Communications subsystem

Draft

The communications subsystem is the only one whose performance is set almost entirely by an equation that can be written on one line. Everything else is consequence.

The link budget

Carrier to noise density

\frac{C}{N_0} = \text{EIRP} + \frac{G}{T} - L_{fs} - L_a - k

All terms in decibels, with $k = -228.6$ dBW/K/Hz, the Boltzmann constant.

EIRP: Effective isotropic radiated power: transmitter power plus antenna gain minus losses ahead of the antenna. What the transmitting end contributes.
G/T: Receive antenna gain divided by system noise temperature. The single figure of merit for a receiving station, and the reason a large cold-feed dish is worth so much.
Free space path loss: Geometric spreading of the wavefront. The dominant term, and the one nothing can be done about.
Atmospheric loss: Absorption and rain attenuation. Negligible at S-band, severe at Ka-band and above.

The margin is what remains after subtracting the required $E_b/N_0$ and the data rate. Link budgets are normally required to close with 3 dB of margin, which is a factor of two in power, held against modelling error and degradation.

Path loss

L_{fs}\,[\text{dB}] = 92.45 + 20\log_{10}d_{\text{km}} + 20\log_{10}f_{\text{GHz}}

Link	Distance	Band	Path loss
LEO, 400 km	400 km	S, 2 GHz	150.5 dB
LEO, 400 km	400 km	X, 8.4 GHz	163.0 dB
GEO	35 786 km	Ku, 12 GHz	205.1 dB
GEO	35 786 km	Ka, 30 GHz	213.1 dB
Lunar	384 400 km	X, 8.4 GHz	222.6 dB
Mars at 1 AU	1.5 × 10⁸ km	X, 8.4 GHz	274.4 dB

Path loss rises with frequency as well as distance, which is initially counterintuitive: higher frequency appears to be penalised. The resolution is that path loss is defined against an isotropic antenna, and a real antenna of fixed physical size gets more gain at higher frequency, by the same square of frequency. The two effects cancel exactly for a fixed-aperture link, and higher frequency then wins on bandwidth. This is why the industry has moved steadily from S to X to Ku to Ka.

The Mars row shows the fundamental problem of deep space communications. A 274 dB path loss is a factor of $2.7 \times 10^{27}$ , and closing that link is what the Deep Space Network exists for.

Antenna gain

G = \eta\left(\frac{\pi D}{\lambda}\right)^2, \qquad \theta_{3\text{dB}} \approx \frac{70\lambda}{D}\ \text{degrees}

Antenna	Diameter	Frequency	Gain	3 dB beamwidth
Small spacecraft dish	0.3 m	8.4 GHz	26.2 dBi	8.3°
GEO satellite spot beam	1.0 m	12 GHz	39.8 dBi	1.75°
DSN station	34 m	8.4 GHz	68.0 dBi	0.07°

Gain and beamwidth are inseparable, and that coupling is the central design tension. A high-gain antenna closes the link but must be pointed to a small fraction of a degree, which imposes a requirement on guidance, navigation and control and usually a gimbal mechanism.

Every spacecraft therefore carries at least two antennas: a high-gain antenna for the mission data rate, and a low-gain or omnidirectional antenna that works at any attitude and low rate. The low-gain antenna is what makes recovery from a tumbling safe mode possible at all, and it is not an accessory but the subsystem’s most important reliability feature.

Bands

Band	Frequency	Use	Character
UHF	0.3 to 3 GHz	Proximity links, relay, low-rate TT&C	Wide beams, no pointing needed; used for Mars surface to orbiter relay
S	2 to 4 GHz	TT&C, low-rate science	Robust, rain-insensitive, congested
X	8 to 12 GHz	Deep space, Earth observation downlink	The deep-space workhorse
Ku	12 to 18 GHz	Commercial communications	Rain fade becomes significant
Ka	26.5 to 40 GHz	High-throughput satellites, high-rate science	Large bandwidth, severe rain fade, needs fade mitigation
V and W	40 to 75 GHz	Feeder links, emerging	Very wide bandwidth, atmospheric absorption bands
Optical	~1550 nm	Very high rate	Enormous bandwidth, extremely narrow beam, blocked by cloud

Spectrum is allocated internationally through the ITU and is a genuine scarcity. A commercial system needs a filing, coordination against existing users, and a national licence. This is a schedule item measured in years, not a formality, and it belongs on the programme plan alongside the hardware.

Optical communications offers orders of magnitude more bandwidth because carrier frequency is a hundred thousand times higher. The obstacles are pointing, since beamwidths are microradians and demand sub-arcsecond pointing plus point-ahead compensation for light travel time, and clouds, which block the link entirely and force a geographically diverse network of ground stations. Inter-satellite optical links avoid the atmosphere altogether and are now operational at scale in large constellations. See Distributed satellite systems.

Modulation and coding

The Shannon-Hartley theorem bounds what any scheme can achieve:

C = B\log_2\left(1 + \frac{S}{N}\right)

Practical systems select a modulation and a forward error correction code to approach it. Uncoded BPSK needs about 9.6 dB of $E_b/N_0$ for a bit error rate of $10^{-5}$ ; modern LDPC and turbo codes achieve the same error rate within roughly 1 dB of the Shannon limit. That coding gain of nearly 9 dB is a factor of eight in transmit power or antenna area, and it is free apart from processing.

Adaptive coding and modulation adjusts the scheme to conditions in real time, using a high-order modulation in clear sky and falling back to a robust one during rain fade. This is standard in commercial systems and is what makes Ka-band viable despite its weather sensitivity.

Ground segment

The receiving end contributes as much as the spacecraft, through $G/T$ .

The Deep Space Network operates 34 m and 70 m antennas at three sites roughly 120° apart in longitude, at Goldstone, Madrid and Canberra, so that any direction in the sky is always visible from at least one. Cryogenically cooled low-noise amplifiers push system noise temperature to a few tens of kelvin, which buys as much link margin as a large increase in spacecraft transmit power would.

Near-Earth missions use commercial ground station networks, which sell contact time on distributed antennas and have largely displaced dedicated ground stations for small operators. See Ground segment.

The ordering in that box is the practical one. Coding gain is nearly free. Moving up a band costs a redesign. More transmit power costs power and thermal capacity, both of which are already scarce. Reducing the data rate is what actually happens on most programmes, and it is why edge processing is attractive: reducing the data is cheaper than transmitting it.

References

Sklar, B. Digital Communications: Fundamentals and Applications, 2nd ed., Prentice Hall, 2001.
Maral, G., Bousquet, M. and Sun, Z. Satellite Communications Systems, 6th ed., Wiley, 2020.
Wertz, J. R., Everett, D. F. and Puschell, J. J. (eds.) Space Mission Engineering: The New SMAD, Microcosm Press, 2011, chapter 13.
CCSDS 401.0-B, Radio Frequency and Modulation Systems, and the CCSDS recommended standards for telemetry channel coding.
Deep Space Network, DSN Telecommunications Link Design Handbook, JPL 810-005. The authoritative source for deep-space link budgets.