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In this paper, we develop a power allocation scheme for the downlink of a two-cell two-user joint transmission system. The objective is to maximize the sum rate under per-cell power constraints. We study a worst case scenario where the carrier phases between the two base stations are un-synchronized, so that joint transmission must be performed without precoding. The derived power allocation scheme is remarkably simple, i.e., each cell transmits with full power to only one user. Note that joint transmission is still possible, when two cells select the same user for data transmission. Moreover, we prove that, in this scenario, the joint transmission case happens with higher probability when the maximum transmit power is high, or the two users are in the overlapped cell-edge area.