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As we know, the degree of freedom approximates the capacity of a network. To improve the achievable degree of freedom in the K-user interference network, we propose a rank minimization interference minimization algorithm. Unlike the existing methods concentrating on the promotion of degree of freedom, our rank optimization method works directly with the interference matrix rather than its projection using the receive beamformers. Moreover, we put the trace constraint of the square root of desired matrix into the rank optimization to prevent the received signal-to-interference-plus-noise ratio from reduction. The decoders are designed through a weight interference leakage minimization method. Considering that the practical obtainable signal-to-noise ratio may be limited, we improve the design of decoders in rank minimization interference minimization, and propose the rank minimization rate maximization. Rank minimization rate maximization aims to reduce the impact of interference on undesired users as much as possible while improving the desired data rate. Simulation results show that rank minimization interference minimization algorithm can provide more interference-free dimensions for desired signals than other rank minimization methods. Rank minimization rate maximization outperforms rank minimization interference minimization at low-to-moderate signal-to-noise ratios, and its performance gets closer to rank minimization interference minimization with the increase in signal-to-noise ratio. Furthermore, in an improper system, rank minimization rate maximization still performs well.

Spatial–degree of freedom improvement of interference alignment in multi-input, multi-output interference channels