Unlocked 5s won't connect to new carrier (docomo) data network I recently moved to Japan and got a new SIM card, with a contract, from docomo (one of the major carriers here). I had my iPhone 5s unlocked by a third party, and inserted the new SIM card into this phone. While my new phone number works fine for phone calls and texts (sent to the number), I cannot connect to the mobile internet network.

Now, 3G appears in the top bar next to "docomo," but no apps that use the internet will load unless I'm connected to WiFi. Usually the error simply states "unable to connect to the internet," but occasionally it will appear as a PDP Authentication error. I have tried all the simple fixes (restoring the phone, resetting network settings, toggling airplane mode on and off), but none of them have any effect. I have also been to the docomo store, but the clerk there was only able to tell me that instead of 3G appearing LTE should appear, and that it was a problem with the phone-->I should talk to Apple. Again, Apple support over the phone was only able to direct me towards the simple fixes, and asked me to go to my nearest Apple store, which is pretty far from where I currently live.

I think the problem has to do with my not having the correct docomo APN settings, but don't know what might work for changing this. Again, the clerk at docomo was not helpful on this front. Any direction would be greatly appreciated.
It sounds as though the issue resides in the LTE bands supported by the device. If the iPhone is model A1533 it will not support LTE bands: 6 and 9. A1533 is the model of most American unlocked devices. On Apple's LTE site it gives a list of each unlocked device, and the supported bands that has been organized geographically. iPhone 5S model A1453 is the correct model.