We consider a multiple-input multiple-output (MIMO) asymmetric two-way relay (A-TWR) system, wherein the base station (BS) serves a transmit-only user (TU) and receive-only user (RU). The TU transmits data to the BS and the RU receives data from the BS. Because of the asymmetric nature of A-TWR, the RU experiences interference and necessitates a joint transceiver design at the TU, RU, and relay. The existing literature has designed such transceivers by assuming perfect channel state information (CSI) at all the nodes. Obtaining perfect CSI at all the nodes is, however, not viable in practice due to the distributed nature of the system. This work constructs a transceiver design with perfect CSI at the relay and perturbed CSI at the TU, RU and BS. The perturbed signal-to-interference-plus-noise ratio (SINR) is analyzed by exploiting the properties of the singular value decomposition and the results from theory of matrix normal distributions. The resulting closed-form SINR expressions are then used to perform robust power allocation at all the nodes. Two different settings, namely maximization of the minimum SINR across all streams and minimization of the total network transmit power are considered. The performance gains from the proposed robust designs are validated numerically.

中文翻译：

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用于 AF 非对称双向 MIMO 中继的稳健收发器设计

我们考虑多输入多输出 (MIMO) 非对称双向中继 (A-TWR) 系统，其中基站 (BS) 为仅发送用户 (TU) 和仅接收用户 (RU) 提供服务。TU向BS发送数据，RU从BS接收数据。由于 A-TWR 的不对称特性，RU 会受到干扰，因此需要在 TU、RU 和中继处进行联合收发器设计。现有文献通过假设所有节点的信道状态信息 (CSI) 来设计此类收发器。然而，由于系统的分布式特性，在所有节点上获得完美的 CSI 在实践中是不可行的。这项工作构建了一个收发器设计，在中继处具有完美的 CSI，在 TU、RU 和 BS 处具有扰动 CSI。利用奇异值分解的性质和矩阵正态分布理论的结果，分析了扰动的信干噪比（SINR）。然后使用所得的封闭形式 SINR 表达式在所有节点上执行稳健的功率分配。考虑了两种不同的设置，即所有流中最小 SINR 的最大化和网络总传输功率的最小化。从所提出的稳健设计中获得的性能增益在数值上得到了验证。即考虑所有流中最小 SINR 的最大化和网络总传输功率的最小化。所提出的稳健设计的性能增益得到了数值验证。即考虑所有流中最小 SINR 的最大化和网络总传输功率的最小化。所提出的稳健设计的性能增益得到了数值验证。