There are some Internet sites which have various construction articles regarding antenna fabrication and build. The XM satellite radio service is in the 2.3GHz frequency band or about 13cm wavelength.
The Internet site:
You must also take into consideration the fact the (both) XM (and its competitor Sirus) both utilize additional terrestrial (ground based) repeaters where "viewing" of the full sky isn't always practical - like in big cities. Therefore, both radio types have dual antenna inputs, each for different receiving antenna - two sets of frequencies, hence different antenna designs. I really don't have much info about the "terrestrial" frequencies.
Being that this application is either vehicular mobile or with the newest XM radio designs, portable, I would really recommend that commercial antennas be best for reliable reception. Figure it this way: if you spend the big bucks for the receiver (and the monthly expenditure for the service) to insure good reliable reception, use a commercial antenna (available from multiple sources). The rule is really: the output of your device is as good as its "cheapest" (weakest) part ...
Hope this helps a bit.
John Stahl Aljon Enterprises CEA Certified MECP