In ultra-dense network with high-throughput applications, users arrive and depart the network randomly, and the inter-cell interference is severe and changes dramatically. To capture the essence of the problem, a network named two-plus-one network is considered, where a third new user is added into a two-user network. The distributed precoding is studied, where the precoding matrix of the third new user is designed and those of the two old users remain unchanged. Using the geometric interpretation of the covariance matrices, we find the principle on how precoding matrices affect the rate of the desired user and the interfered users. Based on the principle, we propose a criterion for precoding design and formulate an optimization problem. Then we solve this problem, and provide a geometric explanation of the optimization result, i.e., how to choose precoding directions and allocate power to the directions under certain constraints. Simulation results indicate that the proposed method achieves almost the same performance as that obtained from Weighted Minimum Mean Square Error criterion but with low complexity, and outperforms Maximum Signal-to-Leakage-plus-Noise Ratio and Block-Diagonal Zero-Forcing under certain circumstances.
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