  In massive multiple-input multiple-output (MIMO) downlink systems, the
physical implementation of the base stations (BSs) requires the use of cheap
and power-efficient power amplifiers (PAs) to avoid high hardware cost and high
power consumption. However, such PAs usually have limited linear amplification
ranges. Nonlinear distortions arising from operation beyond the linear
amplification ranges can significantly degrade system performance. Existing
approaches to handle the nonlinear distortions, such as digital predistortion
(DPD), typically require accurate knowledge, or acquisition, of the PA transfer
function. In this paper, we present a new concept for mitigation of the PA
distortions. Assuming a uniform linear array (ULA) at the BS, the idea is to
apply a Sigma-Delta ($\Sigma \Delta$) modulator to spatially shape the PA
distortions to the high-angle region. By having the system operating in the
low-angle region, the received signals are less affected by the PA distortions.
To demonstrate the potential of this spatial $\Sigma \Delta$ approach, we study
the application of our approach to the multi-user MIMO-orthogonal frequency
division modulation (OFDM) downlink scenario. A symbol-level precoding (SLP)
scheme and a zero-forcing (ZF) precoding scheme, with the new design
requirement by the spatial $\Sigma \Delta$ approach being taken into account,
are developed. Numerical simulations are performed to show the effectiveness of
the developed $\Sigma \Delta$ precoding schemes.
