Energy-Efficient MIMO Integrated Sensing and Communications with On-off Non-transmission Power

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.