Two-Step mmWave Positioning Scheme with RIS-Part II: Position Estimation and Error Analysis

In this series of work, we propose a comprehensive two-step three-dimensional (3D) positioning scheme in a millimeter wave (mmWave) system, where the reconfigurable intelligent surface (RIS) is leveraged to enhance the positioning performance of mobile users (MUs). Specifically, the first step is the estimation error modeling and analysis, while the second step is the corresponding positioning algorithm design and bias analysis. The first step is introduced in Part I of this series of work, and the second step is investigated in this paper. Our aim in this series of work is to obtain the closed-form solution of the MU's position through a two-stage weight least square (TSWLS) algorithm. In the first stage, we construct the pseudolinear equations based on the angle of arrival (AOA) and the time difference of arrival (TDOA) estimation at the RISs, then we obtain a preliminary estimation by solving these equations using the weight least square (WLS) method. Based on the preliminary estimation in the first stage, a new set of pseudolinear equations are obtained, and a finer estimation is obtained by solving the equations using the WLS method in the second stage. By combining the estimation of both stages, the final estimation of the MU's position is obtained. Further, we study the theoretical bias of the proposed algorithm by considering the estimation error in both stages. Simulation results demonstrate the superiority of the proposed positioning scheme.

Two-Step mmWave Positioning Scheme with RIS-Part I: Angle Estimation and Analysis

In this series of work, we propose a comprehensive two-step three-dimensional (3D) positioning scheme in a millimeter wave (mmWave) system, where the reconfigurable intelligent surface (RIS) is leveraged to enhance the positioning performance of mobile users (MUs). Specifically, the first step is the estimation error modeling and analysis based on the two-dimensional discrete Fourier transform (2D-DFT) angle estimation technique, while the second step is the corresponding positioning algorithm design and bias analysis. The first step is introduced in this paper, and the second step is investigated in Part II of this series work. Based on 2D-DFT angle estimation, the angle estimation error is modeled and analyzed by deriving its probability density functions (PDF). More specifically, we first derive the PDF by using the geometric relationship between the angles of arrival (AOAs) and their triangle functions. Then, we simplify the intricate expression of the PDF of the AOA estimation error by employing the first-order linear approximation of triangle functions. Finally, we derive a complex expression for the variance based on the derived PDF. Distinctively, for the azimuth estimation error, the variance is separately integrated according to the different non-zero intervals of the PDF, which will be used in the second part of this series work for the analysis of the position estimation error. Extensive simulation results are also presented to verify the accuracy of the derived results.

Optimal Measurement of Drone Swarm in RSS-based Passive Localization with Region Constraints

Passive geolocation by multiple unmanned aerial vehicles (UAVs) covers a wide range of military and civilian applications including rescue, wild life tracking and electronic warfare. The sensor-target geometry is known to significantly affect the localization precision. The existing sensor placement strategies mainly work on the cases without any constraints on the sensors locations. However, UAVs cannot fly/hover simply in arbitrary region due to realistic constraints, such as the geographical limitations, the security issues, and the max flying speed. In this paper, optimal geometrical configurations of UAVs in received signal strength (RSS)-based localization under region constraints are investigated. Employing the D-optimal criteria, i.e., minimizing the determinate of Fisher information matrix (FIM), such optimal problem is formulated. Based on the rigorous algebra and geometrical derivations, optimal and also closed form configurations of UAVs under different flying states are proposed. Finally, the effectiveness and practicality of the proposed configurations are demonstrated by simulation examples.

Low-complexity Joint Phase Adjustment and Receive Beamforming for Directional Modulation Networks via IRS

Intelligent reflecting surface (IRS) is a revolutionary and low-cost technology for boosting the spectrum and energy efficiencies in future wireless communication network. In order to create controllable multipath transmission in the conventional line-of-sight (LOS) wireless communication environment, an IRS-aided directional modulation (DM) network is considered. In this paper, to improve the transmission security of the system and maximize the receive power sum (Max-RPS), two alternately optimizing schemes of jointly designing receive beamforming (RBF) vectors and IRS phase shift matrix (PSM) are proposed: Max-RPS using general alternating optimization (Max-RPS-GAO) algorithm and Max-RPS using zero-forcing (Max-RPS-ZF) algorithm. Simulation results show that, compared with the no-IRS-assisted scheme and the no-PSM optimization scheme, the proposed IRS-assisted Max-RPS-GAO method and Max-RPS-ZF method can significantly improve the secrecy rate (SR) performance of the DM system. Moreover, compared with the Max-RPS-GAO method, the proposed Max-RPS-ZF method has a faster convergence speed and a certain lower computational complexity.

Providing Location Information at Edge Networks: A Federated Learning-Based Approach

Recently, the development of mobile edge computing has enabled exhilarating edge artificial intelligence (AI) with fast response and low communication cost. The location information of edge devices is essential to support the edge AI in many scenarios, like smart home, intelligent transportation systems and integrated health care. Taking advantages of deep learning intelligence, the centralized machine learning (ML)-based positioning technique has received heated attention from both academia and industry. However, some potential issues, such as location information leakage and huge data traffic, limit its application. Fortunately, a newly emerging privacy-preserving distributed ML mechanism, named federated learning (FL), is expected to alleviate these concerns. In this article, we illustrate a framework of FL-based localization system as well as the involved entities at edge networks. Moreover, the advantages of such system are elaborated. On practical implementation of it, we investigate the field-specific issues associated with system-level solutions, which are further demonstrated over a real-word database. Moreover, future challenging open problems in this field are outlined.

A Rapid Power-iterative Root-MUSIC Estimator for Massive/Ultra-massive MIMO Receiver

For a passive direction of arrival (DOA) measurement system using massive multiple input multiple output (MIMO), the complexity of the covariance matrix decompositionbased DOA measurement method is extremely high. To significantly reduce the computational complexity, two strategies are proposed. Firstly, a rapid power-iterative estimation of signal parameters via rotational invariance technique (RPI-ESPRIT) method is proposed, which not only reduces the complexity but also achieves good directional measurement results. However, the general complexity is still high. In order to further the complexity, a rapid power-iterative root Multiple Signal Classification (RPIRoot-MUSIC) method is proposed. Simulation results show that the two proposed methods outperform the classical DOA estimation method in terms of computational complexity. In particular, the lowest complexity achieved by the RPI-Root-MUSIC method is about two-order-magnitude lower than that of Root-MUSIC in terms of FLOP. In addition, it is verified that the initial vector and relative error have a substantial effect on the performance of computational complexity.

Rapid Phase Ambiguity Elimination Methods for DOA Estimator via Hybrid Massive MIMO Receive Array

For a sub-connected hybrid multiple-input multiple-output (MIMO) receiver with $K$ subarrays and $N$ antennas, there exists a challenging problem of how to rapidly remove phase ambiguity in only single time-slot. First, a DOA estimator of maximizing received power (Max-RP) is proposed to find the maximum value of $K$-subarray output powers, where each subarray is in charge of one sector, and the center angle of the sector corresponding to the maximum output is the estimated true DOA. To make an enhancement on precision, Max-RP plus quadratic interpolation (Max-RP-QI) method is designed. In the proposed Max-RP-QI, a quadratic interpolation scheme is adopted to interpolate the three DOA values corresponding to the largest three receive powers of Max-RP. Finally, to achieve the CRLB, a Root-MUSIC plus Max-RP-QI scheme is developed. Simulation results show that the proposed three methods eliminate the phase ambiguity during one time-slot and also show low-computational-complexities. In particular, the proposed Root-MUSIC plus Max-RP-QI scheme can reach the CRLB, and the proposed Max-RP and Max-RP-QI are still some performance losses $2dB\thicksim4dB$ compared to the CRLB.

Two Low-complexity DOA Estimators for Massive/Ultra-massive MIMO Receive Array

Eigen-decomposition-based direction finding methods of using large-scale/ultra-large-scale fully-digital receive antenna arrays leads to a high or ultra-high complexity. To address the complexity dilemma, in this paper, two low-complexity estimators are proposed: partitioned subarray combining (PSAC) and power iteration max correlation successive convex approximation (PI-Max-CSCA). Compared with the conventional no-partitioned direction finding method like root multiple signal classification (Root-MUSIC), in PSAC method, the total set of antennas are equally partitioned into subsets of antennas, called subarrays, each subarray performs independent DOA estimation, and finally all DOA estimates are coherently combined to give the final estimate. In PI-Max-CSCA method, using a fraction of all subarrays to make an initial coarse direction measurement (ICDM), the power iterative method is adopted to compute the more precise steering vector (SV) by exploiting the total array, and a more accurate DOA value is found using ICDM and SV through the maximum correlation method solved by successive convex approximation.

Performance Analysis of Wireless Network Aided by Discrete-Phase-Shifter IRS

Discrete phase shifters of intelligent reflecting surface (IRS) generates phase quantization error (QE) and degrades the receive performance at the receiver. To make an analysis of the performance loss caused by IRS with phase QE, based on the law of large numbers, the closed-form expressions of signal-to-noise ratio (SNR) performance loss (PL), achievable rate (AR), and bit error rate (BER) are successively derived under line-of-sight (LoS) channels and Rayleigh channels. Moreover, based on the Taylor series expansion, the approximate simple closed form of PL of IRS with approximate QE is also given. The simulation results show that the performance losses of SNR and AR decrease as the number of quantization bits increase, while they gradually increase with the number of IRS phase shifter elements increase. Regardless of LoS channels or Rayleigh channels, when the number of quantization bits is larger than or equal to 3, the performance losses of SNR and AR are less than 0.23dB and 0.08bits/s/Hz, respectively, and the BER performance degradation is trivial. In particular, the performance loss difference between IRS with QE and IRS with approximate QE is negligible when the number of quantization bits is not less than 2.

Federated Learning-Based Localization with Heterogeneous Fingerprint Database

Fingerprint-based localization plays an important role in indoor location-based services, where the position information is usually collected in distributed clients and gathered in a centralized server. However, the overloaded transmission as well as the potential risk of divulging private information burdens the application.Owning the ability to address these challenges, federated learning (FL)-based fingerprinting localization comes into people's sights, which aims to train a global model while keeping raw data locally. However, in distributed machine learning (ML) scenarios, the unavoidable database heterogeneity usually degrades the performance of existing FL-based localization algorithm (FedLoc). In this paper, we first characterize the database heterogeneity with a computable metric, i.e., the area of convex hull, and verify it by experimental results. Then, a novel heterogeneous FL-based localization algorithm with the area of convex hull-based aggregation (FedLoc-AC) is proposed. Extensive experimental results, including real-word cases are conducted. We can conclude that the proposed FedLoc-AC can achieve an obvious prediction gain compared to FedLoc in heterogeneous scenarios and has almost the same prediction error with it in homogeneous scenarios. Moreover, the extension of FedLoc-AC in multi-floor cases is proposed and verified.