Extra large-scale multiple-input multiple-output (XL-MIMO) is a key technology for future wireless communication systems. This paper considers the effects of visibility region (VR) at the base station (BS) in a non-stationary multi-user XL-MIMO scenario, where only partial antennas can receive users' signal. In time division duplexing (TDD) mode, we first estimate the VR at the BS by detecting the energy of the received signal during uplink training phase. The probabilities of two detection errors are derived and the uplink channel on the detected VR is estimated. In downlink data transmission, to avoid cumbersome Monte-Carlo trials, we derive a deterministic approximate expression for ergodic {average energy efficiency (EE)} with the regularized zero-forcing (RZF) precoding. In frequency division duplexing (FDD) mode, the VR is estimated in uplink training and then the channel information of detected VR is acquired from the feedback channel. In downlink data transmission, the approximation of ergodic average {EE} is also derived with the RZF precoding. Invoking approximate results, we propose an alternate optimization algorithm to design the detection threshold and the pilot length in both TDD and FDD modes. The numerical results reveal the impacts of VR estimation error on ergodic average {EE} and demonstrate the effectiveness of our proposed algorithm.

翻译：超大规模多输入多输出（XL-MIMO）是未来无线通信系统的关键技术。本文考虑非平稳多用户XL-MIMO场景中基站（BS）处可见区域（VR）的影响，其中仅有部分天线能够接收用户信号。在时分双工（TDD）模式下，我们首先通过上行链路训练阶段接收信号的能量检测来估计基站处的VR。推导了两种检测误差的概率，并估计了检测所得VR上的上行链路信道。在下行链路数据传输中，为避免繁琐的蒙特卡洛仿真，我们推导了采用正则化迫零（RZF）预编码时遍历平均能量效率（EE）的确定性近似表达式。在频分双工（FDD）模式下，通过上行链路训练估计VR，随后通过反馈信道获取检测所得VR的信道信息。在下行链路数据传输中，同样推导了采用RZF预编码时遍历平均EE的近似表达式。基于近似结果，我们提出了一种交替优化算法，用于在TDD和FDD两种模式下联合设计检测阈值与导频长度。数值结果揭示了VR估计误差对遍历平均EE的影响，并验证了所提算法的有效性。