Joint Beamforming Design for Active RIS-Assisted ISAC Systems with Transmitter Hardware Impairments

This paper investigates an active reconfigurable intelligent surface (RIS)-assisted integrated sensing and communication (ISAC) system with transmitter hardware impairments (HWIs) at the base station (BS). The active RIS provides both phase adjustment and amplitude amplification, which helps mitigate the multiplicative fading effect of passive RIS-assisted cascaded links and establish virtual line-of-sight (LoS) links for the target and multiuser communication users. Considering the coupling among the BS transmitter distortion noise, active RIS amplification noise, and the active RIS power constraint, we formulate a radar output signal-to-noise ratio (SNR) maximization problem. The radar output SNR is maximized by jointly designing the radar receive filter, the BS transmit beamforming matrix, and the active RIS reflection coefficients, while satisfying the quality-of-service (QoS) requirements of communication users, the BS transmit power constraint, and the active RIS power budget constraint. To solve the resulting non-convex problem with fractional objectives and high-order coupling terms, an alternating optimization (AO)-based iterative framework is developed. Specifically, the radar receive filter is updated using the generalized Rayleigh quotient, the BS transmit beamforming subproblem is handled by semidefinite relaxation and the Charnes–Cooper transformation, and the active RIS reflection coefficient subproblem is solved using the Dinkelbach transformation and majorization–minimization. Simulation results demonstrate stable convergence and show that the proposed design improves radar output SNR under BS transmitter HWIs.