In this paper, we investigate the sparse channel estimation in holographic multiple-input multiple-output (HMIMO) systems. The conventional angular-domain representation fails to capture the continuous angular power spectrum characterized by the spatially-stationary electromagnetic random field, thus leading to the ambiguous detection of the significant angular power, which is referred to as the power leakage. To tackle this challenge, the HMIMO channel is represented in the wavenumber domain for exploring its cluster-dominated sparsity. Specifically, a finite set of Fourier harmonics acts as a series of sampling probes to encapsulate the integral of the power spectrum over specific angular regions. This technique effectively eliminates power leakage resulting from power mismatches induced by the use of discrete angular-domain probes. Next, the channel estimation problem is recast as a sparse recovery of the significant angular power spectrum over the continuous integration region. We then propose an accompanying graph-cut-based swap expansion (GCSE) algorithm to extract beneficial sparsity inherent in HMIMO channels. Numerical results demonstrate that this wavenumber-domainbased GCSE approach achieves robust performance with rapid convergence.

翻译：本文研究了全息多输入多输出（HMIMO）系统中的稀疏信道估计问题。传统角度域表示无法捕捉由空间平稳电磁随机场表征的连续角度功率谱，从而导致显著角度功率的模糊检测，即功率泄漏。为应对这一挑战，本文在波数域中表示HMIMO信道，以探索其簇主导的稀疏性。具体而言，一组有限的傅里叶谐波作为一系列采样探针，用于封装特定角度区域上功率谱的积分。该技术有效消除了因使用离散角度域探针导致的功率失配所引起的功率泄漏。随后，信道估计问题被重新表述为在连续积分区域上对显著角度功率谱的稀疏恢复。我们进一步提出了一种基于图割的交换扩展（GCSE）算法，以提取HMIMO信道中固有的有益稀疏性。数值结果表明，这种基于波数域的GCSE方法能够快速收敛并实现稳健的性能。