The antenna for at least the 2000-2005 Impala's is built into the rear windshield. There is actually a little "control box" that the radio antenna wires goes to from the radio. It is located on the drivers side rear pillar under the trim plastic. From there a small antenna wire goes to the defroster terminals. It is a known problem for that module to die. I personally did not want to pay several hundred dollars for a new control box nor a rear windshield. I purchased an active FM antenna from some car audio joint for like $15 that works just fine.
Inspect the defrost lines on the rear windshield.
I was able to spot the place where one was interrupted. If a broken line is not visible, you can try sliding a small piece of aluminum foil along each line and check the spot where the radio reception is static-free. To fix the problem, I have used Permatex Quick Grid Rear Window Defogger Repair Kit. It is a conductive compound that restores the electrical circuit.
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