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In this paper, we propose closed-form precoding schemes with optimalperformance for constructive interference (CI) exploitation in the multiusermultiple-input single-output (MU-MISO) downlink. We first consider anoptimization where we maximize the distance between the constructive region andthe detection thresholds. The cases of both strict and non-strict phaserotation are considered and can further be formulated as convex optimizationproblems. For optimization with strict phase rotation, we mathematically derivethe optimal beamforming structure with Lagrangian and Karush-Kuhn-Tucker (KKT)conditions. By formulating its dual problem, the optimization problem isfurther shown to be equivalent to a quadratic programming (QP) over a simplex,which can be solved more efficiently. We then extend our analysis to the caseof non-strict phase rotation, where it is mathematically shown that aK-dimensional optimization for non-strict phase rotation is equivalent to a2K-dimensional optimization for strict phase rotation in terms of the problemformulation. The connection with the conventional zero-forcing (ZF) precodingis also discussed. Based on the above analysis, we further propose an iterativeclosed-form scheme to obtain the optimal beamforming matrix, where within eachiteration a closed-form solution can be obtained. Numerical results validateour analysis and the optimality of the proposed iterative scheme, and furthershow that the proposed closed-form scheme is more efficient than theconventional QP algorithms with interior-point methods, which motivates the useof CI beamforming in practical wireless systems.

Interference Exploitation Precoding Made Practical: Closed-Form Solutions with Optimal Performance