Design of Uplink ISAC Systems with Cooperative Sensing: Power Control and Receive Beamforming

Integrated sensing and communication (ISAC) has emerged as a key paradigm for next-generation wireless systems, which allows wireless resources to be used for data transmission and target sensing simultaneously. In this paper, multi-user collaborative target detection in the uplink ISAC system is investigated. To incorporate the target sensing functionality, the system relies on the reuse of uplink signals from the communication users. Specifically, we analyze an uplink multi-user single-input multiple-output (MU-SIMO) communication system with bistatic sensing. Using the channel statistics, we formulate the problem of joint optimal pilot and data power allocation to maximize the uplink ergodic sum rate while meeting communication and sensing quality-of-service (QoS) requirements. To address this non-convex problem, we propose an alternating optimization (AO)-based iterative framework, where the joint power allocation problem is decomposed into two sub-problems. Specifically, the pilot power allocation is optimized using a penalty dual decomposition (PDD)-based gradient ascent algorithm, while the data power allocation is solved via successive convex approximation (SCA). Once the long-term power allocation is determined, the base station (BS) estimates the instantaneous channels using a minimum mean-squared error (MMSE) estimator. Subsequently, based on the estimated instantaneous channel state information (CSI), the receive beamforming for communication users is optimized via another SCA-based method to maximize the sum rate. Meanwhile, the optimal receive beamforming for the target is obtained in closed-form through eigenvalue decomposition (EVD).