  We present a joint sub-channel and power allocation framework for downlink
transmission an orthogonal frequency-division multiple access (OFDMA)-based
cellular network composed of a macrocell overlaid by small cells. In this
framework, the resource allocation (RA) problems for both the macrocell and
small cells are formulated as optimization problems. Numerical results confirm
the performance gains of our proposed RA formulation for the macrocell over the
traditional resource allocation based on minimizing the transmission power.
Besides, it is shown that the formulation based on convex relaxation yields a
similar behavior to the MINLP formulation. Also, the distributed solution
converges to the same solution obtained by solving the corresponding convex
optimization problem in a centralized fashion.
