Nonlinear MIMO Communication With π-Periodic Phase Measurements

Abstract

This paper proposes a nonlinear MIMO scheme named as halved-phase only MIMO (HPO-MIMO), whose base station (BS) is equipped with multiple HPO radio-frequency (RF) chains extracting <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula> -periodic phase measurements from RF signals directly by phase detectors, and single classical RF chain sampling the combination of all the RF signals from HPO-RF chains. Compared to MIMO, HPO-RF receivers are simplified significantly, and have much lower power consumption and fabrication cost. Two types of channel estimators and multiuser detectors are developed for HPO-MIMO from the perspectives of numerical optimization and Bayesian inference. Firstly, because <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula> -periodic phases provide tan-relationships between the Inphase (I) and Quadrature (Q) components, the channel estimation (CE) and multiuser detection (MUD) problems are resolved by minimizing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{2}$ </tex-math></inline-formula> -norm cost functions with unit-norm constraint on the recovered vector. Their solutions are obtained by deriving the eigenvector corresponding to the minimum eigenvalue through shifted power method (SPW). Secondly, the CE and MUD problems are categorized as generalized linear mixing problems under (un-)quantized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula> -periodic phase measurements, and then handled by generalized approximate message passing (GAMP), where closed-form solutions for mean-and-variance messages involving <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula> -periodic phases are derived. Finally, magnitude and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula> -phase ambiguities persisting in signal recovery are removed based on the complex-valued full measurements from the single classical RF chain. Simulation results show that GAMP-type algorithms outperform SPW-type ones, and handle nonlinear phase quantization losses. 16-sector quantized HPO-MIMO could work as well as its un-quantized correspondence. HPO-MIMO reserves the MIMO advantages, but is more energy-efficient than the latter.