The authors study algorithms for carrier and rate allocation in cellular systems with distributed components such as a heterogeneous LTE system with macrocells and femtocells. Existing work on LTE systems often involves centralized techniques or requires significant signaling, and is therefore not always applicable in the presence of femtocells. More distributed CSMA-based algorithms (Carrier-Sense Multiple Access) were developed in the context of 802.11 systems and have been proven to be utility optimal. However, the proof typically assumes a single carrier and a single transmission rate. Further, it relies on the CSMA collision detection mechanisms to know whether a transmission is feasible.