  In this paper we investigate the problem of allocating spectrum among radio
nodes under SINR requirements. This problem is of special interest in dynamic
spectrum access networks where topology and spectral resources differ with time
and location. The problem is to determine the number of radio nodes that can
transmit simultaneously while still achieving their SINR requirements and then
decide which channels these nodes should transmit on. Previous work have shown
how this can be done for a large spectrum pool where nodes allocate multiple
channels from that pool which renders a linear programming approach feasible
when the pool is large enough. In this paper we extend their work by
considering arbitrary individual pool sizes and allow nodes to only transmit on
one channel. Due to the accumulative nature of interference this problem is a
non-convex integer problem which is NP-hard. However, we introduce a constraint
transformation that transforms the problem to a binary quadratic constraint
problem. Although this problem is still NP-hard, well known heuristic
algorithms for solving this problem are known in the literature. We implement a
heuristic algorithm based on Lagrange relaxation which bounds the solution
value of the heuristic to the optimal value of the constraint transformed
problem. Simulation results show that this approach provides solutions within
an average gap of 10% of solutions obtained by a genetic algorithm for the
original non-convex integer problem.
