By deploying a large number of antennas with sub-half-wavelength spacing in a compact space, dense array systems(DASs) can fully unleash the multiplexing-and-diversity gains of limited apertures. To acquire these gains, accurate channel state information acquisition is necessary but challenging due to the large antenna numbers. To overcome this obstacle, this paper reveals that exploiting the high spatial correlation of DAS channels is crucial while designing the observation matrix for optimal/near-optimal channel estimation. Firstly, we prove that the observation matrix design is equivalent to a time-domain duality of multiple-input multiple-output precoding, which can be ideally addressed by the water-filling principle. For practical realizations, a novel ice-filling algorithm is proposed to design amplitude-and-phase controllable observation matrices, and a majorization-minimization algorithm is proposed to address the phase-only controllable case. Particularly, we prove that the ice-filling algorithm can be viewed as a ``quantized" water-filling algorithm. To support the sub-optimality of the proposed designs, we provide comprehensive analyses on the achievable mean square errors and their asymptotic expressions. Finally, numerical simulations verify that our proposed channel estimation designs can achieve the near-optimal performance and outperform existing approaches significantly.

翻译：通过在紧凑空间内部署大量亚半波长间距天线，密集阵列系统（DAS）可充分释放有限孔径的复用与分集增益。为获取这些增益，精确的信道状态信息获取虽至关重要，但大规模天线配置使其极具挑战性。为攻克此难题，本文揭示：在设计观测矩阵以实现最优/近最优信道估计时，充分利用DAS信道的高空间相关性至关重要。首先，我们证明观测矩阵设计等价于多输入多输出预编码的时域对偶问题，该问题可通过注水原理理想求解。针对实际实现，本文提出新颖的冰注算法以设计幅度-相位可控观测矩阵，并针对仅相位可控场景提出极大化-极小化算法。特别地，我们证明冰注算法可视为"量化"注水算法。为支撑所提设计的次优性，我们给出了可达均方误差及其渐近表达式的全面分析。最终数值仿真验证：所提信道估计设计方案可实现近最优性能，并显著优于现有方法。