Power Minimizer Symbol-Level Precoding: A Closed-Form Sub-Optimal Solution

Abstract

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. Index TermsConstructive interference, downlink multiuser MISO, power minimization in symbol-level precoding.

Boosting SWIPT via Symbol-Level Precoding

“…where Γ and Ξ are the corresponding SINR and EH demands, as represented in (4) and (5), respectively. In the case ofĤ = H, the SINRs of the received symbols are linearly related to Γ and the EH demand metrics are linearly related to Ξ:…”

An Approximate Solution for Symbol-Level Multiuser Precoding Using Support Recovery

“…On the other hand, the dominant arithmetic operations in (10), (11) and (12), i.e., 2K vector multiplications and two matrix pseudo-inversions, result in computation costs of order KN and N (L 2 1 + L 2 2 ), respectively, for the proposed method. Remark that the closed-form solution in [13] can be implemented in an equivalent way using (10) and (12); therefore we assess the complexity of [13] based on the method of this paper.…”

M-QAM Modulation Symbol-Level Precoding for Power Minimization: Closed-Form Solution

“…To derive the closed-form algorithm to solve the optimization problem (11), we firstly address only the constraint C1 of the problem and then expand the approach to deal with the constraints C1, C2, C3 and C4 jointly. The optimization problem (11) with the constraint C1 has a form of a nonnegative least squares (NNLS) problem. It can be solved using iterative Fast NNLS algorithm [18], [19].…”