Stochastic Gradient Langevin Dynamics for Massive MIMO Detection

Abstract

In this letter a MIMO detector with low computational complexity is proposed based on Stochastic Gradient Langevin Dynamics (SGLD). The proposed detector estimates the modulated symbols through a non-convex optimization problem which is solved by SGLD based algorithm. For <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary phase-shift keying ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -PSK) modulation, the proposed algorithm achieves the performance similar to sphere decoding (SD) in medium-scale MIMO systems, and can be scaled up to massive MIMO systems. Numerical results verify the advantages of the proposed algorithm compared to various existing MIMO detectors. The simulations under the imperfect correlated channel also show the tolerance of the proposed algorithm on channel errors and channel correlations.