In order to improve my XHDATA-D808's reception, I decided to look for a a cheap antenna I could use. It was important for me to be able to either hang it from a window or attach it to an object that's higher up in the sky and I stumpled up on this Tescun one. It's a reel antenna that has approximately 4.5 metres of cable rolled up inside it which makes it very convenient for taking with you; additionally, it has a nice clip that you can use to attach it to objects (such as a window). I ordered it online from a very prominent online retailer for just under €8 and I've been quite happy with it.
The antenna adds about 10 to 20 dB to my reception strength, which can be the difference between not hearing a station and hearing it quite well. It being a reel antenna makes it great for a small apartment like mine as it takes up very little space. Rolling it up once you've unrolled it is slightly annoying however; but you can unscrew it and thus easily roll it up again.