Linear Precoding Based on Truncated Polynomial Expansion - Part I: Large-Scale Single-Cell Systems

Large-scale multi-user multiple-input multipleoutput (MIMO) techniques have the potential to bring tremendous improvements for future communication systems. Counterintuitively, the practical issues of having uncertain channel knowledge, high propagation losses, and implementing optimal non-linear precoding are solved more-or-less automatically by enlarging system dimensions. The computational precoding complexity will, however, still grow with the system dimensions. For example, the close-to-optimal regularized zero-forcing (RZF) precoding scheme cannot be applied in large-scale MIMO systems, because its computation involves the inversion of a large matrix. Motivated by the high performance of RZF, we propose to replace the matrix inversion by a truncated polynomial expansion (TPE), thereby obtaining a TPE precoding scheme with greatly reduced computational complexity. The degree of the matrix polynomial can be adapted to the available hardware resources and enables smooth transition between simple maximum ratio transmission (MRT) and more advanced RZF. Using random matrix theory, we derive a deterministic expression for the asymptotic signal-to-interference-and-noise ratio (SINR) achieved by TPE precoding in large-scale MIMO systems. Furthermore, we provide a closed-form expression for the polynomial coefficients that maximizes this SINR. To maintain a fixed per-user rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signal-to-noise ratio (SNR).