Hmm, I guess I don't know enough about what TMo and AT&T are doing. I thought AT&T was also rolling out LTE? How is HSPA+?
HSPA+ is presently deployed on 5+5 MHz (FDD) and LTE (with Verizon anyway) deployed on 10+10 MHz, while WiMax is deployed on 10 MHz TDD. An upgrade path for HSPA+ allows for use of dual carriers which effectively brings it up to the spectrum utilization that LTE on Verizon is presently using. Both use the same order modulation in the best radio environment (64QAM) and there is an upgrade path for HSPA+ that would keep it's spectral efficiency (bitrate per Hz) at or better than Rev. 8 LTE and once deployed on the same spectrum will basically be just as fast as LTE.
There are other advantages to LTE (all IP for example) that are optional rather than mandatory extensions to HSPA+. I'm not sure how it's being deployed with T-Mobile.
One big advantage that LTE has as deployed by Verizon (and as will be deployed by AT&T mostly) is that it's in the 700-800 MHz frequency range. Atmospheric attenuation increases as a power of the frequency so for the same power an LTE signal will have greater range (or better SNR) as deployed on Verizon. In other countries LTE is deployed on an even higher frequency than HSPA+ is on T-Mobile and thus the advantage isn't inherent to LTE, just a side effect of the deployed frequency.
Of course, the future is probably going to be very small sector sizes both in radial range and angle - people have been talking about beam division multiple access even - since we all are sharing only one electromagnetic spectrum the best way to make use of that spectrum is keep the cell sizes as small as possible (a few hundred meters I imagine, in urban environments) and who knows, maybe atmospheric attenuation is an advantage there.
LTE-Advanced (or rel. 10 LTE) as well as WiMax 2 were the only formally accepted 4Gs originally and there are several requirements for 4G, not just eventual bandwidth to the end user but spectral efficiency and so on - but I think the ITU just gave up and said anyone can call anything that is faster than 3G '4G'.
1000 Mbps can't be the only requirement for 4G (commenting on a below comment). Anyone can come up with a system that would deliver 1000 Mbps even with very simple modulation if allowed to deploy on 1000 MHz of spectrum.
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