Machine Learning Methods for RSS-Based User Positioning in Distributed Massive MIMO

Abstract

We propose a supervised machine learning (ML) approach based on Gaussian process (GP) regression to position users in a distributed massive multiple-input multiple-output (DM-MIMO) system from their uplink received signal strength (RSS). The proposed approach serves as a proof-of-concept that we can localize users by training an ML model with noise-free RSS and using the trained model to estimate the test user locations from their noisy RSS. We consider two GP methods for localization, namely, the conventional GP (CGP) and the numerical approximation GP (NaGP). We find that the CGP provides unrealistically small $2\sigma $ error-bars on the location estimates. Therefore, we derive the true predictive distribution and employ NaGP to obtain realistic $2\sigma $ error-bars on the location estimates. Next, we derive a Bayesian Cramer–Rao lower bound (BCRLB) on the root-mean-squared-error (RMSE) performance of the two GP methods. Numerical studies reveal that: 1) the NaGP indeed provides realistic $2\sigma $ error-bars on the estimated locations; 2) both the CGP and NaGP achieve RMSEs that are close to the BCRLBs; 3) the presence of correlated shadowing improves the RMSE performance; and 4) extrapolation to the zero input noise scenario can significantly improve the RMSE achieved by the NaGP.