Well...a project that involves radio waves that is easy to do is to detect meteors!
Get a shortwave radio, or even an good FM radio, and tune it to a very distant station that you can barely hear at full volume. With some patience, and especially during a meteor shower such as the upcoming April 23 Lyrids, you will occasionally hear the distant station increase in volume for a few seconds .What is happening is that the entering meteorite ionizes the air, and this increases the reflectivity of the ionosphere between you and the radio station, so that the radio waves can more easily 'bounce' off of the ionosphere. It only lasts a short time, but since a meteor shower only lasts a few days, you do not have long to wait.
As for other experiments, unless you are willing to build a simple radio telescope to detect the Sun, or can work with an astronomer, the possibilities are very limited because you will not have the proper resources.