Localization and tracking in imperfect mmwave systems with lower bound benchmarks

Abstract

Radio localization and tracking have enormously grown in the fifth generation (5G) of cellular systems and are no longer limited to emergencies. Furthermore, the data obtained from these processes proves highly beneficial for cellular networks, offering advantages such as enhanced network control and more efficient resource management. Accordingly, this thesis investigates localization and tracking in 5G and beyond. In particular, it targets realistic circumstances where the theoretical assumptions of a perfect synchronous system and ideal transceivers no longer exist. In this thesis, we undertake the task of localizing and tracking objects in progressively challenging scenarios. Subsequent to each localization and tracking process in these scenarios, we offer a performance analysis tool, accompanied by the derivation of benchmark metrics. Notably, we establish the Cramer-Rao Bound (CRB) as the benchmark for localization assessment and introduce the Bayesian Cramer-Rao Bound (BCRB) as the benchmark for tracking evaluation. In the context of localization, the initial scenario involves localizing a mobile station (MS) equipped with a single antenna within a perfectly synchronized millimeter-wave (mmwave) multiple-input single-output (MISO) system implementing the orthogonal frequency division multiplexing (OFDM), taking into account hardware impairments (HWIs) occurring at both the base station (BS) and the MS. Subsequently, the localization task advances to a more intricate environment, where localization accuracy is compromised by non-line of sight (NLoS) effects caused by unknown position scatterers, in addition to the presence of HWIs. Continuing the exploration, the localization process is extended to an environment where it is implemented within an asynchronous reconfigurable intelligent surface (RIS) aided mmwave MISO system. Here, our focus shifts to achieving localization alongside synchronization in a RIS-aided mmwave MISO system that is subject to HWIs. As for tracking, we also delve into this aspect within both a perfectly synchronized mmwave MISO system and a RIS-enhanced mmwave MISO system. In the first system, tracking performance is notably hampered by the presence of HWIs. Specifically, we engage in range-direction tracking of the MS relative to the reference BS. Subsequently, we proceed to track the MS’s position concerning the reference BS. However, in the second RIS-aided mmwave MISO system, tracking accuracy experiences a decline owing to both HWIs and synchronization errors, as we focus on monitoring the MS’s position in this particular configuration. From a technical standpoint, the process of localization, tracking, and even joint localization-synchronization is carried out on the MS board. This is achieved by estimating the downlink channel parameters using a maximum likelihood (ML) estimator. Subsequently, the localization and the joint localization-synchronization tasks are finalized by inputting these estimated parameters into specific geometric equations that establish a connection between the estimated values and the MS’s position and clock drift relative to the reference BS. Regarding the tracking process, the estimated parameters are subjected to processing using the Kalman filter (KF) when the relationships between the measurements and tracked elements exhibit linearity. Conversely, when these connections display nonlinearity, the extended Kalman filter (EKF) is utilized to manage these parameters. Both KF and EKF execute tracking by combining the estimated parameters, which represent the measurements, with prior information pertaining to the transition model of the MS. During the evaluation phase, we determine the localization and synchronization boundaries by calculating the position error bound (PEB) and synchronization error bound (SEB) using the CRB as a reference. Therefore, the CRB serves as a mathematical benchmark for assessing both the localization and the joint localization-synchronization procedures. This benchmark is derived by mathematically inverting the Fisher information matrix (FIM) associated with these processes. To initiate this procedure, we first construct a model for the received pilot signal, which is utilized in the estimation of the downlink channel parameters. Subsequently, we compute the FIM for the estimation of these downlink parameters and then transform it into the FIM for the localization and joint localization-synchronization tasks. The assessment of tracking performance involves a comparison with the BCRB, which results in tracking error limits. The BCRB takes into account not only the valuable information obtained from received pilots but also the valuable information derived from understanding the transition model of the MS. As a result, we follow a similar series of steps as those outlined for localization to compute the FIM related to the measurements. Subsequently, we calculate the FIM matrix associated with the MS’s transition model. The combination of these two FIMs forms the Bayesian information matrix (BIM), which is mathematically inverted to yield the BCRB benchmark. In conclusion, we perform numerical experiments to assess our processes. The results obtained from these computer simulations analyze the level of accuracy achieved in localization and tracking across various suggested scenarios. This accuracy measured by simulation is juxtaposed with the established benchmarks. The findings from both the simulation accuracy and the benchmarks reveal the detrimental effects of HWIs on localization and tracking performance, and this deterioration is inversely proportional to the transceiver quality. An analogous negative effect is observed as a result of the reflected NLoS paths from scatterers with unknown positions. Furthermore, the asynchronous scenarios demonstrate that assuming perfect synchronization masks a portion of the degradation observed in localization and tracking accuracy. However, in these numerical experiments, we achieve the theoretical accuracy presented by CRB for localization and by BCRB for tracking when these processes are implemented with perfect transceivers conditional to negligible NLoS reflections. On the other hand, with non-ideal conditions, the numerical experiments show that applying the proposed Monte Carlo (MC) approach with KF and EKF leads to a significant enhancement in accuracy. Furthermore, we leverage the capabilities of the proposed machine learning techniques (MLT) to offer a streamlined and highly accurate solution that does not rely on prior models and statistics around the MS.