I don't know if the issue I had is related, but I'll share it and really try to be fairly brief. Also on Verizon. When I bought it, the sales rep at the store didn't use the SIM card from my GNex, and set up a new one. He didn't set it up right when he said it did, and I had to wait another hour in the store for the manager to find him and then for him to fix the problem. Lesson learned here is to just wait two extra days and order online. I hate to say it for the employees' sake in general, but it seems like there is always a problem that occurs with buying in the store that wouldn't have happened buying online.
Any way, the signal has been immensely better. I do work for several clients, but for instance, one place where I am at least once a week, my GNex only got 3G and had a hard time with it. My city has pretty good 4G coverage. The S4 gets 4G with ease and speeds are fast at that place.
But just at my home, I was having problems with incoming and outgoing calls. Only about 50% of calls worked. But just from my home. I've lived in this house for more than ten years and had Verizon the whole time and never once had a problem with phone calls. There's four other Verizon phones in the household, and they didn't have any problem with signal or calls.
If the call connected, it was clear and never dropped. Outgoing calls would hang on the "Dialing" screen, with the dots scrolling across. If it didn't connect after 30 seconds, it would cancel the call.
All I can say is thank God for Google Voice for voicemails (I did rule this out as a possibility in causing the problem, btw). I also ruled out lots of things. I put the SIM in my GNex and had similar results. I put my dad's SIM in my S4 and every call connected.
So after one round of troubleshooting with a tech support rep on the phone, I called again and he agreed that it was probably the SIM because of the first problem. So I got a new SIM in the store and that didn't fix it. So I called again, and the next step was to just have them send me another device. Even though I had pretty well ruled that out, I gave it a try. The refurb arrived, I tested it with the same results. I sent the refurb right back and kept my original one that I bought.
The refurb got here last Monday. Last Wednesday, I was preparing to call again and in doing so, I found that whatever the problem was, it was then fixed. I called to update them and this time got a guy who gave me his direct line so that in case it did start again, I wouldn't have to catch someone else up on the problem (which was awesome-- I wish that had happened four calls earlier).
So I'm a pretty methodical person when it comes to troubleshooting. I kept notes on what I was trying and the number and order of calls that did or didn't connect, and how long it took. I'm sure I made at least 200 test calls throughout. With all of that, I found no pattern and have no idea why it all of a sudden started working correctly. But I do think that it was on the service side, and not on my local device side.
I own my own business and have a home office, so this was really screwing me up. I used Talkatone and then changed to GrooveIP so that phone calls went through it on data if it didn't ring through the regular phone service. That helped a lot.
I don't know if this helped, but if any of this sounds familiar, feel free to private message me to see if maybe there's some common thread that could exist.