As described in the previous Moon to Moon Satellite Communication section, the Moon Satellite needs to receive a spread signal with a high enough SNR over the noise floor to successfully repeat the data. The satellite will operate with preknowledge of the noise floor, which should be quite low as the receiving antenna will be pointed away from the Earth, towards the back side of the moon. According to a figure cited in class and checked against a NASA report on a similar topic, deep space may be approximated to have a low noise temperature of T=3K-5K [8]. This Bent Pipe Transponder is summarized in the block diagram below.
Transmit & (Earth Sat.) Receive Antenna
The transmit antenna's design is driven by the 3dB beamwidth necessary to illuminate the Earth. This is done so that Earth Satellite handoff is made simple (passive for the Moon Satellite) and so that antenna steering on the Moon Satellite would not be necessary. However, it can be employed on the Earth Satellite, making the receiving antenna of a narrower beamwidth feasible. From the geometry of the problem, the 3dB beamwidth needs to be about 9 degrees. Using the mean wavelength over the wide transmit band, the diameter can be found using a simple equation [9]. The average gain of the antenna is also found by using a common approximation that requires only the 3dB beamwidth of the antenna. Finally, note that the These calculations may be found below.
Link Budget Analysis of Moon Satellite to Earth Satellite
The distance between the Earth and Moon is approximately 450,000 km and with clear, line of sight, propagation loss serves as the primary form of loss between the two bodies. Using the previously calculated antenna gains, the raw power received at the Earth Satellite when transmitting 1 W from the Moon Satellite is quite low at about -185 dBm as calculated below.
Because a large portion of the higher half of the spread spectrum signal would be attenuated by the atmosphere of Earth [10], it is necessary to do at least some form of processing at one of the Earth Satellites. This processing must involve despreading the CDMA signals into their respective lower original bandwidths. However, because the signal is made up of thousands of samples, each sequence must be kept track of so that it is not lost in the shuffle. With that caveat, from the calculations below it is found that amazingly, 1 W of power is able to yield a carrier to noise ratio of almost 1 dB. With well-iterated Turbo Codes, this would give us nearly error-free communications. Furthermore, this was taken at worst case path loss, using the highest frequency's wavelength for all loss calculations.
