Beamforming design has been widely investigated for integrated sensing and communication (ISAC) systems with full-duplex (FD) sensing and half-duplex (HD) communication. To achieve higher spectral efficiency, in this paper, we extend existing ISAC beamforming design by considering the FD capability for both radar and communication. Specifically, we consider an ISAC system, where the BS performs target detection and communicates with multiple downlink users and uplink users reusing the same time and frequency resources. We jointly optimize the downlink dual-functional transmit signal and the uplink receive beamformers at the BS and the transmit power at the uplink users. The problems are formulated under two criteria: power consumption minimization and sum rate maximization. The downlink and uplink transmissions are tightly coupled due to both the desired target echo and the undesired interference received at the BS, making the problems challenging. To handle these issues in both cases, we first determine the optimal receive beamformers, which are derived in closed forms with respect to the BS transmit beamforming and the user transmit power, for radar target detection and uplink communications, respectively. Subsequently, we invoke these results to obtain equivalent optimization problems and propose efficient iterative algorithms to solve them by using the techniques of rank relaxation and successive convex approximation (SCA), where the adopted relaxation is proven to be tight. In addition, we consider a special case under the power minimization criterion and propose an alternative low complexity design. Numerical results demonstrate that the optimized FD communication-based ISAC brings tremendous improvements in terms of both power efficiency and spectral efficiency compared to the conventional ISAC with HD communication.

翻译：波束赋形设计已在全双工感知与半双工通信结合的通感一体化系统中得到广泛研究。为实现更高的频谱效率，本文通过为雷达和通信系统同时赋予全双工能力，扩展了现有通感一体化波束赋形设计。具体而言，我们考虑一个基站同时进行目标探测、与多下行用户通信、并与多上行用户共享时频资源的通感一体化系统。我们联合优化基站处的下行双功能发射信号、上行接收波束赋形以及上行用户的发射功率。问题模型基于两个准则构建：功耗最小化与总速率最大化。由于基站接收到期望目标回波与非期望干扰的耦合作用，下行与上行传输紧密关联，导致问题求解具有挑战性。针对两种场景中的难题，我们首先分别确定用于雷达目标探测和上行通信的最优接收波束赋形，其闭式解可表示为基站发射波束赋形矩阵与用户发射功率的函数。随后利用这些结果推导等效优化问题，并通过秩松弛与逐次凸逼近技术提出高效迭代算法，其中所采用的松弛被证明是紧致的。此外，我们针对功耗最小化准则下的特殊情形提出一种低复杂度替代设计方案。数值结果表明，与传统半双工通信的通感一体化系统相比，优化后的全双工通信通感一体化系统在功率效率与频谱效率上均实现了显著提升。