Stochastic Geometry Analysis of a New GSCM with Dual Visibility Regions

The geometry-based stochastic channel models (GSCM), which can describe realistic channel impulse responses, often rely on the existence of both {\em local} and {\em far} scatterers. However, their visibility from both the base station (BS) and mobile station (MS) depends on their relative heights and positions. For example, the condition of visibility of a scatterer from the perspective of a BS is different from that of an MS and depends on the height of the scatterer. To capture this, we propose a novel GSCM where each scatterer has dual disk visibility regions (VRs) centered on itself for both BS and MS, with their radii being our model parameters. Our model consists of {\em short} and {\em tall} scatterers, which are both modeled using independent inhomogeneous Poisson point processes (IPPPs) having distinct dual VRs. We also introduce a probability parameter to account for the varying visibility of tall scatterers from different MSs, effectively emulating their noncontiguous VRs. Using stochastic geometry, we derive the probability mass function (PMF) of the number of multipath components (MPCs), the marginal and joint distance distributions for an active scatterer, the mean time of arrival (ToA), and the mean received power through non-line-of-sight (NLoS) paths for our proposed model. By selecting appropriate model parameters, the propagation characteristics of our GSCM are demonstrated to closely emulate those of the COST-259 model.

Novel LoS $β-γ$ THz Channel Unifying Molecular Re-radiation Manifestations

This paper introduces a novel line-of-sight (LoS) $\beta-\gamma$ terahertz (THz) channel model that closely mirrors physical reality by considering radiation trapping. Our channel model provides an exhaustive modeling of the physical phenomena including the amount of re-radiation available at the receiver, parametrized by $\beta$, and the balance between scattering and noise contributions, parametrized by $\gamma$, respectively. Our findings indicate a nontrivial relationship between average limiting received signal-to-noise ratio (SNR) and distance emphasizing the significance of $\gamma$ in THz system design. We further propose new maximum likelihood (ML) thresholds for pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) schemes, resulting in analytical symbol error rate (SER) expressions that account for different noise variances across constellation points. The results confirm that the analytical SER closely matches the true simulated SER when using an optimal detector. As expected, under maximum molecular re-radiation, the true SER is shown to be lower than that produced by a suboptimal detector that assumes equal noise variances.

RIS-Aided Kinematic Analysis for Remote Rehabilitation

This paper is the first to introduce the idea of using reconfigurable intelligent surfaces (RISs) as passive devices that measure the position and orientation of certain human body parts over time. In this paper, we investigate the possibility of utilizing the available geometric information provided by on-body RISs that reflect signals from an off-body transmitter to an off-body receiver for stroke rehabilitation. More specifically, we investigate the possibility of using on-body RISs to estimate the location information over time of upper limbs that may have been impaired due to stroke. This location information can help medical professionals to estimate the possibly time varying pose and obtain progress on the rehabilitation of the upper limbs. Our analysis is focused on two scenarios: i) after assessment exercises for stroke rehabilitation when the upper limbs are resting at predefined points in the rehabilitation center, and ii) during the assessment exercises. In the first scenario, we explore the possibility of upper limb orientation estimation by deriving the Fisher information matrix (FIM) under near-field and far-field propagation conditions. It is noteworthy that the FIM quantifies how accurately we can estimate location information from a signal, and any subsequent algorithm is bounded by a function of the FIM. Coming to our propagation assumptions, the difference between the near-field and far-field regimes lies in the curvature of the wavefront. In the near-field, a receiver experiences a spherical wavefront, whereas in the far-field, the wavefront is approximately linear. The threshold to be within the near-field can be on the order of $10 \text{ m}.$

On the Limits of Single Anchor Localization: Near-Field vs Far-Field

It is well known that a single anchor can be used to determine the position and orientation of an agent communicating with it. However, it is not clear what information about the anchor or the agent is necessary to perform this localization, especially when the agent is in the near-field of the anchor. Hence, in this paper, to investigate the limits of localizing an agent with some uncertainty in the anchor location, we consider a wireless link consisting of source and destination nodes. More specifically, we present a Fisher information theoretical investigation of the possibility of estimating different combinations of the source and destination's position and orientation from the signal received at the destination. To present a comprehensive study, we perform this Fisher information theoretic investigation under both the near and far field propagation models. One of the key insights is that while the source or destination's $3$D orientation can be jointly estimated with the source or destination's $3$D position in the near-field propagation regime, only the source or destination's $2$D orientation can be jointly estimated with the source or destination's $2$D position in the far-field propagation regime. Also, a simulation of the FIM indicates that in the near-field, we can estimate the source's $3$D orientation angles with no beamforming, but in the far-field, we can not estimate the source's $2$D orientation angles when no beamforming is employed.

NTN-based 6G Localization: Vision, Role of LEOs, and Open Problems

Since the introduction of 5G Release 18, non-terrestrial networks (NTNs) based positioning has garnered significant interest due to its numerous applications, including emergency services, lawful intercept, and charging and tariff services. This release considers single low-earth-orbit (LEO) positioning explicitly for {\em location verification} purposes, which requires a fairly coarse location estimate. To understand the future trajectory of NTN-based localization in 6G, we first provide a comprehensive overview of the evolution of 3rd Generation Partnership Project (3GPP) localization techniques, with specific emphasis on the current activities in 5G related to NTN location verification. In order to provide support for more accurate positioning in 6G using LEOs, we identify two NTN positioning systems that are likely study items for 6G: (i) multi-LEO positioning, and (ii) augmenting single-LEO based location verification setup with Global Navigation Satellite System (GNSS), especially when an insufficient number of GNSS satellites (such as 2) are visible. We evaluate the accuracy of both systems through a 3GPP-compliant simulation study using a Cram\'{e}r-Rao lower bound (CRLB) analysis. Our findings suggest that NTN technology has significant potential to provide accurate positioning of UEs in scenarios where GNSS signals may be weak or unavailable, but there are technical challenges in accommodating these solutions in 3GPP. We conclude with a discussion on the research landscape and key open problems related to NTN-based positioning.

Comprehensive Analysis of Maximum Power Association Policy for Cellular Networks Using Distance and Angular Coordinates

A novel stochastic geometry framework is proposed in this paper to study the downlink coverage performance in a millimeter wave (mmWave) cellular network by jointly considering the polar coordinates of the Base Stations (BSs) with respect to the typical user located at the origin. Specifically, both the Euclidean and the angular distances of the BSs in a maximum power-based association policy for the UE are considered to account for realistic beam management considerations, which have been largely ignored in the literature, especially in the cell association phase. For completeness, two other association schemes are considered and exact-form expressions for the coverage probability are derived. Subsequently, the key role of angular distances is highlighted by defining the dominant interferer using angular distance-based criteria instead of Euclidean distance-based, and conducting a dominant interferer-based coverage probability analysis. Among others, the numerical results revealed that considering angular distance-based criteria for determining both the serving and the dominant interfering BS, can approximate the coverage performance more accurately as compared to utilizing Euclidean distance-based criteria. To the best of the authors$'$ knowledge, this is the first work that rigorously explores the role of angular distances in the association policy and analysis of cellular networks.

A Probabilistic Reformulation Technique for Discrete RIS Optimization in Wireless Systems

The use of reconfigurable intelligent surfaces (RIS) can improve wireless communication by modifying the wireless link to create virtual line-of-sight links, bypass blockages, suppress interference, and enhance localization. However, enabling the RIS to modify the wireless channel requires careful optimization of the RIS phase-shifts. Although discrete RIS is more practical given hardware limitations, continuous RIS phase-shift optimization has attracted significantly more attention than discrete RIS optimization, which suffers from issues like quantization error and scalability. To overcome these issues, we develop a comprehensive probabilistic technique to transform discrete optimization problems into optimization problems of continuous domain probability parameters by interpreting the discrete optimization variable as a categorical random vector and computing expectations with respect to those parameters. We rigorously establish that for the unconstrained case, the optimal points of the reformulation and the original problem coincide. For the constrained case, we prove that the transformed problem is a relaxation of the original problem. We apply the proposed technique to two canonical discrete RIS applications: SINR maximization and overhead-aware rate and energy efficiency (EE) maximization. The reformulation enables both stochastic and analytical interpretations of the original problems, as we demonstrate in our RIS applications. The former interpretation yields a stochastic sampling technique, whereas the latter yields an analytical gradient descent (GD) approach that employs closed-form approximations for the expectation. The numerical results demonstrate that the proposed technique is applicable to a variety of discrete RIS optimization problems and outperforms other general approaches, such as closest point projection (CPP) and semidefinite relaxation (SDR) methods.

Optimal Beamforming and Outage Analysis for Max Mean SNR under RIS-aided Communication

This paper considers beamforming for a reconfigurable intelligent surface (RIS)-aided multiple input single output (MISO) communication system in the presence of Rician multipath fading. Our aim is to jointly optimize the transmit beamformer and RIS phase shift matrix for maximizing the mean signal-to-noise (SNR) of the combined signal received over direct and indirect links. While numerical solutions are known for such optimization problems, this is the first paper to derive closed-form expressions for the optimal beamformer and the phase shifter for a closely related problem. In particular, we maximize a carefully constructed lower bound of the mean SNR, which is more conducive to analytical treatment. Further, we show that effective channel gain under optimal beamforming follows Rice distribution. Next, we use these results to characterize a closed-form expression for the outage probability under the proposed beamforming scheme, which is subsequently employed to derive an analytical expression for the ergodic capacity. Finally, we numerically demonstrate the efficacy of the proposed beamformer solution in comparison with the existing algorithmically obtained optimal solution for the exact mean SNR maximization.

RIS-Aided Localization under Position and Orientation Offsets in the Near and Far Field

This paper presents a rigorous Bayesian analysis of the information in the signal (consisting of both the line-of-sight (LOS) path and reflections from multiple RISs) that originate from a single base station (BS) and is received by a user equipment (UE). For a comprehensive Bayesian analysis, both near and far field regimes are considered. The Bayesian analysis views both the location of the RISs and previous information about the UE as {\em a priori} information for UE localization. With outdated {\em a priori} information, the position and orientation offsets of the RISs become parameters that need to be estimated and fed back to the BS for correction. We first show that when the RIS elements have a half wavelength spacing, this RIS orientation offset is a factor in the pathloss of the RIS paths. Subsequently, we show through the Bayesian equivalent FIM (EFIM) for the channel parameters that the RIS orientation offset cannot be corrected when there is an unknown phase offset in the received signal in the far-field regime. However, the corresponding EFIM for the channel parameters in the received signal observed in the near-field shows that this unknown phase offset does not hinder the estimation of the RIS orientation offset when the UE has more than one receive antenna. Furthermore, we use the EFIM for the UE location parameters to present bounds for UE localization in the presence of RIS uncertainty. We rigorously show that regardless of size and propagation regime, the RISs are only helpful for localization when there is {\em a priori} information about the location of the RISs. Finally, through numerical analysis of the EFIM and its smallest eigenvalue, we demonstrate the loss in information when the far-field model is {\em incorrectly} applied to the signals received at a UE experiencing near-field propagation.

Robust Optimization of RIS in Terahertz under Extreme Molecular Re-radiation Manifestations

Terahertz (THz) communication signals are susceptible to severe degradation because of the molecular interaction with the atmosphere in the form of subsequent absorption and re-radiation. Recently, reconfigurable intelligent surface (RIS) has emerged as a potential technology to assist in THz communications by boosting signal power or providing virtual line-of-sight paths. However, the re-radiated energy has either been modeled as a non-line-of-sight scattering component or as additive Gaussian noise in the literature. Since the precise characterization is still a work in progress, this paper presents the first comparative investigation of the performance of an RIS-aided THz system under these two extreme re-radiation models. In particular, we first develop a novel parametric channel model that encompasses both models of the re-radiation through a simple parameter change, and then utilize that to design a robust block-coordinate descent (BCD) algorithmic framework which maximizes a lower bound on channel capacity considering imperfect channel state information. In this framework, the original problem is split into two sub-problems: a) receive beamformer optimization, and b) RIS phase-shift optimization. We also analytically demonstrate the limited interference suppression capability of a passive RIS. Our numerical results also demonstrate that slightly better throughput is achieved when the re-radiation manifests as scattering.