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