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Belief propagation (BP) is a useful probabilistic inference algorithm for efficiently computing approximate marginal probability densities of random variables. However, in its standard form, BP is applicable to only the vector-type random variables, while certain applications rely on set-type random variables with an unknown number of vector elements. In this paper, we first develop BP rules for set-type random variables and demonstrate that vector-type BP is a special case of set-type BP. We further propose factor graphs with set-factor and set-variable nodes by devising the set-factor nodes that can address the set-variables with random elements and cardinality, while the number of vector elements in vector-type is known. To demonstrate the validity of developed set-type BP, we apply it to the Poisson multi-Bernoulli (PMB) filter for simultaneous localization and mapping (SLAM), which naturally leads to a new set-type BP-SLAM filter. Finally, we reveal connections between the vector-type BP-SLAM filter and the proposed set-type BP-SLAM filter and show a performance gain of the proposed set-type BP-SLAM filter in comparison with the vector-type BP-SLAM filter., 17 pages, 7 figures

Localization is envisioned as a key enabler to satisfy the requirements of communication and context-aware services in the fifth/sixth generation (5G/6G) communication systems. User localization can be achieved based on delay and angle estimation using uplink/downlink pilot signals. However, hardware impairments (HWIs) (such as phase noise and mutual coupling) distort the signals at both the transmitter and receiver sides and thus affect the localization performance. While this impact can be ignored at lower frequencies with less severe HWIs, and less stringent localization requirements, modeling and analysis efforts are needed for high-frequency bands to assess degradation in localization accuracy due to HWIs. In this work, we model various types of impairments for a mmWave multiple-input-multiple-output communication system and conduct a misspecified Cram\'er-Rao bound analysis to evaluate HWI-induced performance losses in terms of angle/delay estimation and the resulting 3D position/orientation estimation error. We also investigate the effect of individual and overall HWIs on communication in terms of symbol error rate (SER). Our extensive simulation results demonstrate that each type of HWI leads to a different level of degradation in angle and delay estimation performance, and the prominent impairment factors on delay estimation will have a dominant negative effect on SER.

Positioning with 5G signals generally requires connection to several base stations (BSs), which makes positioning more demanding in terms of infrastructure than communications. To address this issue, there have been several theoretical studies on single BS positioning, leveraging high-resolution angle and delay estimation and multipath exploitation possibilities at mmWave frequencies. This paper presents the first realistic experimental validation of such studies, involving a commercial 5G mmWave BS and a user equipment (UE) development kit mounted on a test vehicle. We present the relevant signal models, signal processing methods (including channel parameter estimation and position estimation), and validate these based on real data collected in an outdoor science park environment. Our results indicate that positioning is possible, but the performance with a single BS is limited by the knowledge of the position and orientation of the infrastructure and the multipath visibility and diversity.

Device localization and radar-like mapping are at the heart of integrated sensing and communication, enabling not only new services and applications, but can also improve communication quality with reduced overheads. These forms of sensing are however susceptible to data association problems, due to the unknown relation between measurements and detected objects or targets. In this chapter, we provide an overview of the fundamental tools used to solve mapping, tracking, and simultaneous localization and mapping (SLAM) problems. We distinguish the different types of sensing problems and then focus on mapping and SLAM as running examples. Starting from the applicable models and definitions, we describe the different algorithmic approaches, with a particular focus on how to deal with data association problems. In particular, methods based on random finite set theory and Bayesian graphical models are introduced in detail. A numerical study with synthetic and experimental data is then used to compare these approaches in a variety of scenarios., This is a preprint of the following chapter: Yu Ge, Ossi Kaltiokallio, Hyowon Kim, Jukka Talvitie, Sunwoo Kim, Lennart Svensson, Mikko Valkama, Henk Wymeersch, MmWave Mapping and SLAM for 5G and Beyond, published in Integrated Sensing and Communications (ISAC), edited by Fan Liu, Yonina C. Eldar, Christos Masouros, 2023, Springer reproduced with permission of Springer

Bayesian receiver autonomous integrity monitoring (RAIM) algorithms are developed for the snapshot cellular positioning problem in a simplified one-dimensional (1D) linear Gaussian setting. Position estimation, multi-fault detection and exclusion, and protection level (PL) computation are enabled by the efficient and exact computation of the position posterior probabilities via message passing along a factor graph. Computer simulations demonstrate the significant performance improvement of the proposed Bayesian RAIM algorithms over a baseline advanced RAIM algorithm, as it obtains tighter PLs that meet the target integrity risk (TIR) requirements.

In the upcoming sixth generation (6G) of wireless communication systems, reconfigurable intelligent surfaces~(RISs) are regarded as one of the promising technological enablers, which can provide programmable signal propagation. Therefore, simultaneous radio localization and mapping(SLAM) with RISs appears as an emerging research direction within the 6G ecosystem. In this paper, we propose a novel framework of RIS-enabled radio SLAM for wireless operation without the intervention of access points (APs). We first design the RIS phase profiles leveraging prior information for the user equipment~(UE), such that they uniformly illuminate the angular sector where the UE is probabilistically located. Second, we modify the marginal Poisson multi-Bernoulli SLAM filter and estimate the UE state and landmarks, which enables efficient mapping of the radio propagation environment. Third, we derive the theoretical Cram\'er-Rao lower bounds on the estimators for the channel parameters and the UE state. We finally evaluate the performance of the proposed method under scenarios with a limited number of transmissions, taking into account the channel coherence time. Our results demonstrate that the RIS enables solving the radio SLAM problem with zero APs, and that the consideration of the Doppler shift contributes to improving the UE speed estimates.

We propose a framework for monostatic sensing by a user equipment (UE), aided by a reconfigurable intelligent surface (RIS) in environments with single- and double-bounce signal propagation. We design appropriate UE-side precoding and combining, to facilitate signal separation. We derive the adaptive detection probabilities of the resolvable signals, based on the geometric channel parameters of the links. Then, we estimate the passive objects using both the double-bounce signals via passive RIS (i.e., RIS-sensing) and the single-bounce multipath direct to the objects (i.e., non-RIS-sensing), based on a mapping filter. Finally, we provide numerical results to demonstrate that effective sensing can be achieved through the proposed framework.

Due to 5G millimeter wave (mmWave), spatial channel parameters are becoming highly resolvable, enabling accurate vehicle localization and mapping. We propose a novel method of radio simultaneous localization and mapping (SLAM) with the Dirichlet process (DP). The DP, which can estimate the number of clusters as well as clustering, is capable of identifying the locations of reflectors by classifying signals when such 5G signals are reflected and received from various objects. We generate birth points using the measurements from 5G mmWave signals received by the vehicle and classify objects by clustering birth points generated over time. Each time we use the DP clustering method, we can map landmarks in the environment in challenging situations where false alarms exist in the measurements and change the cardinality of received signals. Simulation results demonstrate the performance of the proposed scheme. By comparing the results with the SLAM based on the Rao-Blackwellized probability hypothesis density filter, we confirm a slight drop in SLAM performance, but as a result, we validate that it has a significant gain in computational complexity.