  In this letter, we study the optimal solution of the multiuser symbol-level
precoding (SLP) for minimization of the total transmit power under given
signal-to-interference-plus-noise ratio (SINR) 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 (KKT) optimality conditions,
thereby we obtain the necessary and sufficient condition under which the power
minimizer SLP is equivalent to the conventional zero-forcing beamforming
(ZFBF). This further leads us to a closed-form sub-optimal SLP solution
(CF-SLP) for the original problem. 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 $10^3$ in computational time
compared to the optimal solution.
