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.

翻译：在即将到来的5G Advanced和6G技术中，联合感知与通信（JSAC）将在实现通信与感知任务对硬件和频谱资源的同步利用方面发挥关键作用。现有算法主要专注于设计波束图案不变的协方差矩阵以传输多种通信符号，却往往忽略了这些符号之间的距离。虽然这些协方差矩阵能有效支持测距操作，但对通信性能产生不利影响。设计具有最大符号间距离的波束图案不变协方差矩阵是一个极具挑战性的非凸问题。本文提出了一种基于McCormick松弛的新型波形设计方法，称为McCormick联合感知与通信（MJSAC）。MJSAC通过顺序求解优化问题，在确保一致波束图案的同时最大化协方差矩阵之间的距离（Frobenius范数），从而生成一组协方差矩阵。此外，MJSAC无需利用信道信息即可生成协方差矩阵。仿真结果表明，即使与利用发射端信道信息的传统算法相比，MJSAC仍具有更优越的性能。