Abstract-The increasing demand of spectrum resources and the need to keep the size, weight and power consumption of modern radar as low as possible, has led to the development of solutions like joint radar-communication systems. In this paper a novel Fractional Fourier Transform (FrFT) based multiplexing scheme is presented as joint radar-communication technique. The FrFT is used to embed data into chirp sub-carriers with different time-frequency rates. Some optimisation procedures are also proposed, with the objective of improving the bandwidth occupancy and the bit rate and/or Bit Error Ratio (BER). The generated waveform is demonstrated to have a good rejection to distortions introduced by the channel, leading to low BER, while keeping good radar characteristics compared to a widely used Linear Frequency Modulated (LFM) pulse with same duration and bandwidth.