  We formulate throughput maximizing, max-min fair, weighted max-min fair, and
proportionally fair scheduling problems for cognitive radio networks managed by
a centralized cognitive base station. We propose a very general scheduling
model accomplishing goals such as making frequency, time slot, and data rate
allocation to secondary users with possibly multiple antennas, in a
heterogenous multi-channel and multi-user scenario. Moreover, our schedulers
ensure that reliable communication between the cognitive base station and
secondary users are maintained, no collisions occur among secondary users, and
primary users in the service area of the cognitive base station are not
disturbed. Two distinctive features of our fair schedulers are that they
provide joint temporal and throughput fairness, and take throughput values
experienced by secondary users in the recent past, referred to as window size,
into account and use this information in the current scheduling decision. We
also propose a heuristic algorithm for our fair schedulers and demonstrate
through simulations that our proposed heuristic yields very close solutions to
the values obtained from the optimization softwares. Furthermore, we make
extensive simulations to evaluate our schedulers' performance in terms of both
total throughput and fairness for varying number of secondary users,
frequencies, antennas, and window size.
