We consider the problem of allocating transmit power in the downlink of a distributed wireless communication system. We account for the power used in both channel estimation and data transmission, with the objective of minimizing the overall transmitted power while satisfying specified Quality of Service (QoS) constraints to the mobile users. We consider both single user and multi-user power control optimization; the problem formulation for both cases lead to a nonconvex program. We proposed solution strategies for both scenarios: For the single user case, a simple intuitive solution, where power is allocated to the antennas sequentially until the QoS constraint is satisfied, is presented. For the multi-user case, we use successive convex approximation (based on the single condensation method) to find a provably convergent solution. We also demonstrate, via numerical simulation, the convergence of the proposed multi-user power allocation strategy. Our numerical results indicate that the proposed single and multi-user power allocation lead to an overall savings of up to 45% when compared to the baseline method of equal power allocation.