Earth-moon-earth (EME) or "moon bounce" is a radio-communications technique where a signal is transmitted from a ground station to the Moon and then reflected from the moon back to earth to another ground station within view of the Moon (i.e. within its footprint).  In a sense this is the ultimate in satellite communications, where the Moon is the satellite.  Unlike an artificial satellite however, there is no repeater receiving the signal and re-transmitting it. 

EME communications were first proposed in 1940 and are believed to have occurred with RADAR experiments carried out in the United Kingdom and in Germany in 1943.  RADAR is a type of radio transmission at microwave frequencies and it is used to detect objects in the air, at sea or on the ground.  RADAR was developed by the Allies and the Axis Powers during World War 2.  Accidental reflections were observed, from the rising Moon.  Many a radio amateur was involved in RADAR's development.  The first deliberate attempt at communication was carried out in 1946.  A teletype link was established by the US Navy linking Pearl Harbour to Washington, DC - a useful link in the days before artificial satellites in 1957 (and the launch of Sputnik 1). 

Most amateur radio EME communications are on the 2 m, 70 cm and 23 cm bands.  Radio modes used include Morse code (CW) and digital modes (JT65).

There are multiple challenges to EME:

• Media interfaces - radio waves in EME must propagate through the Earth's atmosphere, which is of uneven density and which becomes rarefied with altitude. Parts of the atmosphere may also be ionized.  Eventually the radio waves then must travel through the vacuum of space until they reach the Moon.  The Moon has no atmosphere of significance.  These differences in density cause attenuation and refraction (including reflection) of the radio waves.  This means that the signal that reaches the Moon is weaker than from Earth.  In addition the radio waves become less concentrated (diffused) and therefore even weaker.
• Irregular Surface of the Moon - the Moon has irregular surface features, such as mountains, valleys and craters. In addition the Moon is not flat but rather spherical-like.  Signals aimed at the Moon are therefore reflected by these features and some signals end up being delayed as the travel to the lunar rim.  Such delays result in different echoes.  Echoes and polarization of antennas needs to be thought about.  As the Moon is moving in relation to the ground station (and the ground station is also moving) thanks to rotation, these reflections vary and result in both constructive and destructive interference over time.  This is called libration fading.
• Doppler Shift - as with satellites, the Moon is moving in relation to the ground station. This creates an effect knows as a Doppler Shift.  At 2 m this shift can be a s high as 300 Hz at moonrise or moonset.  Receiving and transmitting frequencies have to be adjusted to compensate. 
• Faraday Rotation - this phenomenon affects polarization of signals. Most antennas have a preferred polarization but as the signals pass through the atmosphere, they may become rotated.  This results in decreased antenna effectiveness if the polarization becomes mismatched.  Since one is dealing with weak signals, that does not help matters.   The effect is more pronounced at lower VHF frequencies, but less so at 1296 MHz and above.  One way to mitigate this is to use antenna arrays.

YARS has a number of members who are interested in EME but to date no operational setup has been constructed or any experiment conducted.  We probably have that capability as we can and do engage in amateur satellite communications. 

• https://science.nasa.gov/
• https://www.electronics-notes.com/articles/ham_radio/amateur-propagation/moonbounce-propagation-eme.php
• https://rsgb.org/main/technical/space-satellites/moonbounce/
• Bouncing Signals Off Venus! (EVE?)
• Moon Phases | Current Moon Phase and Monthly Moon Phase Calendar