In a cognitive radio (CR) framework, the channel state information (CSI) feedback to the secondary transmitter (SU_Tx) can be limited or unavailable. Thus, the statistical model is adopted to determine system performance using the outage concept. In this paper, we adopt a new approach using multilayer-coding (MLC) strategy, i.e., broadcast approach, to enhance spectrum sharing over fading channels. First, we consider a scenario where the SU_Tx has no CSI of both the link between the SU_Tx and the primary receiver (cross link) and its own link. We show that using MLC improves the cognitive rate compared with the rate provided by a single-layer coding (SLC). In addition, we observe numerically that two-layer coding achieves most of the gain for Rayleigh fading. Second, we analyze a scenario where SU_Tx is provided by partial CSI about its link through quantized CSI. We compute its achievable rate, adopting the MLC and highlight the improvement over SLC. Finally, we study the case in which the cross link is perfect, i.e., a cooperative primary user setting, and compare the performance with the previous cases. We present asymptotic analysis at the high-power regime and show that the cooperation considerably enhances the cognitive rate at high values of the secondary power budget.