You may not believe it, but that's noise not going away with the antenna is better than if it did. Filtering the power line is much simpler than the antenna type noise.
All nise is either AC or a 'pulsing' thingy, and botha re handled the same way. Basically, don't let any AC get to the radio. A very handy thing about capacitors is that the let AC get through them and no DC. So use a capacitor to 're-direct' any AC to ground instead of going through that radio. A capacitor from the 'hot' (+) wire to ground (-), does that very nicely and still doesn't provide a direct short for DC. To a completely ridiculous point, a bigger capacitor is better than a little capacitor when doing this. It can get a little 'sticky' if you let it, because how much AC/noise a capacitor will let get through is related to the frequency of that noise. There are formulas for that if you just have to know, otherwise, just use a higher value capacitor and don't worry about it. A sort of 'average' capacitance value for noise is something around 0.1 uF. If you wanna use a 1 farad capacitor, be my guest, but they get sort of expensive and dangerous. The other way capacitors are rated is by how much voltage they can handle. That's a real "iffy" thing if the voltage is not constant. If the voltage can surge, you want a cap that can handle that amount of surging voltage. So a minimum of 2 or 3 times the applied voltage is barely adequate, sort of. For 12 volt systems, a voltage rating of 50 volts is NOT too much by any means (especially for those 1 farad caps, even 100 volts wouldn't be too much). So look for capacitors that are at least 0.1 uF, @ 50 V. It may take more than one, or 2, just depends on the noise. Ceramic disk capacitors are very common in that size, and are cheap. There are polarized capacitors that can be much larger and cost a bit more, but they HAVE to be connected correctly or they certainly will pop no matter what the voltage ratings are. Stick with the ceramic caps, they can go either way (kinky, huh?).
Most cheaper line filters are just a bunch of capacitors in some kind of container. They work.
There's anothe electrical doo-hicky that can help. It's called a 'choke', and it lets DC through if and stops AC. A choke is just a sort of large coil. It has to handle all the current that whatever it's connected to will draw. That means that the wire used to make that coil is larger than you might think. The secondary windings of a 12 volt transformer are an example of that 'largeness'. The wire used is typically 10 to 100 times as large as the wire in the primary side of a transformer. that's one source for a choke if you happen to have a few dozen old transformers laying around. If not, then you can make them fairly easily, there's even a thingy about that on here somewhere.
A choke goes -in- the 'hot' (+) wire, NOT to ground. If you combine a capacitor and a choke you get what's called an 'LC' filter, and you will find them on just about every power supply that's filtered, all of them. So in effect, you are just adding a common power supply filter to your radio.
There ya' go, more than you ever wanted to know about filters. But it do come in handy, especially if you're as cheap as I am...
- 'Doc