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Large array systems use a massive number of antenna elements and clever precoder designs to achieve an array gain at the user location. These precoders require linear front-ends, and more specifically linear power amplifiers (PAs), to avoid distortion. This reduces the energy efficiency since PAs are most efficient close to saturation, where they generate most nonlinear distortion. Moreover, the use of conventional precoders can induce a coherent combining of distortion at the user locations, degrading the signal quality. In this work, novel linear precoders, simple to compute and to implement, are proposed that allow working close to saturation, while cancelling the third-order nonlinearity of the PA without prior knowledge of the signal statistics and PA model. Their design consists in saturating a single or a few antennas on purpose together with an negative gain with respect to all other antennas to compensate for the overall nonlinear distortion at the user location. The performance gains of the designs are significant for PAs working close to saturation, as compared to maximum ratio transmission (MRT) precoding and perfect per-antenna digital pre-distortion (DPD) compensation.