ed in the k-th SU information decoding circuit is (5.5) where nD - is the AWGN imposed by the information decoding receiver. 5.2.3 Bounded CSI Error Model In this model, we consider a bounded error imposed on the estimated CSI, which can be treated as the worst-case scenario. Specifically, the channels can be modeled as follows. (5.6a) (5.6b) (5.6c) 5 Robust Beamforming in NOMA Cognitive Radio Networks: Bounded CSI AgnECMAg< (5.6d) where hk and gn are the estimated channel vectors for hk and gn' respectively, while and O n define the set of channel variations due to estimation errors. The model defines all the uncertainty regions that are confined by power constraints. Furthermore, we use block Rayleigh fading channels, which remain constant within each block, but change from block to block independently. 5.2.3.1 NOMA Transmission Without loss of generality, we sort the estimated channel of SUs in the ascending order, i.e. ||h1||2 ||h2||2 ||h||2. According to the SIC principle, SU i can detect and remove SU k's signal, for <k<i<K. Thus, when SU i decodes signal Sk, the signals of the pre- vious (k - 1) SUs have already been removed from the composite received signal. Due to channel estimation errors, however, these (k - 1) signals may not be completely removed, leaving some residual signals as interference. Therefore, the signal at UE i when decoding Sk becomes Here, the first term is the desired received signal, the second term is the interference due to imperfect channel estimation, and the third term represents the NOMA interfer- ence. For notational simplicity, let us = = and The corresponding SINR for the i-th SU after the SIC applied at the receiver is given by: Since the signal Sk can be detected at every SU i, as long as k < i, there will be a set of SINRs for signal Sk. For CBS, the maximum data rate for SU k should be Rk = log2(1 mink<i<<SINR'). Moreover, the channel estimation error should be considered. The worst-case data rate for SU k becomes (5.7) 5.3 Power Minimization-Based Problem Formulation Si