Error Bounds for Uplink and Downlink 3D Localization in 5G Millimeter Wave Systems

Abstract

Location-aware communication systems are expected to play a pivotal part in the next generation of mobile communication networks. Therefore, there is a need to understand the localization limits in these networks, particularly, using millimeter-wave technology (mmWave). Towards that, we address the uplink and downlink localization limits in terms of 3D position and orientation error bounds for mmWave multipath channels. We also carry out a detailed analysis of the dependence of the bounds on different system parameters. Our key findings indicate that the uplink and downlink behave differently in two distinct ways. First of all, the error bounds have different scaling factors with respect to the number of antennas in the uplink and downlink. Secondly, uplink localization is sensitive to the orientation angle of the user equipment (UE), whereas downlink is not. Moreover, in the considered outdoor scenarios, the non-line-of-sight paths generally improve localization when a line-of-sight path exists. Finally, our numerical results show that mmWave systems are capable of localizing a UE with sub-meter position error, and sub-degree orientation error. communications [7], assisted living applications [8], or to support the communication robustness and effectiveness in different aspects such as resource allocation [9], beamforming [10], [11], and pilot assignment [12]. Therefore, the study of positioning in 5G mmWave systems becomes specially imperative. Due to the use of directional beamforming in mmWave, in addition to the UE position also the UE orientation plays an important role in location-aided systems.Conventionally position information is obtained by GPS, though this has several limitations.Most importantly, GPS suffers from degraded performance in outdoor rich-scattering scenarios and urban canyons, and may fail to provide a position fix for indoor scenarios. Even in good conditions, GPS positioning accuracy ranges between 1-5 meters. To address these limitations, there has been intense research on competing radio-based localization technologies. To understand the fundamental behavior of any technology, the Cramér-Rao lower bound (CRLB)[13] or related bounds can be used. The CRLB provides a lower bound on the variance of an unbiased estimator of a certain parameter. The square-root of the CRLB of the position and the orientation are termed the position error bound (PEB), and the orientation error bound (OEB), respectively. PEB and OEB can be computed indirectly by transforming the bounds of the channel parameters, namely: directions of arrival (DOA), directions of departure (DOD), and time of arrival (TOA). For conventional MIMO systems, the bounds of the 2D channel parameters are derived in [14], based on received digital signals and uniform linear arrays (ULA), while bounds are derived in [15] based on 3D channel matrix with no transmit beamforming. It was found that having more transmit and receive antennas is beneficial for estimating the DOA and DOD. In both [14], [15] beamforming was not considered. The b...

A Survey of Enabling Technologies for Network Localization, Tracking, and Navigation

“…al. shows that the 5G mmWave system provides sub-meter localization capacity by computing Cramer-Rao lower bound in [52].…”

Millimeter-Wave Downlink Positioning With a Single-Antenna Receiver

“…To formulate the estimation problem, we exploit the fact that, under typical mmWave assumptions, all the paths are resolvable in either the time or space domains, and the multipath components are likely uncorrelated with the LOS [11]. Since we are interested in estimating the sole LOS position-related parameters, NLOS paths can be omitted from (3) and the multipath parameter estimation can be then reduced to a problem of single-path estimation, that is, the channel vector given in (3) can be re-defined as…”

“…The theoretical localization performance achievable using mmWave MIMO have been recently investigated in [11]- [13]. In [13], the Cramér-Rao Lower bound (CRLB) on the position and rotation angle estimates obtained using mmWave from a single transmitter has been derived.…”

“…Furthermore, a novel position and rotation estimation algorithm based on compressed sensing that attains the CRLB for average to high signal-to-noise ratio (SNR) is proposed. In [11], fundamental limits of position and orientation estimation for uplink and downlink in 3D-space were presented. Authors in [12] have shown that non-line-of-sight (NLOS) components can also be exploited to gain additional information for position and orientation estimation.…”

“…More specifically, the paper provides two kinds of contributions. First, we thoroughly analyze the problem from a theoretical perspective, deriving the exact solution to the Maximum Likelihood (ML) estimation problem and complementing the CRLB-analysis available in the literature [11] with a precise assessment of the achievable performance under the considered MISO setup.…”