Generalized Approximate Message Passing Based Bayesian Learning Detectors for Uplink Grant-Free NOMA

Abstract

The existing sparse Bayesian learning (SBL) and pattern coupled sparse Bayesian learning (PCSBL) multiuser detection (MUD) algorithms for grant-free non-orthogonal multiple access (GF-NOMA) have high computational complexity, i.e. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(N{K^{2}})$</tex-math></inline-formula> , considering mainly the calculation of posterior distribution of the transmitted signals. In this paper, we embed generalized approximate message passing (GAMP) to SBL and PCSBL, and develop two efficient Bayesian learning algorithms for GF-NOMA systems, that is, generalized approximate message passing sparse Bayesian learning (GAMP-SBL) and generalized approximate message passing pattern coupled sparse Bayesian learning (GAMP-PCSBL). It is shown that the Bayesian algorithms can significantly reduce the computational complexity from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(N{K^{2}})$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(NK)$</tex-math></inline-formula> . Simulation results show that these two low complexity detectors still have superior recovery performance than the conventional MUD methods, and nearly have the same performance compared with SBL and PCSBL.