Concealing objects from interrogation has been a primary objective since the integration of radars into surveillance systems. Metamaterial-based invisibility cloaking, which was considered a promising solution, did not yet succeed in delivering reliable performance against real radar systems, mainly due to its narrow operational bandwidth. Here we propose an approach, which addresses the issue from a signal-processing standpoint and, as a result, is capable of coping with the vast majority of unclassified radar systems by exploiting vulnerabilities in their design. In particular, we demonstrate complete concealment of a 0.25 square meter moving metal plate from an investigating radar system, operating in a broad frequency range approaching 20% bandwidth around the carrier of 1.5 GHz. The key element of the radar countermeasure is a temporally modulated coating. This auxiliary structure is designed to dynamically and controllably adjust the reflected phase of the impinging radar signal, which acquires a user-defined Doppler shift. A special case of interest is imposing a frequency shift that compensates for the real Doppler signatures originating from the motion of the target. In this case the radar will consider the target static, even though it is moving. As a result, the reflected echo will be discarded by the clutter removal filter, which is an inherent part of any modern radar system that is designed to operate in real conditions. This signal-processing loophole allows rendering the target invisible to the radar even though it scatters electromagnetic radiation.