Communications, Command, and Telemetry

Once in orbit a spacecraft must be able to communicate with the ground.  The spacecraft transmits telemetry to its ground station and receives commands.  Its communication system is therefore critically important.  Because of the range between the spacecraft and ground the spacecraft must have a very strong antenna.
An antenna couples, or links, electromagnetic radiation (radio waves) in free space and the transmitter/receiver.  It converts the radio waves into electrical signals (or vice versa) and can focus signals.  Antennas can be directional, focused in one direction, or omnidirectional, having no focus.
Gain is a measure of the concentrating ability of an antenna.  Gain is the ratio of the strength of a signal from the antenna's design direction and one from another direction.  Omnidirectional antennas, by definition, have a gain of one.  The shape of an antenna determines its gain.
A whip antenna, like the one on a car, has a gain of one, it's omnidirectional.  A parabolic reflector antenna, or dish, has a gain based on the area of the dish and the wavelength of the signal.  This is because long wavelength waves have a chance of passing through the dish instead of being reflected and concentrated by it.  The gain naturally scales up with area since a larger area dish collects more of the wave than a smaller one.
From the transmitter waves spread out through space.  No matter how strong the source is at a distance the signal is week, because the same intensity is spread over a larger area.  A number of photons starts at the transmitter, as they move out their number is the same but they become more spread.  Signal strength at the receiver depends not only its gain, the power and gain of the transmitter, but also the distance between the two:

The middle term in parentheses is the effect of separation between transmitter and receiver, called the space loss factor.  Because of space loss very powerful transmitters and antennas are necessary for spacecraft communication.
When the antenna receives radio waves it converts them into electrical signals.  The receiver's job is to convert those electrical waves into meaningful information.  Carrier waves have three defining properties: amplitude, frequency, and phase.  Information is transmitted through modulation, one of these three properties changes while the others remain the same.  The change corresponds to information.
Amplitude modulation (AM) is the simplest method.  The height, or intensity, of the wave changes while frequency stays the same.  AM radios are simpler to design and build than the other two techniques. Terrestrially AM also has the advantage of longer range.
Frequency modulation (FM) involves the amplitude remaining constant while the frequency (or length) of the wave varies.  FM radio can carry more information than AM radio, at the expense of range.
Phase modulation (PM) is a technique where neither the height nor length of a wave is changed, but rather the start point.  Sine waves start at zero traditionally and one full wave consists of both a high crest and low valley and returns to start.  PM radio changes the start point after one length to another start point, perhaps so that it starts from zero and passes a valley followed by a crest.  This technique is rarely used for analog information (like music stations) but is optimal for digital information and is widely used on spacecraft.
What determines the amount of information that can be carried by a carrier wave is its signal-to-noise ratio.  Noise is unwanted interference with the signal and comes in two varieties: white noise and random noise.  White noise is predictable and repeating and can often be filtered out by the receiver.  Random noise is just that: random and unpredictable, it cannot be filtered out.  Noise comes from any source of EM radiation including nearby electronics, other radio sources, the sun, earthshine, and reflected signals in the atmosphere.
A large source of noise is actually the temperature of the antenna itself.  All bodies emit electromagnetic radiation based on their temperature which can interfere with received signals.  In fact temperature is used to describe all noise.  The total effect of noise power is expressed as the operating noise temperature:

Bandwidth (the B here) is the frequency range of the receiver.  Higher bandwidth means more information can be contained in the signal, however it also means more noise.  FM's functional difference from AM is its higher bandwidth, it carries more information (for music stations that means higher sound fidelity and stereo sound) but it pays in higher noise, which means lower range.  To be understood the carrier has to have a high signal to noise ratio (S/N).
To increase the amount of information we can send we use multiplexing.  Multiplexing sends multiple signals at once.  The technique we see every day is called frequency multiplexing, many radio signals are available at once and the receiver simply focuses on the desired one.  We can also send multiple signals over a single carrier.
Time multiplexing combines the multiple signals into a single stream.  Each receiver is timed to check for its signal at different times.  First one, then the next, then the next:

Code multiplexing involved the multiple signals being sent with vastly different encoding.  In essence each decoder ignores the signals that it can't understand.  Each system has its own decoder and each decoder receives the same signal.  Each one decodes the signal differently, and so receives a different result.  An analogy would be standing in a crowded room with only one other person speaking a language you understand.  It becomes easy to ignore the other voices (they become noise) and focus only on the one you understand.  In this method each signal is another signal's noise.

Commands sent to the spacecraft begin at its ground station.  Here operators develop operation code or look up instructions in the command dictionary, a collection of commands already prepared for the mission.  Signals are encoded and modulated before being transmitted.  Spacecraft commands are usually transmitted in the S-band (1.6 - 2.2 GHz), C-band (5.9 - 6.5 GHz), and Ku-band (14 - 14.5 GHz) ranges.
On the spacecraft the carrier wave is picked up by the antenna and converted into electrical signals which are amplified and sent to the receiver/demodulator.  The purpose of this device is to convert the carrier wave signal into usable data.  Often times the demodulated signal is, itself, another wave, in the 14 - 16 kHz range.  This subcarrier is then converted into a bitstream by the decoder.  The subcarrier contains the encoded instructions, converted from digital data in the form of bits.  As an analog signal the subcarrier can be modulated into a transmissible carrier wave.
Once decoded the information is sent as a bitstream, a sequence of logical ones and zeros.  The decoder also produces two other signals: enable/lock signal, and clock.  Enable signals tell the command processor that a command is about to follow, clock tells it at what rate to expect bits.  Clock tells the command processor to expect bits (which is essentially either an on or off signal) so far apart in the signal.  Different clocks for each system creates time division multiplexing, each system looks for its own bitstream without reading any of the others yet each is receiving the same continuous signal.
Telemetry is collected by the spacecraft before being transmitted back to the ground station.  Data acquisition is the first step of this process.  Data is collected by transducers, devices that convert some stimulus (like light, pressure, temperature, etc.) into an electrical signal.  The signal is conditioned, usually by amplifying the voltage to make changes more noticeable.  It is then passed through an analog-to-digital converter a device that samples the voltage of the continuous signal at discrete times.
Analog-to-digital conversion is necessary for data to be processed by a computer, which understands only digital information.  Sampling rate is how many times each second the converter reads the voltage and sends that value to the processor.  Sampling rate must be taken a minimum number of times for accurate readings, this minimum is known as the Nyquist criterion.  The bare minimum says that the sample frequency must be at least twice the highest expected signal frequency.  Or if we expect the value to change 10 times each second then we must sample it at least 20 times each second.  Rarely is the bare minimum used, more often instead of a factor of two a factor of ten is used.  However, too many samples floods us with useless information.
Data is sent to the processor, which must store and format it.  Data processing converts the raw data into usable information.  While the data input is a string of voltage readings, the information sent back to ground has been converted into the actual values measured by the transducers (the original light, temperature, pressure, etc.) and is time stamped so that it has some meaning and value to users.  We'll look at this more in the next lesson on spacecraft computer systems.