HackRF can't do it, because it's only half-duplex. But there are plenty of full duplex SDR devices - check out UmTRX and USRP B210. We're also developing a really tiny high performance SDR specifically for LTE - http://XTRX.io
Are you sure? hackrf usually can only provide half-duplex operation, and somewhat full duplex after certain tweaks. Still usb2.0 will be a limiting factor in this case. USRP boards will probably be a lot better.
HackRF/USB2 has enough bandwidth to do LTE, particularly since LTE can be configured to use between 1.4 and 20 MHz. I think the lack of full duplex or an FPGA on board would be the major limiting factors.
If you're running both sides on SDRs you should be able to tweak the frequencies in use. Several LTE bands neighbor and/or overlap amateur radio bands, so adjusting the settings a bit should allow you to move your test operations in to a range that is trivial to gain permission to use.
Bands 30 and 40 actually exist entirely within the amateur 33cm band, band 42 overlaps with 9cm, and band 46 overlaps with 5cm. Two of those also overlap with unlicensed spectrum, so there's extra room to play in that no one reasonable expects those bands to be clean anywhere people have electronics.
If you have cooperative endpoint devices you could also bodge other more common LTE bands in to amateur frequencies. Band 31 is just a 20 MHz drop away from fitting in 70cm, and cutting down the duplex spacing could make part of band 8 usable in region 2.
If you want commercial hardware to work it's probably best to stick to the first group, but if you're doing SDR on both sides and just want to experiment the second group should technically work.
