An optimization framework for spectrum sharing in white space bands formulates an objective function as a linear function of channels and power levels, and constructs a linear set of equations based on a general graph model according to constraints, including spectrum usage regulations and/or resource re-use constraints. The optimization framework provides joint power control and channel assignment where the solution is implemented by an algorithm that allocates time/power/channel to each network to avoid interference while re-using time and/or frequency resources. The solution allocates a fair and orthogonal portion of time on each channel for a certain power level to the networks. The solution can be implemented by a central entity having at least location information of the networks and, upon solving the optimization problem, signals scheduling information of each channel assigned.