Orthogonal frequency-division multiplexing (OFDM) is a promising waveform candidate for future joint sensing and communication systems. It is well known that the OFDM waveform is vulnerable to in-phase and quadrature-phase (IQ) imbalance, which increases the noise floor in a range-Doppler map (RDM). A state-of-the-art method for robustifying the OFDM waveform against IQ imbalance avoids an increased noise floor, but it generates additional ghost objects in the RDM [1]. A consequence of these additional ghost objects is a reduction of the maximum unambiguous range. In this work, a novel OFDM-based waveform robust to IQ imbalance is proposed, which neither increases the noise floor nor reduces the maximum unambiguous range. The latter is achieved by shifting the ghost objects in the RDM to different velocities such that their range variations observed over several consecutive RDMs do not correspond to the observed velocity. This allows tracking algorithms to identify them as ghost objects and eliminate them for the follow-up processing steps. Moreover, we propose complete communication systems for both the proposed waveform as well as for the state-of-the-art waveform, including methods for channel estimation, synchronization, and data estimation that are specifically designed to deal with frequency selective IQ imbalance which occurs in wideband systems. The effectiveness of these communication systems is demonstrated by means of bit error ratio (BER) simulations.