  We introduce a framework for linear precoder design over a massive
multiple-input multiple-output downlink system in the presence of nonlinear
power amplifiers (PAs). By studying the spatial characteristics of the
distortion, we demonstrate that conventional linear precoding techniques steer
nonlinear distortions towards the users. We show that, by taking into account
PA nonlinearity, one can design linear precoders that reduce, and in
single-user scenarios, even completely remove the distortion transmitted in the
direction of the users. This, however, is achieved at the price of a reduced
array gain. To address this issue, we present precoder optimization algorithms
that simultaneously take into account the effects of array gain, distortion,
multiuser interference, and receiver noise. Specifically, we derive an
expression for the achievable sum rate and propose an iterative algorithm that
attempts to find the precoding matrix which maximizes this expression.
Moreover, using a model for PA power consumption, we propose an algorithm that
attempts to find the precoding matrix that minimizes the consumed power for a
given minimum achievable sum rate. Our numerical results demonstrate that the
proposed distortion-aware precoding techniques provide significant improvements
in spectral and energy efficiency compared to conventional linear precoders.
