In this thesis, we investigate two different system infrastructures in underlay cognitive radio network, in which two popular techniques, cross-layer design and cooperative communication, are considered, respectively. In particular, we introduce the Aggressive Adaptive Modulation and Coding (A-AMC) into the cross-layer design and achieve the optimal boundary points in closed form to choose the AMC and A-AMC transmission modes by taking into account the Channel State Information (CSI) from the secondary transmitter to both the primary receiver and the secondary receiver. What’s more, for the cooperative communication design, we consider three different relay selection schemes: Partial Relay Selection, Opportunistic Relay Selection and Threshold Relay Selection. The Probability Density Functions (PDFs) of the Signal-to- Noise Ratio (SNR) in each hop for different selection schemes are provided, and then the exact closed-form expressions for the end-to-end packet loss rate in the secondary link considering the cooperation of the Decode-and-Forward (DF) relay for different relay selection schemes are derived.