  We study the performance of cognitive radio networks (CRNs) when
incorporating adaptive modulation at the physical layer. Three types of CRNs
are considered, namely opportunistic spectrum access (OSA), spectrum sharing
(SS) and sensing-based SS. We obtain closed-form expressions for the average
spectral efficiency achieved at the secondary network and the optimal power
allocation for both continuous and discrete rate types of adaptive modulation
assuming perfect channel state information. The obtained numerical results show
the achievable performance gain in terms of average spectral efficiency and the
impact on power allocation when adaptive modulation is implemented at the
physical layer that is due to the effect of the cut-off level that is
determined from the received signal-to-noise ratio for each CRN type. The
performance assessment is taking place for different target bit error rate
values and fading regions, thereby providing useful performance insights for
various possible implementations.
