In the literature, Cognitive radio (CR) as well as full-duplex (FD) communication technologies are proposed to increase the spectrum efficiency. The main contribution of this thesis is to introduce prediction and estimation techniques with low control overhead, and use the predicted or estimated information in resource allocation in CR networks, both in the overlay networks and the underlay networks. Prediction and estimation are important in increasing the data rate and keeping the interference at a low level. In the overlay scheme, I modeled the primary user (PU) traffic characteristics of the channels using the Probabilistic Suffix Tree (PST) algorithm. Then using this PST algorithm, I introduced a frequency hopping based control channel and derived its theoretical properties. Then I proposed two methods for selecting a channel set for transmission, which took into account both the PU channel usage statistics and, secondary user (SU) channel usage statistics as perceived by an SU of interest. The first scheme selected channels having the highest probability of successful transmission, while the second calculated a net reward using a marked Markov chain. Then using simulations, I showed that our scheme caused acceptable interference to the PUs and has better throughput performance, compared to a scheme selecting channels randomly. Then I proposed two joint channel assignment and power allocation schemes for a bi-directional FD underlay CR network with network assistance. The first scheme used the information on the number of total SU pairs present in the network. In the second scheme, I used least squares based estimation and Kalman filtering to estimate the interference at the monitoring stations using the local interference. It reduced the control overhead of keeping track of active SUs. In both of these schemes each SU pair decided on the channels to be used in the half-duplex mode and the full-duplex mode using local information. This joint optimization was done running channel assignment and power allocation algorithms alternatively. In the power allocation problem, I used a technique called monotonic optimization. After simulating both of these schemes I showed that the scheme based on estimation performs satisfactorily given that it has less control overhead. / October 2016