite equipped with a patch antenna with a diameter of 0.25 m, fed with a power, PT of 10 W at a frequency of 1.5 GHz. It radiates power towards an Earth station 1,000 km from the spacecraft, on the axis of the receive antenna with an effective aperture area of 9 m2:
The EIRP of the transmitting satellite is PTGT = 10 dBW + 9.2 dBi = 19.2 dBW
The power flux density at the receiver is PTGT / 4𝝅r2 = -111.7 dBW/m2
The free-space loss over 1,000 km at 1.5 GHz is (4𝝅r / λ)2 = 156 dB
The gain of the satellite receiving antenna, GR = (4𝝅Aeff / λ) 2 = 34.5 dB
The received, carrier power is EIRP – free-space attenuation + gain of receiving antenna = 19.2 – 111.7 + 34.51 = -102.1 dBW, which is equivalent to 60.7 pW or 156 µV peak-to-peak for a 50 Ω input.
If we assume an Eb/N0 of 10.5 dB, a feeder attenuation of 3 dB, polarisation and de-modulation losses of 1.5 and 2.5 dB respectively, the required and received C/N0 are 62 dB and 97.3 dB respectively, resulting in a positive link margin of 35.2 dB.
In terms of correctly specifying the transponder’s transmitter, you need to reconcile its output power based on physical size and mass limits, as well as the available power budget, to ensure that PT delivers positive link margin to achieve the required performance. Price, reliability and heritage can also influence the procurement! For downlinks, ground-station providers typically specify G/T, the frequency range, antenna polarisation and maximum data rate to assist RF planning and analyses.
Both of the above examples have been simplified; in practice, there will be other considerations such as formal, regulated limits on power-flux density, out-of-band emissions and off-axis EIRP Link performance can be affected by leakage from terrestrial communication services or deliberate interference, and your analyses may need to account for these noise sources.
Tracking a satellite accurately maximizes link margin and the elevation and azimuth angles are used to locate the spacecraft from a point on the Earth’s surface. Azimuth tells you what direction to face, starting with North at 0°, East at 90°, South at 180° and West at 270°, while elevation indicates how high up in the sky to look, with 0° barely rising over your horizon and 90° (the zenith) directly overhead as shown below:
Figure 2 Illustration of elevation and azimuth angles.
Elevation affects antenna gain, noise temperature and atmospheric attenuation, and your link-budget analyses needs to account for the location of the satellite with respect to the ground station/user.
In this post, I’ve introduced some basic calculations for transmitters and receivers, and if you would like to learn more about calculating margins, the analyses for other types of links, e.g., inter-satellite communication between orbiting satellites, or the effects of backed-off, multi-carrier operation, Spacechips offers a one-day training course on, Mission Design, Spectrum Management & Link-Budget Analyses. I will be teaching Australian/Asian time zones on 19th of October and further information is available by emailing, firstname.lastname@example.org.
If you have the opportunity to work with a Mission Operations team, ask them for the transmission logs to reconcile measured link margins with predicted estimates. This can help you understand the origin of any unexpected losses in performance or communication drop-outs.
Until next month, the first person to tell me the difference between zenith and nadir will win a Courses for Rocket Scientists World Tour tee-shirt. Congratulations to Chris from South Africa, the first to answer the riddle from my previous post.
This article was originally published on EDN.
Dr. Rajan Bedi is the CEO and founder of Spacechips, which designs and builds a range of advanced, L to K-band, ultra high-throughput on-board processors, transponders and Edge-based OBCs for telecommunication, Earth-Observation, navigation, internet and M2M/IoT satellites. The company also offers Space-Electronics Design-Consultancy, Avionics Testing, Technical-Marketing, Business-Intelligence and Training Services. (www.spacechips.co.uk). Rajan can also be contacted on Twitter to discuss your space-electronics’ needs: https://twitter.com/DrRajanBedi