Default How to Unlock LTE bands

Please, would a moderator help me to post my help request in the right forum?

My factory unlocked Samsung Note 3 N9005, with KK 4.4.2 Polish fw, rooted, will not operate in LTE data even though it has the right frequencies/bands hardware. I have the right APN.

I need to access LTE Bands 1, 3, 8 and 20 (Vodafone Italy and Softbank Japan).

Do I need a new radio? A new modem? Do I only need to flash a specific firmware...? Which one? Where can I download it? How do I install it? It's it sufficient to flash another CSC?

Please help me to post this question in the right section! Thanks!

Sent from my SM-N9005 using Tapatalk
Italians do it better... !