This paper investigates the spectral efficiency (SE) of multi-user holographic MIMO (HMIMO) uplink transmission. The authors propose a channel model based on electromagnetic field equations and a colored noise model that accounts for both electromagnetic interference and hardware noise. The continuous channel model is approximated using Fourier space series, enabling the representation of the channel in a finite-dimensional space. This allows for the optimization of the continuous current density function (CDF) for each user to maximize SE. The authors introduce an iterative water-filling algorithm to solve the optimization problem, which is validated through simulations. The results show that the proposed algorithm effectively enhances SE and highlights the impact of colored noise and system parameters on SE. The paper also discusses the challenges of modeling HMIMO systems, including the need for accurate channel models and the effects of array size, propagation distance, and wave frequency on SE. The authors emphasize the importance of considering the continuous nature of HMIMO arrays and the role of electromagnetic information theory in optimizing transmission. The study contributes to the understanding of HMIMO systems and provides a framework for optimizing SE in multi-user HMIMO uplink transmission.This paper investigates the spectral efficiency (SE) of multi-user holographic MIMO (HMIMO) uplink transmission. The authors propose a channel model based on electromagnetic field equations and a colored noise model that accounts for both electromagnetic interference and hardware noise. The continuous channel model is approximated using Fourier space series, enabling the representation of the channel in a finite-dimensional space. This allows for the optimization of the continuous current density function (CDF) for each user to maximize SE. The authors introduce an iterative water-filling algorithm to solve the optimization problem, which is validated through simulations. The results show that the proposed algorithm effectively enhances SE and highlights the impact of colored noise and system parameters on SE. The paper also discusses the challenges of modeling HMIMO systems, including the need for accurate channel models and the effects of array size, propagation distance, and wave frequency on SE. The authors emphasize the importance of considering the continuous nature of HMIMO arrays and the role of electromagnetic information theory in optimizing transmission. The study contributes to the understanding of HMIMO systems and provides a framework for optimizing SE in multi-user HMIMO uplink transmission.