[Galaxy Note 3 Q&A, Help & Troubleshooting] rekt:
Problem solved

i found a fix guys. anyone else with an SM-N9005 whos having trouble getting LTE to switch on can follow my lead here.

NOTE: YOU WILL NEED ROOT ACCESS FOR THIS, SO GET THAT DONE FIRST. where possible, try use a method that won't trip your knox flag.

this first potential fix below did not work for me, but i understand it may work for others depending on which firmware you have. credit goes to smokey's wordpress for this. (i cant yet post outside links or i would link the page here, just google it)

1. Change with a root explorer of your choice (e.g. Root Explorer, Solid Explorer or EF File Explorer) the value “false” in file persist.radio.lteon into “true” by way of build-in text editor of the root explorer. The file is located in root/data/property. Be sure permissions of persist.radio.lteon are set to rw, after altering the file save the file and make it read-only. Reboot your phone, now you will see and be able to pick the option “LTE/WCDMA/GSM (auto connect)” in Network Mode menu. Important: before altering ANY file on your phone be sure you have a copy of the original, unaltered file!!! Advantage of this solution: even after a phone reboot the option “LTE/WCDMA/GSM (auto connect)” will remain visible/activated.

if the above works for you then by all means, do it, and forget the rest of this post. but for me it didn't change anything, ALTHOUGH i did do the rest of this fix with the above already done. im now outside lte coverage so i cant be bothered going for a drive just to do some more trial and error lol. so it cant hurt to have this done first.

do this in an area that you KNOW has good LTE coverage, so you can at least get confirmation that things are working (or not working) throughout the process. if not, you will have no idea whether it worked or not, and if you missed something, it will be a pain in the ass to go back and forth trying to get it right.

its important that you do things in the order i mention below. i have done some trial and error and if the order is messed up, you will remain stuck on 3g.

1. download an app called "Advanced Signal Status" from the play store, and open it up. select "additional info", then select "device information".

2. open the first drop down menu, it has options like GSM ONLY, CDMA ONLY, LTE ONLY, GSM/CDMA, LTE/GSM, LTE/CDMA, LTE/GSM/CDMA. these all determine which radio combinations can be active at any given time. for most networks, choose LTE/GSM/CDMA. afterwards, it may revert back to LTE/GSM or whatever. thats fine, as long as you still get reception where you should. this should force your phone into LTE mode, but we're not finished yet. keep reading.

3. you may need to switch your data connection off then on again for lte to start working. if it still goes into 3g, go back into advanced signal status and select "LTE ONLY" to force any other connections off.

4. once LTE is active, then go back and select LTE/GSM/CDMA or whatever your network uses, as long as theres LTE/something else. the first page of advanced signal status should show signal strength values under LTE (4g). if everything is still n/a and you're not getting LTE reception, this solution isn't going to work for you. if the LTE is now working, awesome, but we still aren't finished, because it will reset the next time you reboot your phone and you'll be back to step one. not a huge deal, but just annoying. if you can live with that, then you can stop here if you want. personally, i like my fix to be permanent.

5. you need a root explorer app with a built in txt editor function. while doing my trial and error for this i tried a few different ones but the only one that really worked properly for me was called "Root Explorer". but use whatever works for you. root explorer is a paid app ($4.85 when i did it), the free version does not access root files. easily worth the money.

6. you now need to browse to /root/system and you are looking for a file called "build.prop". BEFORE GOING ANY FURTHER, BACK THAT FILE UP! if you are using Root Explorer, like me, then it will create a backup automatically when you save changes, but do it anyway just to be safe.

7. open "build.prop" using the explorer's built-in text editor. it may ask you whether you want to alter the file's permissions in order to edit it, so yes you want to do that.

8. scroll about 2/3 of the way down and you will find a few lines that look like this:

#

# System props for telephony

# System prop to turn on CdmaLTEPhone always

telephony.lteOnCdmaDevice=0

9. while being very careful not to change anything else, change the last character on the last line so that it looks like this:

telephony.lte.OnCdmaDevice=1

10. save changes and exit.

11. make sure LTE is still active, and reboot your phone.

12. open up the settings gui and go to Connections/More Networks/Mobile Networks/

13. you should now have an ADDITIONAL network mode selector (the original one won't have changed, and still won't have an lte option) and it should be set to something like GSM/WCDMA/LTE. if not, then change it so it is. and DONT TOUCH IT AGAIN.

14. if you want, you can now uninstall the "advanced signal status" app because you won't need it unless you do this all again some day. if you mess around with anything we've just done and you lose your lte service, you'll need to start again and do things in this order.

i hope this helps some of you. i got my note 3 a week ago and have been tearing my hair out over not having lte because that was the main reason i bought a new phone. i'm by no means an expert (but i am an IT student, so thats something), so theres probably a tidier way to do this, but hey, it works so i'll take it :D