An LTE network compatible iPhone needs an LTE chip/radio, just as a 3G iPhone needs a 3G chip/radio in order to connect to an available 3G network. The original iPhone is not a 3G phone - it doesn't include a 3G chip/radio. The iPhone 4 is not an LTE network compatible phone - it doesn't include an LTE chip/radio. There were no LTE networks available last summer when the iPhone 4 was released, and design and testing for the iPhone didn't begin a few weeks before the iPhone 4 was released - this had been in the works for some time even longer before an LTE network was available. Verizon just started making their LTE network available in some select markets, which requires an LTE network compatible phone. With Verizon's LTE network, the LTE network compatible phone must be a combination LTE/CDMA phone for when in an area where Verizon doesn't have their LTE network available or when their LTE network is down where it is available for whatever reason. It will take Verizon several years to have their LTE network widespread which probably won't be available in 100% of their geographic coverage area just as Verizon's 3G network is not available in all of their network coverage area.
AT&T will have their LTE network available to the general public in some select major markets sometime this year, which will require an LTE network compatible phone. The LTE network compatible phone for AT&T's LTE network will need to be a combination LTE/GSM phone for when in an area where AT&T does not have their LTE network available so the phone can connect via 3G, EDGE, or GPRS - whichever is available at the time.
Copied from this link.
http://www.apple.com/iphone/specs.html
Cellular and wireless
GSM model: UMTS/HSDPA/HSUPA (850, 900, 1900, 2100 MHz); GSM/EDGE (850, 900, 1800, 1900 MHz)
CDMA model: CDMA EV-DO Rev. A (800, 1900 MHz)
The iPhone 4 is not an LTE network compatible phone. A firmware update cannot change hardware into something it does not include.
