Efficient spectrum allocation in multiband CSMA networks

We consider the problem of assigning a group of users with different rate requirements to a set of frequency bands, which may have different bandwidths, when the users access the channel via carrier-sense multiple access (CSMA). For example, in systems that employ dynamic spectrum access (DSA), secondary users may interleave their transmissions into space-time-frequency slots left open by primary users. The set of primary users that are active at a given time may leave a set of available channels that have unequal bandwidths. The use of CSMA by the secondary users reduces the need to coordinate transmissions among the users allocated to a particular frequency band, but it also results in potential collisions, which reduce the overall data rate that can be accommodated in the band. This is especially true when the presence of a finite sensing delay is considered. In this paper, we consider the layer problem of allocating users to the available frequency bands to minimize the bandwidth used (to accommodate other groups of secondary users), while taking into account the CSMA interactions of assigning multiple users to a band. We formulate this as a new form of bin packing problem, in which the size of the bin depends on the number of users that are assigned to the bin. A near optimal solution to this problem is found numerically using the Gurobi solver, and the performance is compared with the suboptimal first-fit algorithm, which has complexity that is appropriate for online implementation. Simulation results are provided to compare the optimal and online algorithms in terms of efficiency in allocating the bandwidth to the users and their complexity.