The communications system between spacecraft and/or the ground stations can be specified fairly easily.

Ultimately, a certain data rate, or bandwidth, needs to be transmitted and received over a specific range. This will require a certain amount of transmitter power, and style of antennas. Specifics like antenna pointing, equipment power requirements, size, mass, etc drop out pretty fast.

The general governing equation for communications is the Link Equation. It is pretty much just an accounting of different signal losses including the dilution via spreading of radio energy over distance (Path Loss). Since communications predates modern computers or calculators, The link equation is commonly written in deciBells (dB) form. This allows adding of factors rather than multiplication.

An example of this in caculator form is at

Another way of looking at the problem is to consider the amount of signal energy impinging on the receiving antenna, a comparing that with the amount of thermal noise. The thermal noise is the sum of the environment (sky) temperature and the 'effective' temperature of the receiving equipment multiplied by Boltsman's Constant and the bandwidth of the receiver.

Signal to Naise Ratio (SNR) = Signal Power / Noise Power.

This gives a little insight on why narrow bandwidths and Low Noise Amplifiers on receivers make sense. (LNA's amplify the incoming signal above all the miscellaneous receivers component noises to make such things as cable losses and other parts insignificant.)

Another obvious improvement is to get the biggest antenna possible. Antennas are generally specified in Gain and beamwidth at a certain frequency. For a simple, efficiently fed dish see.

As is alluded to above, there is some advantages to using previously defined bands and commercially available equipment for communications. An all digital system can carry voice easy enough and 2.4 or 5.6 GHz data equipment is plentiful. Consider a 802.11g system from the above link.

```Frequency  2.4 GHz
Earth station Antenna 20 meter (yea one is available, but not for 5GHz)  = 52 dBi
Transmitter output power 4 watts = 36dBm  (yea, we'll need an FCC waiver or ham)
Cable/connector losses very small, -0.1dB
Transmitting antenna  2 m = 31 dB  (The earth is about 1.8 degrees across from the moon)
Range 400,000 km (Lunar) = -212 dB (used 40 km then add 10000x = 80dB)
Receiver Sensitivity ( good at 1 Mbps)  = -94 dBm
link margin 0.8 dB  (very marginal)
LNA and Temperature gain (temps of earth = 300k temps of space <30k)
```

This shows that a 2 meter dish on the lunar surface, pointed correctly, and given about 4 watts of transmit power, (probably 10 watts electrical) can support a 1Mbps link. A spacecraft unable to point a 2 meter dish needs a better system. Consider 440MHz and Ham Radio equipment.

```(Frequency  0.44 GHz)
Transmitter output power 40 watts = 46dBm  (could go up to 1500 Watts)
Cable/connector losses very small, -0.1dB
Transmitting antenna  10 dB  (helix pointed in general direction 40 deg beamwidth)
Effective Incident Radiated Power (EIRP) = = 400 Watts
Range 400,000 km, sphere of 8.5E25 meters = 47 E-25 W/M^2
Earth station Antenna 20 meter (315 m^2) =  receives 148 E -23 Watts
Sky temp = 10 Kelvin
Sky+LNA Temp = 45 K
Boltzmann's constant = 1.3806488E−23 J/K
Bandwidth PSK31 style system can have 1 Hz (1 bps)
Noise Power = Boltzmann's constant * Temp * Bandwidth
SNR =  148 / (1.38*45*1.0)  = 2.38 or 3.8dB ( anything above 3 db is ok )

40 watts of RF power for 1 bps (and thats with a 20 meter dish !)
```

So the radios are not magic, but such long range does give some limitations.

Since pointing a large dish at the earth is required for high speed communications at lunar range, then perhaps a lunar communications center with antennas always pointed at the earth and local radio links to nervy settlements or orbital relay satellites may make sense. The relay satellites can be little more than Cubesats with all the heavy lifting left to the big dishes on the surface.