You could make a Cantenna out of a large paint tin or drum for the receiver and point that into the sky.
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scroll down to the excel file and plug in 1.2 and 203 (that's 1.2GHz and mm for 8") then have a look at the dimensions it gives you. You'd need to use a N-type connector and some rg59 or whatever coax works well at that frequency. I'm not sure what beam width and gain you'd get from that design but it would surely be better than the little whip it has at the moment.
here's dimensions for an 8" tin:
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You can also ghetto it and stick the end of your whip into the can itself:
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Also you have to have the Tx antenna using the same polarity as the cantenna, that means if you do any fancy aerobatics you may lose reception, or even gain better reception