Max-Min Fair Energy-Efficient Beam Design for Quantized ISAC LEO Satellite Systems: A Rate-Splitting Approach

Low earth orbit (LEO) satellite systems with sensing functionality is envisioned to facilitate global-coverage service and emerging applications in 6G. Currently, two fundamental challenges, namely, inter-beam interference among users and power limitation at the LEO satellites, limit the full potential of the joint design of sensing and communication. To effectively control the interference, rate-splitting multiple access (RSMA) scheme is employed as the interference management strategy in the system design. On the other hand, to address the limited power supply at the LEO satellites, we consider low-resolution quantization digital-to-analog converters (DACs) at the transmitter to reduce power consumption, which grows exponentially with the number of quantization bits. Additionally, optimizing the total energy efficiency (EE) of the system is a common practice to save the power. However, this metric lacks fairness among users. To ensure this fairness and further enhance EE, we investigate the max-min fairness EE of the RSMA-assisted integrated sensing and communications (ISAC)-LEO satellite system. In this system, the satellite transmits a quantized dual-functional signal serving downlink users while detecting a target. Specifically, we optimize the precoders for maximizing the minimal EE among all users, considering the power consumption of each radio frequency (RF) chain under communication and sensing constraints. To tackle this optimization problem, we proposed an iterative algorithm based on successive convex approximation (SCA) and Dinkelbach's method. Numerical results illustrate that the proposed design outperforms the strategies that aim to maximize the total EE of the system and conventional space-division multiple access (SDMA) in terms of max-min fairness EE and the communication-sensing trade-off.