We have been working on the communications problem since we received the SETI Institute information at the February 21, 2008 “Kick Off”. The 42 presently installed antennas at SETI should provide about 1000 square meters of signal capture area (+51 dBi at 1200 MHz, assuming 80% capture efficiency). (The eventual array is planned to produce almost ten times this signal capture). The estimated “Gigabyte” of information required for the prize can be sent at reduced speed. Using 1000 seconds for this transmission gives about 10 Million bits per second rate including error correction data. Using BPSK modulation with Reed Solomon (255, 223) plus R-1/2, K=7 Viterbi error correction reduces Eb/No to 2x for an excellent Bit Error Rate (10 exp -7).

As discussed previously, the “Oversize” nature of the SETI antenna array gives an advantage over a single large antenna (or close spaced array) by reducing the radio noise temperature for signals from the Moon. This comes at the cost of introducing “sidelobes” which are the mathematical equivalents of “Aliases” in sampled signal processing. (The “esoteric” part of the prior discussion mentioned that widely spaced radio antennas in an array have the same mathematical effect as widely spaced samples (beyond the Nyquist Criteria) in signal processing. The “Aliases” produced in signal processing are like the “side lobes” in antenna theory. Regularly spaced samples produce discrete aliases, often related to harmonics of the desired signal. The same is true of the spaced antennas. Both can be moved to pseudo random spacing which increases the number of aliases, but decreases their amplitude.) The sidelobes and the increased resolution have major impact on the use of such arrays in Radio Astronomy. To receive communication from the Moon, such an array, with proper phasing of its receivers, provides all the signal of a 40 meter diameter antenna, with a lower noise level than that huge unit would provide!

Our estimate of a 20 to 30 K noise temperature should be well above the floor the cryo-cooled receivers in the SETI system should produce, and includes a portion of the 213K Lunar Radio Noise Emission. With systems noise temperature below 28K, No is (4 exp -22) Joules and Eb/No = 2.0 is achieved with 8 exp -22 Joules/bit received power. Combining this with the 10^8 bps rate assumed above produces a minimum of 8 exp -15 Watts received power, or 8 exp -18 Watts/m^2 received for this antenna array. Using 400,000 km to the Moon = 4 exp 8 meters, 4xPixR^2 equals 2 exp 18 m^2. Thus only 16 Watts Isotropic ERP is required from the Moon to achieve reliable wideband communication! This would be increased to 160 Watts ERP if a single, 40 meter diameter receiving parabola were used (with the higher noise temperature that results), and would increase to 16,000 watts if a single, 1.2 meter receiving parabola were used.

The Lunar Lander could produce this wideband communication with a single Watt of transmitter power if a thin, lightweight transmitting antenna 14 inches square (12 dBi) were aimed at the Earth (at 1200 MHz). This transmitting array would have a beam width of 40 degrees, so aiming would not be very critical. But keep in mind that if the services of SETI were not secured (including payment for the ½ of the data capture not offered free), the power requirements would be much larger! The 1.2 meter diameter antenna mentioned above would need 1000 Watts transmitter power, continued for 20 minutes, even with this transmitting antenna. Any antenna or array more than ten times this area (still requiring 100 Watts transmitter power on the Moon) would be a major development and construction project. A few Ham (Amateur Radio) operators have built such systems for “Moon Bounce” (EME) communications, and might be induced to cooperate if a suitable communications frequency were selected.