In the upcoming 5G Advanced and 6G technologies, joint sensing and communication (JSAC) will play a pivotal role in enabling the simultaneous utilization of hardware and spectrum resources for communication and sensing tasks. While current algorithms primarily focus on designing beampattern invariant covariance matrices for transmitting various symbols for communication, they often overlook the distances among these symbols. While these covariance matrices effectively facilitate ranging operations, they have adverse effects on communication performance. Designing beampattern invariance covariance matrices with maximal distances among themselves poses a challenging non-convex problem. In this paper, we introduce a novel waveform design method based on McCormick relaxation called McCormick-based JSAC (MJSAC). MJSAC sequentially solves an optimization problem to generate a set of covariance matrices by maximizing the distances (Frobenius norm) among themselves while ensuring a consistent beam pattern. Also, MJSAC eliminates the requirement for channel information to generate the covariance matrices. Through simulations, we demonstrate that MJSAC outperforms conventional algorithms, even those utilizing channel information at the transmitter.