  In this correspondence, the comprehensive problem of joint power, rate, and
subcarrier allocation have been investigated for enhancing the spectral
efficiency of multi-user orthogonal frequency-division multiple access (OFDMA)
cognitive radio (CR) networks subject to satisfying total average transmission
power and aggregate interference constraints. We propose novel optimal radio
resource allocation (RRA) algorithms under different scenarios with
deterministic and probabilistic interference violation limits based on a
perfect and imperfect availability of cross-link channel state information
(CSI). In particular, we propose a probabilistic approach to mitigate the total
imposed interference on the primary service under imperfect cross-link CSI. A
closed-form mathematical formulation of the cumulative density function (cdf)
for the received signal-to-interference-plus-noise ratio (SINR) is formulated
to evaluate the resultant average spectral efficiency (ASE). Dual decomposition
is utilized to obtain sub-optimal solutions for the non-convex optimization
problems. Through simulation results, we investigate the achievable performance
and the impact of parameters uncertainty on the overall system performance.
Furthermore, we present that the developed RRA algorithms can considerably
improve the cognitive performance whilst abide the imposed power constraints.
In particular, the performance under imperfect cross-link CSI knowledge for the
proposed `probabilistic case' is compared to the conventional scenarios to show
the potential gain in employing this scheme.
