On-board radar would only work in a very small fraction (near-similar orbital planes/altitudes). In a head-on, the closing velocity is 15.5km/s. You would need a radar with range (against very small objects) of nearly 1000km to get even a minute of warning...more than 5-10 min, and you would be near the horizon. Earthbound radars are used to track debris, then the orbital elements are propagated, and collision risk determined. On-board sensors would need to be SBX size to really do anything (too big, easier to put on earth, after all, orbits are predictable) or yield far too little warning time.