Power allocation is a promising approach for optimizing the performance of mobile radio systems in interference channels. In the present paper, the non-convex objective function of the power allocation problem aiming at maximizing the sum rate with a total power constraint is reformulated as a difference of two concave functions. A global optimum power allocation is found by applying a branch and bound based algorithm to the new formulation. The algorithm basically splits the feasible region consecutively into subregions where for every subregion the objective function is upper and lower bounded. For a certain partition of the feasible region, a power allocation corresponding to the highest lower bound which is upper bounded by the highest upper bound with some insignificant difference is found as the global optimum. A convex maximization formulation of the optimization problem with a piecewise linearly outer approximated feasible region is essentially applied for finding an upper bound which only requires solving a linear program problem. The simulation results show a significant improvement in the sum rate of the proposed algorithm over the conventional suboptimal techniques.