COGNITIVE radio (CR) is a promising technology to alleviate the spectrum shortage problem and to improve the spectrum utilization. In CR networks, the secondary user (SU) is allowed to access the same spectrum owned by the primary user (PU) Robust Beamforming for Cognitive Multi-Antenna Relay Networks with Bounded Channel Uncertainties subject to the interference constraint that the interference power from the SU to the PU is below a threshold. Thus, the CR networks can achieve higher spectrum utilization. To satisfy the interference constraint, the SU transmitter (SU-Tx) should know the perfect channel state information (CSI) from the SU-Tx to the PU. In practice, however, the perfect CSI from the SU-Tx to the PU is seldom perfectly known becaus In general, Robust Beamforming for Cognitive Multi-Antenna Relay Networks with Bounded Channel Uncertainties the channel uncertainty is characterized by two different models: the stochastic and deterministic (or worst-case models . In the stochastic model, the channel uncertainties are modeled as Gaussian random variables and the system design is then based on optimizing the average or outage performance Alternatively, the worst-case model assumes that the channel uncertainties, though not exactly known, are bounded by possible values . Robust Beamforming for Cognitive Multi-Antenna Relay Networks with Bounded Channel Uncertainties In this case, the system is optimized to achieve a given quality of service (QoS) for every possible channel uncertainty if the problem is feasible, thereby, achieving absolute robustness. It was also shown in that a bounded worst-case model is able to cope with quantization errors in CSIs. We consider a non-regenerative CRN as where an SU transmitter (SU-Tx), an SU receiver (SU-Rx) and a cognitive relay are allowed to share the same spectrum with M PUs. Each of the SU-Tx, SU-Rx, and PUs is equipped with a single antenna and the cognitive relay is equipped with N antennas. Robust Beamforming for Cognitive Multi-Antenna Relay Networks with Bounded Channel Uncertainties We assume that there is no direct link between the SU-Tx and the SU-Rx, where the reliable communication link is established by the relay. The scenario is typical for deviceto- device communications where two mobile phones in a underlaying cellular system communicate directly with the help of a femtocell or a laptop. It is noted that in practical CR system, there is usually a bunch of secondary users trying to access the network. To generalize the point-to-point CRN communication to the multi-user CRN communication is an interesting future work.