A cognitive radio (CR) network is often described as a secondary network operating in a frequency band originally licensed/allocated to a primary network consisting of one or multiple primary users (PUs). A fundamental challenge for realizing such a system is to ensure the quality of service (QoS) of the PUs as well as to maximize the throughput or ensure the QoS, such as signal-to-interference-plus-noise ratios (SINRs), of the secondary users (SUs). In this paper, we study singleinput multiple output multiple access channels (SIMO-MAC) for the CR network. Subject to interference constraints for the PUs as well as peak power constraints for the SUs, two optimization problems involving a joint beamforming and power allocation for the CR network are considered: the sum-rate maximization problem and the SINR balancing problem. For the sum-rate maximization problem, zero-forcing based decision feedback equalizers are used to decouple the SIMO-MAC, and a capped multi-level (CML) water-filli...