Sam G4DDK and John G4BAO published a page on Wiki about EME on the higher bands. The article is full of very useful and interesting information.
From Introduction od article:
Above the amateur radio 144MHz band low sky noise means EME takes on a different character. Low sky noise (noise temperature) means that very weak signals can be heard against the background noise that would otherwise be swamped by galactic and manmade noise on 144MHz and below. Sensitive receivers, using very low noise amplifiers (LNA,) are even able to detect ‘noise’ from the moon. Being a ‘black body radiator’ at a physical temperature of between 200 and 240k, depending on the phase of the moon, its noise temperature can be readily detected against the much lower background sky temperature of 2.7k. This is only possible when the beamwidth of the receiving antenna is small and the noise temperature of the LNA is very low. In practice it is very difficult to detect moon noise at 432MHz with an ‘amateur size’ antenna, but at 1296MHz and above it becomes increasingly easy up to 10GHz within purely amateur radio means. Above 10GHz atmospheric gases contribute noise due to absorption and it again becomes increasingly difficult to detect moon noise. The frequency range between 1GHz and 10GHz is commonly known as the microwave low noise window due to the prevalent low sky noise temperature. There are five amateur radio bands between these frequency limits and all of them are exploited by EME enthusiasts in order to make DX EME contacts. 432MHz also exhibits low sky noise, but it is still higher than the five ‘microwave bands’. It is this ability to detect weak signals against a low sky noise that makes the microwave bands attractive to many EME enthusiasts. It is not critical that the EME operator is able to detect moon noise except on the higher of these bands, only that the ability to do so shows that the receiving system is working as expected. Detecting moon noise on 1296MHz is not essential and usually only possible with larger dish antennas. Note that I said that the beamwidth of the antenna must be small in order to detect moon noise. What if the beamwidth is not narrow? Then the antenna will see more cold sky than ‘warm’ moon. That also means that signals reflected from the moon will be weaker since the moon fills less of the aperture that is the receive antenna. Ideally, the beamwidth of the receive antenna will be exactly the same as the beamwidth that the moon subtends on the surface of the earth (about 0.5°). However, it is not quite that simple, as you might expect. As radio operators we are interested in achieving enough signal to noise ratio (SNR) to be able to communicate. The signal part is provided by the reflected signal and the more power that is directed at the moon, the bigger the reflected signal received back on earth
Direct link: https://wiki.microwavers.org.uk/Microwave_EME
Photo: from https://wiki.microwavers.org.uk/Microwave_EME