In this paper, a 2-dimensional water-filling (2D-WF) based transmit weight that maximizes the channel capacity is theoretically derived for the downlink transmit diversity of single-carrier distributed antenna network (SC DAN) in a frequency-selective channel. The 2D-WF transmit weight allocates the transmit power in both transmit antenna dimension and frequency dimension: power allocation across frequencies based on WF theory and across transmit antennas based on maximal ratio transmission (MRT). The cumulative distribution function (CDF) of the achievable channel capacity by 2D-WF transmit diversity is evaluated by the Monte-Carlo numerical computation method. Channel capacities achievable with 2D-WF, MRT, and 1D WF transmit weight are compared. It is shown that the 2D-WF transmit weight provides the highest channel capacity among three transmit weights.