You don't just pound in another rod because without bonding to the house ground there's actually measurable electrical potential between the 2 electrically separate rods.
I put in a second rod, bought 100 feet of #6 and ran it around to the house ground rod and tied it in. Didn't cost that much. Hardest part would have been putting in the ground rod, but my electrician taught me a couple tricks for that and it went surprisingly fast.
I didn't ground it with any thought that it would keep lightning from damaging my house if it hit. I grounded it to dissipate static and *possibly* lower the chance of getting hit in the first place. Static builds on the antenna just from wind-borne dust particles blowing across it.
You can introduce a hum into your AV equipment by not having the 2nd ground rod bonded to the main ground. The 2 separate rods act almost like 2 poles of a battery and the measurable voltage between them varies with soil conditions.
Doing it yourself and NOT doing it right, could possibly open you up to some liability in a case where let's say.... lightning strikes your house, the insurance adjuster comes out. "Oh, look. Homeowner modified electrical system and it's not to code. I see contributing factor. I guess this damage isn't covered." How likely is that scenario? Depends how good the adjuster is at his job (which is to see if this was truly an accident or if it was INDUCED which mitigates insurance liability). REGARDLESS of the fact that in case of a lightning strike, all bets are off as to whether the antenna ground does any real good, it's how current code is written and you'll be doing yourself a favor to do it right or leave it alone.