Single waveform design for automotivejoint radar-communications (JRC) is being increasingly considered of late. This paper formulates the JRC design as an optimization problem exploiting the co-location of the two systems and investigates the trade-off between them. We propose an algorithm to maximize the performance of communication and radar receivers (e.g., BER and probability of detection, respectively). This intractable optimization problem is decomposed into two subproblems, which are subsequently solved in succession through a combination of gradient projection method and convex relaxations. The benefits of the proposed waveform are illustrated through numerical simulations.