A quasi-static flat multiple-antenna channel is considered. We show how real multilevel modulation symbols can be detected via deep neural networks. A multi-plateau sigmoid function is introduced. Then, after showing the DNN architecture for detection, we propose a twin-network neural structure. Batch size and training statistics for efficient learning are investigated. Near-Maximum-Likelihood performance with a relatively reasonable number of parameters is achieved.

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Point lattices and their decoding via neural networks are considered in this paper. Lattice decoding in R n , known as the closest vector problem (CVP), becomes a classification problem in the fundamental parallelotope with a piecewise linear function defining the boundary. Theoretical results are obtained by studying root lattices. We show how the number of pieces in the boundary function reduces dramatically with folding, from exponential to linear. This translates into a two-layer ReLU network requiring a number of neurons growing exponentially in n to solve the CVP, whereas this complexity becomes polynomial in n for a deep ReLU network.

We consider the positioning problem in non line-ofsight (NLoS) situations, where several base stations (BS) try to locate a user equipment (UE) based on uplink angle of arrival (AoA) measurements and a digital twin of the environment. Ray launching in a Monte Carlo manner according to the AoA statistics enables to produce a map of points for each BS. These points represent the intersections of the rays with a xy plane at a given user equipment (UE) elevation. We propose to fit a parametric probability density function (pdf), such as a Gaussian mixture model (GMM), to each map of points. Multiplying the obtained pdfs for each BS enables to compute the position probability of the UE. This approach yields an algorithm robust to a reduced number of launched rays. Moreover, these parametric pdfs may be fitted and stored in an offline phase such that ray tracing can be avoided in the online phase. This significantly reduces the computational complexity of the positioning method.

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