  An uplink multi secondary user (SU) cognitive radio system having average
delay constraints as well as an interference constraint to the primary user
(PU) is considered. If the interference channels between the SUs and the PU are
statistically heterogeneous due to the different physical locations of the
different SUs, the SUs will experience different delay performances. This is
because SUs located closer to the PU transmit with lower power levels. Two
dynamic scheduling-and-power-allocation policies that can provide the required
average delay guarantees to all SUs irrespective of their locations are
proposed. The first policy solves the problem when the interference constraint
is an instantaneous one, while the second is for problems with long-term
average interference constraints. We show that although the average
interference problem is an extension to the instantaneous interference one, the
solution is totally different. The two policies, derived using the Lyapunov
optimization technique, are shown to be asymptotically delay optimal while
satisfying the delay and interference constraints. Our findings are supported
by extensive system simulations and shown to outperform existing policies as
well as shown to be robust to channel estimation errors.
