In this paper, we investigate a joint communications and sensing (JC&S) system using zero-padded orthogonal frequency division multiplexing (ZP-OFDM) to simplify the hardware design at the receiver of a monostatic radar. This is possible because, unlike with cyclic-prefix OFDM (CP-OFDM) radar, ZP-OFDM radar does not need full duplexing, as there is no self-interference during the guard interval (GI), which can be used for radar detection. We derive the required receiver signal processing for radar detection in that case, and show that when the self-interference in CP-OFDM JC&S is high, the ZP-OFDM is beneficial. This advantage depends on the target distance, because it influences the relative amount of energy from the reflected energy that can be captured in the GI. We show then that ZP-OFDM can be a cost-effective and efficient alternative to CP-OFDM under certain conditions.