The whine follows the revs of the motor. The noise is RX and TX.
OK, next step is to see if the alternator is working correctly before pointing any fingers. This will require the use of a digital volt meter.
The first test would be to measure the battery at rest voltage first thing in the morning before even starting the vehicle. Write this voltage down. Should be about 12.5 volts or so.
Next, start the engine and measure the battery voltage again. You should see between 13.8 and 14.5 volts. A more normal reading is 13.6 to 14.0 volts. Write this value down.
Now lets start putting a load on the alternator. Turn on the headlights on low beam. Measure the voltage. Write it down.
Next, turn on the high beam headlights. Measure the battery voltage. Write it down.
Next, turn on the A/C or heater on high. Measure the battery voltage. Write it down.
Only a couple of other items left to add to the mix. Leave the high headlights on, leave the heater or A/C on high. Now turn on the windshield wipers. Again measure and write down the voltage.
Last item left is to turn on the direction indicators like your making a turn. Leave everything else turned on. Measure the battery voltage and write it down.
Now while you have a max load on the alternator, take your volt meter and put it on the AC scale and measure the battery voltage. What your looking for is how much ripple is in the output. This should be down in the 50 milivolt range or less. Anything higher will point to a bad diode in the alternator.
With all the voltages recorded, take a look and see just where the voltage starts to drop off. If the alternator can't hold the headlights and heater at full blast, then you could have a bad voltage regulator. As just about all the vehicles today have the voltage regulator built into the alternator, I would get some auto shop to verify you have a bad alternator.
Another test I always make is to turn on the headlights and make a voltage measurement from the battery post and then from the battery clamp where the wire is. Have found poor connections between the battery post and the wire connector many times was causing strange electrical problems.
Once your happy that the alternator is working the way it should, I would then start looking at the radio, it's ground connection and the antenna ground connection. Most of the mounts today rely on a good ground right at the antenna. If your mounting the antenna to a fender to the trunk, it might not have a good connection. You might have to add a ground strap between the body and the fender or the trunk lid itself.
Notice I used the term strap and not a wire. Your looking for a low impedance connection, not just a ground connection. The flat strap made from the braid of a piece of coax is much better than a number 14 piece of wire. Solder a lug on each end and put a screw into the metal to finish the connection. I use some anti oxidant compound on these connections to keep long term corrosion from doing in your work over time.
Have fun. Make the noise go away.