This thesis focuses on optimal power allocation problems for various types of spectrum-sharing based cognitive radio networks in the presence of delay-sensitive primary links.To guarantee the quality of service in the delay-sensitive primary network, primary user's outage probability constraint (POC) is imposed such that the transmission outage probability of each primary user is confined under the predefined threshold.We first consider a cognitive radio network consisting of a secondary user (SU) equipped with orthogonal frequency-division multiplexing (OFDM) technology able to access N randomly fading frequency bands for transmitting delay-insensitive as well as delay-sensitive traffic.Each band is licensed to an individual single-antenna and delay-sensitive primary user (PU) whose quality of service is assured by a POC.Assuming full channel state information (CSI) is available at the secondary network, we solve the SU's ergodic capacity maximization problem subject to SU's average Foremost, I would like to thank my supervisor Professor Subhrakanti Dey for his continuing guidance, encouragement and support throughout my PhD study.