Extremely large aperture arrays can enable unprecedented spatial multiplexing in beyond 5G systems due to their extremely narrow beamfocusing capabilities. However, acquiring the spatial correlation matrix to enable efficient channel estimation is a complex task due to the vast number of antenna dimensions. Recently, a new estimation method called the "reduced-subspace least squares (RS-LS) estimator" has been proposed for densely packed arrays. This method relies solely on the geometry of the array to limit the estimation resources. In this paper, we address a gap in the existing literature by deriving the average spectral efficiency for a certain distribution of user equipments (UEs) and a lower bound on it when using the RS-LS estimator. This bound is determined by the channel gain and the statistics of the normalized spatial correlation matrices of potential UEs but, importantly, does not require knowledge of a specific UE's spatial correlation matrix. We establish that there exists a pilot length that maximizes this expression. Additionally, we derive an approximate expression for the optimal pilot length under low signal-to-noise ratio (SNR) conditions. Simulation results validate the tightness of the derived lower bound and the effectiveness of using the optimized pilot length.

翻译：超大孔径阵列凭借其极窄的波束聚焦能力，可在超5G系统中实现前所未有的空间复用。然而，由于天线维数庞大，获取空间相关矩阵以实现高效信道估计是一项复杂任务。针对密集排列阵列，近期提出了一种名为"约化子空间最小二乘（RS-LS）估计器"的新型估计方法，该方法仅依赖阵列几何结构来限制估计资源。本文填补了现有文献空白：针对特定用户设备（UE）分布场景，推导了采用RS-LS估计器时的平均频谱效率及其下界。该下界由信道增益与潜在UE归一化空间相关矩阵的统计特性共同决定，但关键优势在于无需获知特定UE的空间相关矩阵。我们证明了存在使该表达式最大化的最优导频长度，并推导了低信噪比（SNR）条件下最优导频长度的近似表达式。仿真结果验证了所推导下界的紧致性以及采用优化导频长度的有效性。