Power Minimizer Symbol-Level Precoding: A Closed-Form Suboptimal Solution

In this letter, we study the optimal solution of multiuser symbol-level precoding (SLP) for minimization of the total transmit power under given signal-to-interference-plus-noise ratio constraints. Adopting the distance preserving constructive interference regions (DPCIR), we first derive a simplified reformulation of the problem. Then, we analyze the structure of the optimal solution using the Karush–Kuhn–Tucker optimality conditions. This leads us to obtain a closed-form suboptimal SLP solution (CF-SLP) for the original problem. Meanwhile, we obtain the necessary and sufficient condition under which the power minimizer SLP is equivalent to the conventional zero-forcing beamforming (ZFBF). Simulation results show that CF-SLP provides significant gains over ZFBF, while performing quite close to the optimal SLP in scenarios with rather small number of users. The results further indicate that the CF-SLP method has a reduction of order
$\mathbf {10^3}$
in computational time compared to the optimal solution.