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In a communication network, it is often impractical for each node to learn the global channel knowledge (network connectivity and channel state information of each link). In this paper, we address distributed rate optimization for Time-Division Duplex (TDD) Multiple-Input Multiple-Output (MIMO) networks when part of the local channel knowledge is learned via message passing between each transmitter and its intended receivers. The distributed optimization algorithm is based on a rate duality and the corresponding input covariance matrix transformation between the forward and reverse links of TDD MIMO networks under the assumption of global channel knowledge. Noting that the key information required by the proposed transformation is the interference-plus-noise covariance matrix, we propose a local covariance matrix transformation such that each node can distributedly optimize its input covariance matrix by only exchanging interference-plus-noise covariance matrix locally. It is observed from the simulation that the proposed algorithm achieves a performance close to the one with global channel knowledge and outperforms the existing distributed algorithms.