On Optimal Precoding for MISO with Nonlinear Power Amplifiers

Optimal precoding for multiple-input single-output (MISO) systems with nonlinear power amplifiers (PAs) is proposed. The idea behind the precoding is to generate a set of transmitted signals s.t., after passing through the nonlinear PAs and MISO channel, a desired signal will be obtained at the receiver's antenna. The channel is assumed to be frequency selective. It is assumed that the channel and noise power are known at the transmitter (TX). The specific aim of the proposed precoding is to maximize signal-to-interference and noise ratio (SINR) per symbol at the receiver. The proposed technique can be seen as a generalization of the constant envelope (CE) precoding approach, based on the same concepts. However, in this work we assume a general PA nonlinearity and, therefore, the TX signals may have varying amplitude. Moreover, while in the CE only the nonlinear distortions (interference), seen at the receiver, are minimized, we propose to maximize the SINR. This approach shows better symbol error rate (SER) performance than CE precoding. For given SER requirement, the PSNR gap is clearly seen for a low number of TX antennas, although, as the number of TX antennas increases the PSNR gap decreases.