1 CSI-Based Multi-Antenna and Multi-Point Indoor Positioning Using Probability Fusion Emre Gönülta¸s,Eric Lei, Jack Langerman, Howard Huang, and Christoph Studer Abstract—Channel state information (CSI)-based fingerprint- A. The Challenges of Indoor Positioning using RF Signals ing via neural networks (NNs) is a promising approach to enable accurate indoor and outdoor positioning of user equipments (UEs), even under challenging propagation conditions. In this paper, we propose a positioning pipeline for wireless LAN MIMO- An alternative to camera-based positioning methods is to OFDM systems which uses uplink CSI measurements obtained from one or more unsynchronized access points (APs). For each use radio-frequency (RF) signals [3], [10]–[15]. However, RF- AP receiver, novel features are first extracted from the CSI based localization techniques typically incur significant costs in that are robust to system impairments arising in real-world calibrating the infrastructure access points (APs), depending on transceivers. These features are the inputs to a NN that extracts a the required level of accuracy. For example, achieving meter- probability map indicating the likelihood of a UE being at a given level accuracy with RF time-difference-of-arrival measurements grid point. The NN output is then fused across multiple APs to provide a final position estimate. We provide experimental results requires synchronization of the APs with nanosecond accuracy with real-world indoor measurements under line-of-sight (LoS) and knowledge of their locations with sub-meter accuracy. and non-LoS propagation conditions for an 80 MHz bandwidth IEEE 802.11ac system using a two-antenna transmit UE and two A type of RF localization technique which has the advantage AP receivers each with four antennas. Our approach is shown of not requiring AP calibration is known as fingerprinting. to achieve centimeter-level median distance error, an order of Instead, these techniques rely on the offline creation of an magnitude improvement over a conventional baseline. empirical database that records RF measurements, such as Index Terms—Channel-state information (CSI), indoor local- the received signal strength indicator (RSSI) from multiple ization, multi-point fingerprinting, probability fusion. APs, as a function of the UE location. An algorithm then estimates the location of a UE given its RF measurements I. INTRODUCTION and the fingerprinting database. The database could be created with relatively low cost, for example, using an RF receiver Positioning of mobile user equipment (UE) devices is mounted on a robot that periodically moves through a space essential for a broad range of applications, including navigation, for cleaning. virtual reality, asset tracking, advertising, industrial automation, and many more [1]–[5]. While global navigation satellite system As an alternative to RSSI measurements, fingerprinting could (GNSS) technologies enable ubiquitous positioning in outdoor instead be based on estimates of channel state information environments with a view of the sky, there is no similarly (CSI), which is always required for data demodulation. For ubiquitous solution for indoor environments. In addition, some wideband MIMO-OFDM systems, complex-valued CSI can be of the indoor positioning applications, such as drone or robot estimated for each active subcarrier and each transmit-receive navigation, require centimeter-level precision for executing antenna pair, resulting in significantly richer measurement their missions, which is not achievable using conventional sets compared to RSSI. CSI-based fingerprinting has been GNSS. One class of solutions for indoor positioning uses shown to enable accurate localization in both indoor [12], infrastructure cameras for visible or infra-red light, viewing [16]–[18] and outdoor [19]–[22] applications. Recently, a arXiv:2009.02798v2 [eess.SP] 31 Aug 2021 an object of interest which is equipped with either an active range of CSI-based fingerprinting methods that use machine transmitter or passive reflector [6]–[9]. While such systems can learning—rather than sophisticated geometrical models—has achieve sub-centimeter accuracy, they are expensive, require been proposed [16], [17], [20], [21], [23]–[26]. For all of these unobstructed views, and may not work in rooms with bright methods, carefully designed features from CSI turn out to sunlight. be critical, as real-world channels exhibit small-scale fading and wireless transceivers suffer from a number of hardware E. Gönülta¸sand E. Lei are with the School of Electrical and Computer impairments. In addition, most of these methods rely on Engineering, Cornell University, Ithaca, NY (e-mail: [email protected]; [email protected]). supervised learning to train a neural network (NN) that maps J. Langerman and H. Huang are with Nokia Bell-Labs, Murray Hill, CSI to UE position, which requires dedicated measurement NJ (e-mail: [email protected]; howard.huang@nokia-bell- campaigns to acquire CSI and associated ground-truth position. labs.com). C. Studer is with the Department of Information Technology and Electrical If relative location information is sufficient, self-supervised Engineering at ETH Zürich, Zürich, Switzerland (e-mail: [email protected]). methods known as channel charting [27]–[29] avoid expensive The work of EG and CS was supported in part by Xilinx Inc. and by measurement campaigns. If CSI measurements from multiple the US NSF under grants CCF-1652065, CNS-1717559, CNS-1955997, and ECCS-1824379. The Quadro P6000 GPU used for this research was donated APs are available, then the accuracy of channel charting can by the NVIDIA Corporation. be improved significantly [30], [31]. 2 B. Contributions as a classification problem in which the labels correspond to In this paper, we propose a CSI-based positioning pipeline for grid points nearest to the UE locations. Instead of one-hot multiple-input multiple-output (MIMO) orthogonal frequency- vectors, we propose an improved strategy that enables NN division multiplexing (OFDM) wireless systems, which lever- training for general grid structures and for general probability ages the availability of CSI acquired at multiple MIMO links. mass functions (PMFs). To compute the PMFs, we propose an Our positioning system can be built by using off-the-shelf optimization-based minimum-variance approach that assigns hardware, e.g., using the framework put forward in [32], without probabilities to the individual grid points so that the expected knowing the details of the wireless infrastructure. Our main location exactly matches the UE position. While the references contributions can be summarized as follows: [44]–[46] also rely on a probabilistic description of UE position, these methods perform positioning using geometrical models • We propose a NN-based positioning pipeline that combines instead of NNs. so-called probability maps from multiple MIMO links NN-based positioning from CSI measurements requires (transmit antennas and/or APs). The proposed method does carefully-designed features, which are robust to small-scale not require accurate synchronization between transmit fading as well as system and hardware impairments. The use antennas and/or APs, and minimizes the amount of of beamspace representations to extract the incident angles location information to be transmitted to a centralized has been used in [21], [27], [28], [47]. The conversion processor. of subcarrier CSI into the delay domain to extract relative • We evaluate different methods to combine the probability time-of-flight information has been used in [21], [47]–[49]. maps, which indicate the likelihood of the UE location on a The use of cross-correlation in the spatial domain and 1- predefined grid. The proposed methods include probability dimensional autocorrelation in the delay domain has been used conflation, Gaussian conflation, and NN-based probability in [27], [28] and [20], [29], [50], respectively. Such methods fusion, which improve positioning accuracy over existing improve resilience to small-scale fading and common hardware NN-based CSI fingerprinting solutions. impairments, including time synchronization errors as well as • We calculate the probability maps from CSI features using residual carrier frequency and sampling rate offsets. To improve NNs. The proposed method enables probability maps robustness of our positioning pipeline to small-scale fading as with irregular grid structures. Furthermore, NN training is well as system and hardware impairments that typically arise accomplished by assigning probabilities to multiple grid in IEEE 802.11ac MIMO-OFDM systems, we improve the points using a minimum-variance approach. CSI feature extraction pipeline in [20] specialized for massive • We extract CSI features that are robust to hardware MU-MIMO cellular systems by (i) taking the “instantaneous impairments typically arising in IEEE 802.11ac MIMO- autocorrelation” over the antenna and delay domains (no OFDM-based systems operating indoors. The proposed averaging over multiple measurements), (ii) computing the CSI features outperform existing features that were autocorrelation in the antenna domain (not just the delay designed for massive multiuser MIMO basestations. domain), (iii) processing both the real and imaginary parts • We provide experimental results with real-world indoor (instead of taking the magnitudes), and (iv) not taking the channel measurements under line-of-sight (LoS) and logarithm on the resulting features. non-LoS conditions and for