It is said that wireless is a half-duplex medium. "Dual-band" stations are now common, with one antenna in the 2.4 GHz band, and the other in the 5GHz band. Suppose now we have stations with both antennas in, say, the 5GHz band, but on different channels, would full-duplex communication be possible?
A while back I read several articles about researchers using signal inversion cancellation to achieve full-duplex wireless. With a quick google search I found the below links to similar articles to the ones I read back when.
TLDR; It's for sure possible...though I think they're using signal inversion cancellation instead of two channels (I.E. two different frequencies). People are working on it. Only a matter of time.
I'd love to get a true RF engineers thoughts on this though. I'm by no means an RF guy.
If you're using two different channels then that would be two half-duplex connections, not a full-duplex connection. This is what MIMO does, multiple frequencies on multiple antennas operating simultaneously to increase throughput.
@bigmstone has the answer for wireless full-duplex, sending and receiving simultaneously on the same frequency, it's being researched but nothing is in production yet.
MIMO is as close to full duplex as you'll get, at least with current technology.
In fact, a single channel space is split into multiple "streams" which allow for the increased throughput via OFDM (http://en.wikipedia.org/wiki/Orthogonal_frequency-division_multiplexing).
However, on a single channel (assuming no overlap), only one device can be transmitting. I don't think there will be a way around this.
There's not a great deal of non-overlapping channels even on 5gHz (you want to avoid the DFS channels). Couple that with possibly getting interference on some but not all channels if you could use multiple channels at once, and it starts to become quite messy and adds a lot of overhead.
But look into 802.11ac or 802.11ad, those use very very wide channels to achieve silly throughput (up to about 7Gbps estimated). More speed is on the way.
I just looked at an installation of this equipment (http://www.ubnt.com/airfiber). They're running two antennas in the 24GHz range, each with a 750M throughput.
This is basically a 750M Full Duplex wireless solution, since even for ethernet you're really just two independent unidirectional 100M (or whatever) media.
Though it's not a true Full Duplex solution because this device still needs a mechanism to detect collisions and then back off a random amount of time, else it becomes useless if you install more than one in an area. And because of the shared medium (the radio spectrum) it can never be "Full Duplex" due to the necessity of detecting collisions.
I'm not a wireless spectrum expert, but one thing to remember in this idea is that full duplex is not just the ability to simultaneously send and receive, but also to do so without a danger of collisions. In a wired environment, if you install a hub you have to fall back to half-duplex because of the possibility of a collision. In wireless, even if you used a separate non-overlapping channel (it wouldn't even have to be 2.4/5) you still have the possibility for collisions on 1 of those channels (the one the hosts are using to transmit).
Now wireless uses CSMA/CA (instead of CSMA/CD in a Ethernet network), which is suppose to *A*void collisions not just *D*etect them. Maybe CSMA/CD would solve that issue, just wanted to point it out as a consideration in full-duplex.
You'll need two physical wireless interfaces in order to achieve true full-duplex. One thing to note, though, is that IEEE 802.11 doesn't support pure TX or pure RX on a single interface, so you wouldn't be able to use easily-obtainable Wi-Fi equipment. This, unfortunately, would also be a PtP solution, as you would still need to avoid collisions in PmP (as others here have also pointed out).
See this microwave full duplex wireless system. It is claimed to be a single channel, full duplex, single antenna wireless radio. They named this Simultaneous Transmit And Receive STAR.