RF real time measurement

I am looking at building a system to measure time of arrival of a bullet at a target and would like timing resolution of .1 millisecond where there is a distance between the base station (Arduino UNO) and the microphone picking up the bullet's passage. There is no network or wiring of any kind between the base station and the downrange microphone so either I need an RF system that can transmit a pulse to the RF receiver at the base station when the bullet arrives, or a means such as a GPS unit at each end to synch the clocks up for reducing the effects of drift. The GPS solution would also require an RF solution, to transmit the number of cycles since the last PPS. I have implemented an XBee system on another project and I would probably use this for the GPS solution if I had to go that route. The distances are up to a mile.

I would prefer the first type of solution as I would not have to have a GPS unit at each end just outputting its PPS to synch the clocks. Does anyone know of a low-cost RF-based method of transmitting and receiving the pulse, think of it as a switch opening or closing.

The mic unit has an amp and signal conditioning that outputs a TTL pulse a noise load enough to be a bullet is heard.

Thanks

wade

Assuming that this station will not be moving, how about a controlled ir laser and an. Ir led reciever?
that would be the fastest way of doing it
and you could set it up that the ttl pulse triggers the laser, then you don't even need an mcu at the station, just have the base station detect the bullet being fired then time until it gets the laser pulse

I forgot to add that this needs to be a portable system that is easy and quick to set up, if this was to be a fixed permanent system the laser would be a great idea. After doing some work in optical comms I am surprised I did not think of it in an early go around.

Thanks

wade

I think unfortutly any rf comm will have a significant delay you will have to adjust for in different fields