  In this paper, we propose a green beamforming design for the integrated
sensing and communication (ISAC) system, using beam-matching error to assess
radar performance. The beam-matching error metric, which considers the mean
square error between the desired and designed beam patterns, provides a more
practical evaluation approach. To tackle the non-convex challenge inherent in
beamforming design, we apply semidefinite relaxation (SDR) to address the
rank-one relaxation issue, followed by the iterative rank minimization
algorithm (IRM) for rank-one recovery. The simulation results showcase the
effectiveness of our proposed optimal beamforming design, emphasizing the
exceptional performance of the radar component in sensing tasks.
