- This has been done before extensively for both the radar (from Roger) and re-transmitted. There are things called transponders (transmission responders) which may re-radiate the transmitted signal or radiate a different signal in response (This is how we get IFF, inceidentally)
As noted, the simplest way is to just reflect the signal. If this is not possible (because you don't have a clear line of sight), then a transponder is appropriate.
The pitfalls are ensuring a known and repeatable time between reception and retransmission / new transmission of the signal.
Radar range is very simply Distance = C t / 2 where C = velocity of electromagnetic radiation [n free space], and t is the time between transmission and reception. The division by 2 simply shows that the pulse travels twice the distance (there and back :)
Things to watch for. (Straight radar principles) Minimum range. This is set by the transmitted pulse (you can't receive while you are transmitting, but this may not be so for a separate receiver at perhaps a different frequency, such as a transponder). Distance (min) = C t / 2 where t in this case is the pulse width of the transmitted signal.
Maximum range. Set by the pulse repetition rate. If there is some time t between pulses, then the maximum time to wait for a single pulse (with simple techniques, anyway) is the amount of time between the pulses. (Once another pulse starts, we reset the range - this can lead to aliasing). So Distance (max) becomes simply C t / 2 where t in this case is the time between pulses.