This paper investigates the energy efficiency of a multiple-input multiple-output (MIMO) integrated sensing and communications (ISAC) system, in which one multi-antenna base station (BS) transmits unified ISAC signals to a multi-antenna communication user (CU) and at the same time use the echo signals to estimate an extended target. We focus on one particular ISAC transmission block and take into account the practical on-off non-transmission power at the BS. Under this setup, we minimize the energy consumption at the BS while ensuring a minimum average data rate requirement for communication and a maximum Cram\'er-Rao bound (CRB) requirement for target estimation, by jointly optimizing the transmit covariance matrix and the ``on'' duration for active transmission. We obtain the optimal solution to the rate-and-CRB-constrained energy minimization problem in a semi-closed form. Interestingly, the obtained optimal solution is shown to unify the spectrum-efficient and energy-efficient communications and sensing designs. In particular, for the special MIMO sensing case with rate constraint inactive, the optimal solution follows the isotropic transmission with shortest ``on'' duration, in which the BS radiates the required sensing energy by using sufficiently high power over the shortest duration. For the general ISAC case, the optimal transmit covariance solution is of full rank and follows the eigenmode transmission based on the communication channel, while the optimal ``on'' duration is determined based on both the rate and CRB constraints. Numerical results show that the proposed ISAC design achieves significantly reduced energy consumption as compared to the benchmark schemes based on isotropic transmission, always-on transmission, and sensing or communications only designs, especially when the rate and CRB constraints become stringent.

翻译：本文研究了多输入多输出（MIMO）集成感知与通信（ISAC）系统的能效问题。在该系统中，一个多天线基站（BS）向多天线通信用户（CU）发送统一的ISAC信号，同时利用回波信号对扩展目标进行估计。我们聚焦于一个特定的ISAC传输块，并考虑基站实际存在的通断式非传输功率。在此设定下，通过联合优化发射协方差矩阵和主动传输的"导通"时长，我们在确保通信最低平均数据速率要求和目标估计最大克拉美-罗界（CRB）要求的同时，最小化基站的能耗。我们以半封闭形式获得了速率与CRB约束下的能量最小化问题的最优解。有趣的是，所得到的最优解被证明统一了频谱高效与能量高效的通信及感知设计。特别地，对于速率约束不激活的MIMO感知特例，最优解遵循具有最短"导通"时长的各向同性传输模式，即基站通过最短时长内使用足够高的功率辐射所需的感知能量。对于一般ISAC情况，最优发射协方差解满秩，并基于通信信道采用本征模传输，而最优"导通"时长则由速率和CRB约束共同决定。数值结果表明，与基于各向同性传输、持续传输以及仅感知或仅通信设计的基准方案相比，所提出的ISAC设计在速率和CRB约束变得严格时，能显著降低能耗。