This paper advances the design of transmit precoder for a secondary user (SU) coexisting with a primary user (PU) in multiple-input multiple-output (MIMO) cognitive radio, where the channel state information at transmitter (CSIT) of SU is inaccurate in both the desired link (DL) to its receiver and the interference link (IL) to the PU. The design seeks to maximize performance in the worst scenario, by optimizing the capacity of SU while maintaining a given quality of service (QoS) of PU at the most unfavorable uncertainty errors of the two links. The proposed technique improves the previous design by solving for the precoder in a more accurate and efficient manner, and by using the variable metric projected subgradient method. The most unfavorable realization in the DL is obtained by the alternate-iterate optimization method and the worst uncertainty realization in the IL is derived from the projected subgradient method. The convergence properties and computational complexity of the proposed algorithm are analyzed. Numerical results confirm the proposed precoder has better performance than the previous solution while having lower practical time complexity, especially when the PU has higher tolerance level of SU interference.

本文提出了多输入多输出 (MIMO) 认知无线电中与主用户 (PU) 共存的次用户 (SU) 发射预编码器的设计，其中 SU 的发射机 (CSIT) 处的信道状态信息不准确在到其接收器的所需链路 (DL) 和到 PU 的干扰链路 (IL) 中。该设计旨在通过优化 SU 的容量，同时在两条链路最不利的不确定性误差下保持 PU 的给定服务质量 (QoS) 来最大化最坏情况下的性能。所提出的技术通过以更准确和有效的方式求解预编码器并使用可变度量投影次梯度方法来改进先前的设计。DL 中最不利的实现是通过交替迭代优化方法获得的，IL 中最差的不确定性实现是从投影次梯度方法中得出的。分析了该算法的收敛性和计算复杂度。数值结果证实，所提出的预编码器具有比以前的解决方案更好的性能，同时具有更低的实际时间复杂度，尤其是当 PU 具有更高的 SU 干扰容忍度时。