A novel scheme to enhance the spectral efficiency (SE) for an underlay cognitive radio system (UCRS) is proposed. A cross-layer optimization (CLO) of both the physical layer (PHY) and the data link control layer (DLC) of a secondary user (SU) transmission is considered. The transceiver uses discrete Fourier transform modulated filter banks. An optimum scheme for joint bit and power loading (JBPL) as well as coding adaptation (CA) using punctured convolutional codes is employed at the PHY. At the DLC, a truncated automated repeat request (TARQ) is implemented to ensure reliable transmission. A lower bound on the SE for coded transmission is derived analytically and maximized subject to different quality-of-service (QoS) and stochastic chance-based constraints as well as third-party colored Gaussian interference at the SU receiver. The system performance is analyzed in terms of the number of retransmissions and the achievable SU SE. It turns out that the bound tightens for increasing values of the average energy-per-bit-to-noise-ratio.