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Distributed sum-rate-maximizing covariance matrices design for full-duplex multi-input multi-output communication is considered, where the information of the loopback interference channels cannot be exchanged reliably due to their large dynamic ranges. We propose a structured covariance matrices design which finds the optimal balance between the two solutions in the extremes of the weak and strong self-interference through a single-parameter optimization. We further propose a low-complexity null projection matrix design algorithm, in which the solution in the strong self-interference regime is designed in the sense to maximize the received channel gain. Exploiting the well-posed structure, the proposed scheme nearly achieves the sum-rate of the previous scheme based on the gradient projection with significantly less amount of inter-node iterations, yielding an increased effective sum-rate and reduced overall complexity for the practial channel block lengths.