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I have had calls drop, garbled with or without a headset, and have even purchased a new phone that is DECT 6.0. The base is in close proximity to the router (just replaced it also) and modem. The phone base is about 3 feet from the router and 5 feet from the Cox modem with two other handsets in the house. On calls, I constantly get drops, garbling, and told I sound like I am underwater. I have had Cox out here numerous times with no luck finding problem. I purchased a better headset, but even when not using it, I still have some problems. This issue is intermittent. I have Cox Hub in my backyard, so I am close to it. This happens on long distant calls the most, as that is the calls I am usually on. The problem is the same as with the previous phone and previous router. In addition, there are times that the Caller ID does not work and just displays 'incoming call'.
Have you tried plugging a good old 2500 type set (not electronic, pure analog), like everyone had 20 or 30 years ago?
Aren't all landline phones analog...or do you mean "corded?"