Optimization of Massive Full-Dimensional MIMO for Positioning and Communication

Massive Full-Dimensional multiple-input multiple-output (FD-MIMO) base stations (BSs) have the potential to bring multiplexing and coverage gains by means of three-dimensional (3D) beamforming. Key technical challenges for their deployment include the presence of limited-resolution front ends and the acquisition of channel state information (CSI) at the BSs. This paper investigates the use of FD-MIMO BSs to provide simultaneously high-rate data communication and mobile 3D positioning in the downlink. The analysis concentrates on the problem of beamforming design by accounting for imperfect CSI acquisition via Time Division Duplex (TDD)-based training and for the finite resolution of analog-to-digital converter (ADC) and digital-to-analog converter (DAC) at the BSs. Both \textit{unstructured beamforming} and a low-complexity \textit{Kronecker beamforming} solution are considered, where for the latter the beamforming vectors are decomposed into separate azimuth and elevation components. The proposed algorithmic solutions are based on Bussgang theorem, rank-relaxation and successive convex approximation (SCA) methods. Comprehensive numerical results demonstrate that the proposed schemes can effectively cater to both data communication and positioning services, providing only minor performance degradations as compared to the more conventional cases in which either function is implemented. Moreover, the proposed low-complexity Kronecker beamforming solutions are seen to guarantee a limited performance loss in the presence of a large number of BS antennas.Comment: 30 pages, 6 figure

Statistical Inference for Generative Models with Maximum Mean Discrepancy

While likelihood-based inference and its variants provide a statistically efficient and widely applicable approach to parametric inference, their application to models involving intractable likelihoods poses challenges. In this work, we study a class of minimum distance estimators for intractable generative models, that is, statistical models for which the likelihood is intractable, but simulation is cheap. The distance considered, maximum mean discrepancy (MMD), is defined through the embedding of probability measures into a reproducing kernel Hilbert space. We study the theoretical properties of these estimators, showing that they are consistent, asymptotically normal and robust to model misspecification. A main advantage of these estimators is the flexibility offered by the choice of kernel, which can be used to trade-off statistical efficiency and robustness. On the algorithmic side, we study the geometry induced by MMD on the parameter space and use this to introduce a novel natural gradient descent-like algorithm for efficient implementation of these estimators. We illustrate the relevance of our theoretical results on several classes of models including a discrete-time latent Markov process and two multivariate stochastic differential equation models