I was thinking about using the moon to bounce radio waves for long distance communication and after looking into it it turns out that it was investigated with success by the US (at least) in the 1950s.
I wanted to think that modern amateur radio hobbyists could replicate and extend this feat. After talking to an American radio friend about my idea he found the following online.
That is pretty cool, so once the aliens invasion takes out our satellite
comms, there is still hope 
This is the sort of the thing that has always made me want to get my HAM
license, just haven’t had time.
Oh, it’s definitely something that’s been done by amateur hams ever
since it was figured out. It’s something I’d be interested in doing as
well. I’m currently taking the radio course that Farrell is putting on
at VHS, so I’m hoping to have my HAM license in the next few
months. Maybe figure out how to do a moon bounce in 2015?
There are a few things that get in the way of moon bouncing being a
practical method of communication though.
The first is that the delay is just crazy. The signal has to travel all
the way to the moon and then all the way back. It takes ~2.7 for a
signal to get to the moon and back – not exactly
great for conversations.
From what I understand it also requires some pretty powerful
equipment – costly, dangerous, and possibly requiring more than the
basic amateur radio license.
Don’t get me wrong, it’s definitely on my list of things to do when I
get my license, I just think if long distance communication is what
you’re after there are better ways to do it with radio.
Bouncing waves off the ionosphere is a bit easier, and I don’t think it
requires equipment as powerful as what you’d need for a moon bounce ( I
could be dead wrong on that, though ). There are also amateur radio
satellites orbiting overhead, which are probably a bit easier ( and
cheaper ) to contact – maybe a stepping stone to a moon bounce?
The biggest difficulty is probably the high-gain antenna required. Without supreme quality rx and tx equipment you won’t be able to pull it off without a 2-3m dish. While you can sometimes get these free from folks tearing them out of their backyards, that supply has mostly dried up now, and if you do get one, where do you site it?
Very cool though, and should be doable with commercial equipment so you wouldn’t need an advanced license.
I was looking into doing E-M-E communications a while back and found some people are doing it with a helical antenna or helical array (a group of four helix antennae in a square arrangement). The nice thing about helix antennas is they’re very easy to build using copper tape and plastic tubes if you take the time to lay out accurately.
The real trick with operating this method is that you need a very good antenna over having a lot of power. Increasing your power doesn’t increase your sensitivity whereas having a better dish or antenna or array does.
The other thing that’s handy to have for talking to other space-born things is a good pan-tilt arrangement. I was working on one a few years back for Tank but never got it finished. We were wanting to talk to the ISS at the time. I really ought to finish that up and give it back to him.
Oh, also, we have a few advanced hams about such as myself; If your interested in playing with larger transceivers and making your own equipment, it’s the way to go. The test isn’t that bad though the block diagrams can be annoying to memorize. If you have equipment that requires an advanced operator be present, I don’t mind giving a hand.
only marginally off topic; Before I got my license, I used to donk around on the CB bands, on a good day you can pull ‘skip’ off of the various layers of atmosphere. For a few months in the mid 2000’s, you could chat direct to Louisiana from Port Coquitlam, no license, no heavy boots. (aka ‘illegal amplifiers’)
edit: here’s a couple links on the subject:
Isn’t the path loss for EME something on the order of 100 to 200 dB? You’ll need a lot of forward error correction…
Man, I really want to get my Advanced license. Studying for the Basic
right now, hopefully will have that by December. Being able to build my
own radios though? That’d be awesome.