Performance Bounds for Near-Field Multi-Antenna Range Estimation of Extended Targets

In this paper, performance bounds for the multi-antenna near-field range estimation of extended targets are provided. First, analytic expressions of the ambiguity functions are obtained, emphasising the cooperation between the waveform delay and the near-field phase shift information. The impact of estimating the range of an extended target with a point target model is analysed, showing that a model mismatch leads to severe performance degradation in the near-field region. Secondly, Cramer-Rao bounds are derived. Expressions emphasising the parameters' impact are obtained, the parameters being the carrier frequency, and the central frequency and root-mean-square bandwidth of the waveform. The near-field range information is shown to depend on the root-mean-square value of the propagation delay derivatives, this value scaling with the fourth power of the ratio between the antenna array dimension and the target range.

Near-Field EM-Based Multistatic Radar Range Estimation

Radar targets are traditionally modelled as point target reflectors, even in the near-field region. Yet, for radar systems operating at high carrier frequencies and small distances, traditional radar propagation models do not accurately model the scatterer responses. In this paper, a novel electromagnetic-based model is thus developed for the multistatic radar detection of a rectangular plate reflector in the near-field region. This model is applied to an automotive scenario, in which a linear antenna array is spread out at the front of a vehicle, and performs a radar measurement of the distance to the back of the vehicle ahead. Based on the developed received signal model, the maximum likelihood estimator of the range is designed. By exploiting the near-field target model, this estimator is shown to provide a significant gain with respect to traditional range estimators. The impact of the system and scenario parameters, i.e. the carrier frequency, bandwidth and distance to the target, is furthermore evaluated. This analysis shows that the radar resolution in the near-field regime is improved at high carrier frequencies, while saturating to the traditional bandwidth-dependent resolution in the far-field region.

Cellular Load Dependent Sleep Control for Energy Efficient HetNets with Non-Uniform User Distributions

This study proposes a novel stochastic geometry framework analyzing power control strategies in spatially correlated network topologies. Heterogeneous networks are studied, with users modeled via the superposition of homogeneous and Poisson cluster processes. First, a new expression approaching the distribution of the number of users per base station is provided. This distribution defines the load associated with each Vorono\"i cell, capturing non-uniformities in user locations and correlation to BSs positions. The power allocation is adjusted based on this load, allowing BSs to enter sleep mode when their activity falls below a defined threshold. Furthermore, the propagation model features millimeter wave transmission characteristics and directional beamforming. Considering these aspects, revisited definitions of coverage probability, spectral efficiency, and energy efficiency are proposed. Tractable expressions for these metrics are derived and validated using Monte-Carlo simulations. Asymptotic expressions are also proposed, providing further understanding on the influence of the system parameters. Our numerical results finally analyze the impact of the sleep control on the performance and display the optimal strategies in terms of energy efficiency.

Fully Differentiable Ray Tracing via Discontinuity Smoothing for Radio Network Optimization

Recently, Differentiable Ray Tracing has been successfully applied in the field of wireless communications for learning radio materials or optimizing the transmitter orientation. However, in the frame of gradient based optimization, obstruction of the rays by objects can cause sudden variations in the related objective functions or create entire regions where the gradient is zero. As these issues can dramatically impact convergence, this paper presents a novel Ray Tracing framework that is fully differentiable with respect to any scene parameter, but also provides a loss function continuous everywhere, thanks to specific local smoothing techniques. Previously non-continuous functions are replaced by a smoothing function, that can be exchanged with any function having similar properties. This function is also configurable via a parameter that determines how smooth the approximation should be. The present method is applied on a basic one-transmitter-multi-receiver scenario, and shows that it can successfully find the optimal solution. As a complementary resource, a 2D Python library, DiffeRT2d, is provided in Open Access, with examples and a comprehensive documentation.

Novel Electromagnetism-Based Radar Propagation Model for 5G and Beyond

In order to evaluate the performance of radar and communication systems in future wireless networks, accurate propagation models are needed to predict efficiently the received powers at each node, and draw correct conclusions. In this paper, we present new radar propagation models based on the electromagnetism theory. The target is modelled as a flat or curved square plate to compute the scattered field and derive accurate radar cross section modellings. With a flat square plate, the model makes the link between the radar equation and the geometrical optics propagation model used in ray-tracing applications. It is then applied to popular automotive scenarios within the stochastic geometry framework to observe the impact of such modelling.

Joint data rate and EMF exposure analysis in user-centric cell-free massive MIMO networks

The objective of this study is to analyze the statistics of the data rate and of the incident power density (IPD) in user-centric cell-free networks (UCCFNs). To this purpose, our analysis proposes a number of performance metrics derived using stochastic geometry (SG). On the one hand, the first moments and the marginal distribution of the IPD are calculated. On the other hand, bounds on the joint distributions of rate and IPD are provided for two scenarios: when it is relevant to obtain IPD values above a given threshold (for energy harvesting purposes), and when these values should instead remain below the threshold (for public health reasons). In addition to deriving these metrics, this work incorporates features related to UCCFNs which are new in SG models: a power allocation based on collective channel statistics, as well as the presence of potential overlaps between adjacent clusters. Our numerical results illustrate the achievable trade-offs between the rate and IPD performance. For the considered system, these results also highlight the existence of an optimal node density maximizing the joint distributions. (This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.)

Joint data rate and EMF exposure analysis in Manhattan environments: stochastic geometry and ray tracing approaches

The objective of this study is to jointly analyze the data rate and electromagnetic field (EMF) exposure in urban environments. Capitalizing on stochastic geometry (SG), a network level analysis is performed by modelling these environments via Manhattan Poisson line processes (MPLP). Using this framework, a number of performance metrics are derived: first moments, marginal distributions and joint distributions of the data rate and exposure. In addition, the original Manhattan model is generalized to include advanced features: corner diffraction, presence of potential blockages in streets, and users positioned at crossroads. As a second approach, deterministic ray tracing (RT) is utilized to compute the same metrics. The two methods are shown to provide close results on the condition that the model parameters are coherently selected. Furthermore, the numerical results enable to gain insight into several aspects: the role of the propagation mechanisms in the performance metrics, existing trade-offs between the rate and exposure requirements, as well as the impact of the user location (at a crossroad or in a single street). (This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible)

Min-Path-Tracing: A Diffraction Aware Alternative to Image Method in Ray Tracing

For more than twenty years, Ray Tracing methods have continued to improve on both accuracy and computational time aspects. However, most state-of-the-art image-based ray tracers still rely on a description of the environment that only contains planar surfaces. They are also limited by the number of diffractions they can simulate. We present Min-Path-Tracing (MPT), an alternative to the image method that can handle diffractions seamlessly, while also leveraging the possibility to use different geometries for surfaces or edges, such as parabolic mirrors. MPT uses implicit representations of objects to write the path finding challenge as a minimization problem. We further show that multiple diffractions can be important in some situations, which MPT is capable to simulate without increasing neither the computational nor the implementation complexity.