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

We propose a machine learning approach, based on analytical inference in Gaussian process regression (GP), to locate users from their uplink received signal strength (RSS) data in a distributed massive multiple-input-multiple-output setup. The training RSS data is considered noise-free, while the test RSS data is assumed to be noisy due to shadowing effects of the wireless channel. We first apply an analytical moment matching-based GP method, namely, the Gaussian approximation GP (GaGP), and make the necessary extensions to suit the problem under study. The GaGP method learns from the stochastic nature of the test RSS data to provide more realistic 2\sigma error-bars on the estimated locations than the conventional GP (CGP) method. Despite the improvement in 2\sigma error-bars, simulation studies reveal that the GaGP method achieves similar root-mean-squared estimation error (RMSE) performance as the CGP method. To address this concern, we propose a new GP method, namely the reconstruction-cum-Gaussian-approximation GP (RecGaGP) method. RecGaGP not only achieves lower RMSE values than the CGP and GaGP methods, but also provides realistic 2\sigma error-bars on the estimated locations. This ability is achieved by first reconstructing the test RSS from a low-dimensional principal subspace of the noise-free training RSS and then learning from the statistical properties of the residual noise present. For both the GaGP and RecGaGP methods, closed-form expressions are derived for the estimated user locations and the associated 2\sigma error-bars. Numerical studies reveal that the GaGP and RecGaGP methods indeed provide realistic 2\sigma error-bars on the estimated user locations and their RMSE performances are very close to the Cramer-Rao lower bounds. Also, their RMSE performances saturate beyond a certain point when the number of BS antennas and/or the number of training locations are increased.