A promising waveform candidate for future joint sensing and communication systems is orthogonal frequencydivision multiplexing (OFDM). For such systems, supporting multiple transmit antennas requires multiplexing methods for the generation of orthogonal transmit signals, where equidistant subcarrier interleaving (ESI) is the most popular multiplexing method. In this work, we analyze a multiplexing method called Doppler-division multiplexing (DDM). This method applies a phase shift from OFDM symbol to OFDM symbol to separate signals transmitted by different Tx antennas along the velocity axis of the range-Doppler map. While general properties of DDM for the task of radar sensing are analyzed in this work, the main focus lies on the implications of DDM on the communication task. It will be shown that for DDM, the channels observed in the communication receiver are heavily timevarying, preventing any meaningful transmission of data when not taken into account. In this work, a communication system designed to combat these time-varying channels is proposed, which includes methods for data estimation, synchronization, and channel estimation. Bit error ratio (BER) simulations demonstrate the superiority of this communications system compared to a system utilizing ESI.