You have a problem. The roof will block out the signal, for sure. Trees may cause a problem, too.
Wiki says:
Each receiver must be connected to an external antenna, which is included with the receiver. Antenna placement is crucial to receiving a clear signal. In some locations users have experienced difficulty receiving the Sirius programming because the signal is not consistently strong. For best reception, antennas should be placed such that they have an unobstructed view of the sky (preferably on rooftops without overhanging eaves or trees). If this is not an option, the antenna should be placed on an exterior wall. When placing on an exterior wall, the antenna should be mounted to a wall which faces the center of the continental United States in order to minimize the likelihood of the building itself blocking the signal.[18][19]
My satellite radio will only work if I have a clear view of the sky. When I am on wooded back country roads the reception is poor at best, and I get "Acquiring signal" about half the time.
If the antenna can "see" the sky, it should work just fine. Most radios can employ a rather long run of shielded antenna cable to place the receiver in a location far above the actual radio allowing a clear shot of the sky.
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The smart-aleck literalist in me want to reply that the radio will work fine, it just won't be able to receive the satellite signal because the roof and trees will block it.
The good news is that a solution is available and probably for under $50. Just Google for external antennas for satellite radio and you will come up with a ton. Mysirius has several and also lists which receivers they are compatible with.
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I have XM and I have not had any problems with trees blocking my signal .. but I do live in a house with aluminum siding, and must place the antenna in a window to receive the signal.