A radar activated light... so that the driver of a car knows that the cyclist knows that the car is getting closer to the cyclist? Huh? How about just a light that blinks really fast to begin with, and a rearview mirror on the bike so the cyclist can see the car, rather than depend on LEDs to tell him there's a car behind him. Total savings, several thousand dollars and the heartbreak of putting your heart and soul into a project that will never go anywhere.
If the inventor was bound and determined to go high tech, then how about handlebar a mounted smart phone with a rear-facing bluetooth camera. Putting together some image processing software that recognizes something approaching from the rear and notifies the cyclist with a flash or a tone would be a lot easier than building a radar, and you get the added bonus of having the rearview camera image on the smartphone display too.
Either way you are using off-the-shelf hardware. As it stands, at the frequency he's working at, in any kind of weather that diminishes visibility to the point where you'd want to have it, it would be useless. 24GHz will give you returns off of humid portions of air, let alone actual smog, fog, or mist, and doppler isn't the be-all-end-all in an environment where air currents and gusts can move the stuff you're getting returns off of at the speed of a car.
I hope those venture capitalists haven't put real money into this.