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Vector Perturbation Precoding (VPP) can speed up downlink data transmissionsin Large and Massive Multi-User MIMO systems but is known to be NP-hard. Whilethere are several algorithms in the literature for VPP under total powerconstraint, they are not applicable for VPP under per-antenna power constraint.This paper proposes a novel, parallel tree search algorithm for VPP underper-antenna power constraint, called \emph{\textbf{TreeStep}}, to find goodquality solutions to the VPP problem with practical computational complexity.We show that our method can provide huge performance gain over simple linearprecoding like Regularised Zero Forcing. We evaluate TreeStep for several largeMIMO~($16\times16$ and $24\times24$) and massive MIMO~($16\times32$ and$24\times 48$) and demonstrate that TreeStep outperforms the popularpolynomial-time VPP algorithm, the Fixed Complexity Sphere Encoder, byachieving the extremely low BER of $10^{-6}$ at a much lower SNR.

TreeStep: Tree Search for Vector Perturbation Precoding under per-Antenna Power Constraint