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An asymptotic approach to derive the ergodic capacity achieving covariance matrix for a multiple-input multiple-output (MIMO) channel is presented. The method is applicable to MIMO channels affected by separately correlated Rician fading and co-channel interference. It is assumed that the number of transmit, receive and interfering antennas grows asymptotically while their ratios, as well as the SNR and the SIR, approach finite constants. Nevertheless, it is shown that the asymptotic results represent an accurate approximation in the case of a finitely many antennas and can be used to derive the ergodic channel capacity. This is accomplished by using an iterative power allocation algorithm based on a water-filling approach. The convergence of a similar algorithm (nicknamed frozen water-filling) was conjectured in a work by Dumont Here, we show that, in the Rayleigh case, the frozen water-filling algorithm may not converge while, in those cases, our proposed algorithm converges. Finally, numerical results are included in order to assess the accuracy of the asymptotic method proposed, which is compared to equivalent results obtained via Monte-Carlo simulations.