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Based on the non line-of-sight (NLOS) indoor measurements performed in the corridors on the third floor of the Electronics and Telecommunications Research Institute (ETRI) building in Daejeon city, Republic of Korea, we investigated the distribution of the eigenvalues of HH*, where H denotes a 2×2 multiple-input multiple-output (MIMO) channel matrix. Using the observation that the distribution of the measured eigenvalues matches well with the Gamma distribution, we propose a model of eigenvalues as Gamma distributed random variables that prominently feature both transmitting and receiving correlations. Using the model with positive integer k_i, i=1, 2, which is the shape parameter of a Gamma distribution, we derive the closed-form ergodic capacity of the 2×2 MIMO channel. Validation results show that the proposed model enables the evaluation of the outage and ergodic capacities of the correlated 2×2 MIMO channel in the NLOS indoor corridor environment.