Abstract-In this paper, we address the problem of designing a joint scheduling and power control algorithm in a downlink coordinated multi-point (CoMP) cluster supporting CoMP joint transmission. The objective is to maximize the cell-edge throughput under per-point power constraints. By an analytical derivation, binary power control is proved to be the optimal solution for any given selected user group. Utilizing this analytical result, a centralized and a semi-distributed version of joint user selection and power control algorithms are proposed. Compared to algorithms without considering joint transmission and algorithms without considering power control, simulation results show that the proposed algorithms achieve a good tradeoff between joint transmission and interference coordination, which helps to improve the cell-edge performance.