The paper explores the spectral efficiency (SE) of multi-user holographic MIMO (HMIMO) uplink transmission, where both the base station and users are equipped with holographic planar arrays. The authors construct an HMIMO channel model using electromagnetic field equations and incorporate colored noise to account for electromagnetic interference and hardware noise. To simplify the continuous model, they approximate it within a finite-dimensional space using Fourier series, which maps high-dimensional physical quantities to a finite-dimensional space. They analyze the channel model's characteristics, demonstrating that degrees of freedom in HMIMO systems are inversely related to propagation distance but directly related to the size of the transmitting array. The paper formulates the problem of maximizing SE in a multi-user HMIMO uplink transmission system and proposes an iterative water-filling algorithm to solve it. Simulation results validate the algorithm's effectiveness and show the impact of colored noise and system parameters on SE.The paper explores the spectral efficiency (SE) of multi-user holographic MIMO (HMIMO) uplink transmission, where both the base station and users are equipped with holographic planar arrays. The authors construct an HMIMO channel model using electromagnetic field equations and incorporate colored noise to account for electromagnetic interference and hardware noise. To simplify the continuous model, they approximate it within a finite-dimensional space using Fourier series, which maps high-dimensional physical quantities to a finite-dimensional space. They analyze the channel model's characteristics, demonstrating that degrees of freedom in HMIMO systems are inversely related to propagation distance but directly related to the size of the transmitting array. The paper formulates the problem of maximizing SE in a multi-user HMIMO uplink transmission system and proposes an iterative water-filling algorithm to solve it. Simulation results validate the algorithm's effectiveness and show the impact of colored noise and system parameters on SE.