Wavenumber Domain Sparse Channel Estimation in Holographic MIMO

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.