Sketch of the configuration of a BBH+cBLR system, with the BBHs and BLR clouds rotating in the same direction. For the BBHs co-rotating in elliptical orbits, the longitude of ascending node is set to be Ω = 0° for simplicity, i.e., the sky plane (yellow) and the BBH orbital plane (gray) share the same x-axis in the barycentric coordinate system. The argument of periapsis is denoted as ω. The observer’s line of sight is set in the y − z plane with an inclination angle of i_obs to the BBH orbital plane. The BLR has an opening angle of θ_o and its middle plane is the same as the BBH orbital plane.