A coexistence scheme enables spectrally-efficient and fair spectrum sharing between a first wireless network and a coexisting wireless network in the same frequency bands. The spectrum sharing problem is modeled as a fairness constrained mixed integer nonlinear optimization problem, by jointly determining dynamic channel selection, carrier aggregation and fractional spectrum access for the first wireless networks, while guaranteeing fair spectrum access for the coexisting wireless network based on a cross-technology fairness criterion. An algorithm based on a combination of branch and bound and successive convex relation techniques is provided to optimally solve the problem, i.e., maximize the utility of the first wireless network with guaranteed optimality precision that can be set arbitrarily at the expense of computational complexity. The coexistence scheme requires no signaling exchange between the first wireless network and the coexisting wireless network, and does not require any changes to the communication protocol stack of the coexisting wireless network.