Binary Radio Tomographic Imaging in Factory Environments Based on LOS/NLOS Identification

Radio tomographic imaging (RTI) is a technique for estimating spatial loss fields (SLFs), which maps the quantified attenuation of radio signals at every spatial location within monitored regions. In this study, we investigate RTI techniques in indoor factory environments, where the RTI techniques deteriorate because of severe multipath channels. We propose the binary radio tomographic imaging (binary RTI) method, where the attenuation level of each pixel in a SLF is defined as a binary value. The binary RTI method is suited for factory environments, including metallic objects, because radio signals are almost fully reflected rather than getting absorbed by such objects. In the proposed method, we suppose that transmitted signals are modulated with an orthogonal frequency division multiplexing (OFDM) format, and each receiver is equipped with multiple antenna elements. By adopting the two-dimensional multiple signal classification (MUSIC), the proposed method identifies whether the signals are transmitted in a line-of-sight (LOS) or a non-line-of-sight (NLOS) path. From the LOS/NLOS identification, we propose two algorithms to estimate the binary SLF: a simple greedy algorithm and a relaxation algorithm with low-rank approximation. We evaluate the performance of the proposed method via simulation experiments. To assess the applicability of the proposed method to factory environments, we assume a severe multipath environment where all the objects, wall, and ceiling are perfect electrical conductors, and show that by using an appropriate threshold parameter for the LOS/NLOS identification, the proposed method can estimate the binary SLF in the test environment.

communication devices, such as APs are fixed; however, it is not suitable for non-static environments where their positions are altered, because 3D layer scanning should be conducted each time the positions are changed. To efficiently generate industrial products, facility layouts in factory environments are occasionally reconfigured and optimized, which is referred to as the factory layout planning problem [7], [8]. Furthermore, 3D laser scanning is based on physical optics and does not necessarily reflect the characteristics of the radio frequency (RF) signals used for communication, such as diffraction and reflection. Therefore, in this study, we address the factory radio design with RF signals.
We consider radio tomographic imaging (RTI) [9], [11], [12], [14], [16], [17], [18], [19], [20], [21] in non-static environments. RTI is a technique for estimating spatial loss fields (SLFs), maps quantifying the attenuation of radio signals at each spatial location within monitored regions, and provides useful information for designing reliable wireless networks considering obstructions. In RTI, the monitored region is divided into pixels, and an SLF is represented with a set of attenuation levels of the pixels. The relationship between a measurement vector and an SLF is formulated as a system of linear equations according to the positions of the transmitters and receivers. As it does not require any spatial information of the layout, it is suitable for non-static environments. The formulation is based on an assumption that the received power of a radio signal is dominated by the direct path component in multipath components. However, in factory environments, this assumption is inappropriate because there are several highly reflective metallic objects in the factory environments, which cause severe multipath channels [4], [22].
In this study, we propose binary radio tomographic imaging (binary RTI) for factory environments. In factory environments with metallic objects, radio signals are almost fully reflected rather than absorbed. Therefore, we model the attenuation level of each pixel in an SLF with a binary value, i.e., the pixel represents a perfectly reflective object if the attenuation level equals to one, and it does not cause any attenuation if the level is zero.
The proposed method comprises two steps: line-ofsight (LOS)/non-line-of-sight (NLOS) identification and SLF estimation. In the first step, a transmitted signal between an AP and a mobile terminal is identified as a LOS signal or NLOS signal via of multiple signal classification (MUSIC) [23]. We suppose that transmitted signals are modulated with an orthogonal frequency division multiplexing (OFDM) format and each receiver is equipped with multiple antenna elements. By analyzing an OFDM signal, a 2D MUSIC spectrum is developed as a function angleof arrivals (AoAs) and time-of arrivals (ToAs) of multipath components (incident signals) in the OFDM signal. From the MUSIC spectrum, the path of each incident signal is identified as LOS or NLOS. In the second step, the SLF is estimated from the results of the first step. The SLF estimation is formulated as a combinatorial optimization problem. First, we consider a greedy algorithm to solve the problem. Furthermore, by relaxing the problem, we consider a low rank approximation to estimate the SLF.
1) We propose the idea of the binary RTI, which is a completely different approach from existing methods. The proposed method formulates the RTI problem as a combinatorial optimization problem, whereas the conventional RTI methods formulate it as a linear inverse problem. In the conventional methods, a calibration technique, which sets adequate values to parameters, such as the antenna gains and pathloss exponent, is required to correctly retrieve measurement vectors [16]. In contrast, the proposed method does not require any calibration technique as it relies on the LOS/NLOS identification and positions of transmitters and receivers. 2) To estimate SLFs in the binary RTI, we consider two methods: the simple greedy method and the low rank optimization method, and evaluate these methods through simulation experiments in an indoor wireless channel assuming a factory environment. The remainder of this paper is organized as follows. In Section II, we review related studies. In Section III, we describe the system model and problem formulation. We propose binary RTI in Section IV, and evaluate the performance of the proposed method in Section V. Finally, we conclude the paper and provide directions for future studies in Section VI.

II. RELATED WORK
RTI techniques have been studied for device free localization [9], [11], [18], [19], [20] and obstacle mapping [12], [14], [16], [17], [21]. In device free localization, target positions are identified by the change in the SLF. Let x(t) and y(t) denote an SLF and a measurement vector obtained from RSSs between transmitters and receivers at time t, respectively. For given t 1 and t 2 (t 2 > t 1 ), we define the change of t 1 ,t 2 x and 1,2 y as 1,2 x = x(t 2 ) − x(t 1 ), 1,2 y = y(t 2 ) − y(t 1 ), respectively, and the relationship between 1,2 x and 1,2 y is given by where A and w represent a measurement matrix and a noise vector, respectively. Since 1,2 x includes only the change of the SLF due to moving targets, the positions of the targets can be identified by estimating 1,2 x. However, obstacle VOLUME 11, 2023 mapping attempts to reveal obstacles within a measured regions by estimating an SLF. The problem formulation of obstacle mapping is described in Section III. In this study, we focus on obstacle mapping.
As described in Section I, multipath fading deteriorates the performance of RTI and several mitigation techniques of the multipath fading effect have been studied in literature. Table 1 presents a summary of the related works. As mentioned in Section I, these techniques are classified into four types. Wang et al. [11] proposed a multipath mitigation technique to extract the direct path component in each received signal, which is referred to as the LOS component in Section III-D. In this technique, the direct path component is extracted with the chirp FFT. Each transmitter transmits a chirp signal and the received signal is demodulated with a local chirp signal at the receiver. The magnitude of the direct path component is obtained from the fast Fourier transform (FFT) of the demodulated signal.
In [10] and [18], multipath mitigation techniques using directional antennas or spatial diversity are proposed. Kaltiokallio et al. [10] proposed directional RTI (dRTI), which mitigates the influence of multipath fading by using electrically switched directional antennas. In [18], spatial diversity was adopted to mitigate the influence of multipath fading. Each wireless node contains multiple antennas, and multiple links are established between transmitters and receivers. The influence of the multipath fading is reduced by averaging the RSS values on these links.
In [15], [19], and [20], Bayesian learning techniques are employed to mitigate the influence of multipath fading. In these techniques, Bayesian modeling is applied to SLFs or noise variance due to multipath fading. In [19], a sparse Bayesian learning approach with the Laplace prior is utilized to enhance the robustness against multipath fading based on the fact that SLFs in device-free localization are sparse. In [15] and [20], a sparse Bayesian approach based on noise adaptive optimization was applied and the influence of multipath fading was modeled with a mixture of Gaussian distribution.
The binary RTI method proposed in this study uses a new approach where elements of SLFs are defined as binary values, where each pixel in an SLF equals to one if there exists some object on it, and it equals to zero otherwise. To the best of our knowledge, this approach has not been considered so far. By binarizing the SLFs, the SLFs can be estimated with LOS/NLOS identification of measurement paths. In other words, accurate levels of LOS components are not required. In a severe multipath environment, the proposed RTI method estimates a two-dimensional MUSIC spectrum as a function of AoAs and ToAs of incident signals in received signals [24], [25], [26], and each received signal is identified as a LOS or a NLOS signal, where a LOS (NLOS) signal implies that it is transferred over a LOS (NLOS) path. To the best of our knowledge, the approach using the LOS/NLOS identification in RTI techniques has not been studied to date. The idea of binarization in network performance metrics has been studied in binary network tomography (or Boolean network tomography) [29], [30], [31], [32], [33]. Network tomography is a technique for estimating network internal characteristics such as link loss rates and link delays from observable measurements. In binary network tomography techniques, the relationship between end-to-end measurements and links states is formulated as a group testing problem [34], and link failures or congested links in a network can be detected from end-to-end measurements. To the best of our knowledge, the proposed binary RTI method is the first technique that adopts this idea in RTI.

III. RADIO TOMOGRAPHIC IMAGING A. NOTATION
The superscripts () T and () H represent the and conjugate transposes, respectively. ∥ · ∥ p (p = 1, 2) represents the ℓ p norm and for a vector For a matrix Z = [z n 1 ,n 2 ] 1≤n 1 ≤N 1 ,1≤n 2 ≤N 2 ∈ C N 1 ×N 2 , ∥Z∥ * and ∥Z∥ F denote the nuclear norm and Frobenius norm of Z, respectively, given by Fig. 1 presents an example of the factory layout, where there are N AP APs and N MT mobile terminals (MTs), such as AGVs and AMRs. Let A 3 ∈ R 3 denote the entire area in the factory environment, while A 2 ∈ R 2 denote the 2D space obtained by projecting A 3 onto the X -Y plane. Let r . . , N MT ) denote the positions of the i-th AP and the j-th MT, respectively, where (r and h AP and h MT denote the heights of APs and MTs, respectively. We assume that APs are placed at fixed positions and MTs are moving within a restricted area in A 3 . Each AP is equipped with N A antenna elements and each MT is equipped with a single antenna element. We assume that MTs can communicate only , S i m ,j m , and w i m ,j m denote the transmission power, path loss, shadowing loss, and multipath fading loss, respectively. With constant parameters α and β, P path (∥r where α (α ≥ 2) denotes as the path loss exponent.

C. PROBLEM FORMULATION
If APs and MTs are placed at various heights, SLFs in higher (three or four) dimensional spaces can be estimated using tensor recovery techniques [14]. However, because the heights of APs and MTs are fixed in this study, we focus on the SLF estimation in 2D space A 2 .
We divide A 2 into N pixels with the same size. Let x n (n = 1, 2, . . . , N ) denote the attenuation of signals at pixel n. SLF is then defined as x = (x 1 x 2 · · · x N ) T . Assume that P TX , positions r (AP) i m and r (MT) j m , and parameters α and β are known beforehand. The measurement y m for (i m , j m ) is then given by S m can be approximated as a weighted sum of x n [9] and is described as  . Inverse area elliptical model [12], [16] for radio signals with 5 GHz frequency.
between y and x is described as Several models for a m,n have been considered [12]. In the inverse area elliptical model [12], [16], a m,n is set to a m,n = 0 if ∥r n − r j m ∥ and λ denote the wavelength of the radio signals. Otherwise, a m,n is set to a m,n = 4 π ζ β r n ; r

D. INFLUENCE OF MULTIPATH FADING
In a multipath channel, the channel impulse response h(τ ) can be described as where L, h l , and τ l denote the number of paths, complex amplitude of the l-th path, and delay of the l-th path, respectively. Without loss of generality, we set τ 1 < τ 2 < · · · < τ L . The first path then corresponds to the direct path. Let P TX denote the transmission power of radio signals. The received power P RX of a radio signal and the power P LOS of the direct path are given by respectively. We refer to P LOS as the LOS component of the channel. To represent LOS and NLOS signals in a unified manner, we consider that NLOS signals have the LOS component with h 1 = 0. Fig. 3 presents the received powers of radio signals measured in the simulation environment in Section V. Figs. 3a and 3b exhibit received powers of LOS signals and NLOS signals vs. the distance between transmitters and receivers, respectively. We observe that NLOS signals have comparable received powers even though they have no direct path component. As demonstrated by the inverse area elliptical model in Section III-C, each element in measurement vector y is dominated by the LOS component. Therefore, these figures indicate that the SLF is underestimated, particularly in pixels that these NLOS signals pass through. Fig. 3c presents LOS components vs. received powers for LOS signals. We observe that some signals have significantly smaller received powers although the direct path components are included in the signals. These LOS signals trigger the overestimation of the SLF in some pixels because RTI considers that the signals are highly attenuated.
In summary, highly reflective areas such as factory environments deteriorate the performance of RTI. In the proposed method, we address this problem by LOS/NLOS identification. In the binary RTI, SLF x = (x 1 x 2 · · · x N ) T is defined as a vector with binary elements, where x n = 1 if there is an object to attenuate the signal power in the pixel n, and x n = 0 otherwise. x is estimated from the estimated path statesq = (q 1q2 · · ·q M ) T . The algorithms to estimate x are described in section IV-B. We assume that SLF x does not change when estimating it. Therefore, x is estimated after all q m (m = 1, 2, . . . , M ) are obtained. Sequential or adaptive estimators of x are not considered in this study.

A. LOS/NLOS IDENTIFICATION
Let h n A (t) denote the channel impulse response of signals received at the n A -th antenna element (n A = 1, 2, . . . , N A ). From (1), h n A (τ ) can be expressed as where c l θ l denote the complex channel gain and AoA of the l-th path, respectively. When adopting a uniform linear array with n A antenna elements spaced by d, a n A (θ) is given by where λ denotes the carrier wavelength. Let f k = (k − 1)f 0 denote the k-th subcarrier frequency, where f 0 represents the subcarrier spacing. Subsequently, the t-th received coefficient y (m) n A ,k (t) (t = 1, 2, . . . , T ) of the k-th subcarrier at the n A -th antenna element is then given by   1,2 (t) · · · y (m) N A ,K (t)) T . In this subsection, we focus on the LOS/NLOS identification for the (i m , j m )-th path, and omit the superscript (m) to simplify the notation.
We define steering vector b(θ l , τ l ) as

S(t)Bc(t)c H (t)B H S H (t) = Bc(t)c H (t)B H .
By assuming that η n A,k (t) (n A = 1, 2, . . . , N A , k = 1, 2, . . . , K ) are zero mean uncorrelated complex Gaussian variables with variance σ 2 η , the correlation matrix R is obtained as Let µ p and u p (p = 1, 2, . . . , N A K , µ 1 ≥ µ 2 ≥ · · · µ N A K ) denote the p-th eigenvalue of R and the eigenvector associated with µ p . We define a column span S = span{u 1 , u 2 , . . . , u N A K } and divide S into a signal subspace S S = span{u 1 , u 2 , . . . , u N S } and a noise subspace S N = span{e 1 , e 2 , . . . , e N N }, where N S + N N = MK and e p = u p+N S (p = 1, 2, . . . , N N ). The MUSIC spectrum P MUSIC (θ, τ ) is then defined as , where E N = (e 1 e 2 · · · e N N ). We assume that all the MTs are perfectly localized by adopting a localization method without RF signals such as light detection and ranging (LiDAR) [36], [37], [38]. Recall that r where c denotes the speed of light. With threshold P th , q m is given by for arbitrary complex vector z ∈ C N A K ×1 . Therefore, we set P th > 1. In general, for AoA estimation problems, to identify AoAs, it is necessary to search peaks in the MUSIC spectrum with a peak search algorithm [39], or to solve a polynomial equation in Root-MUSIC methods [40]. However, in the proposed method, the above LOS/NLOS identification method is advantageous in terms of computational complexity because it does not require such a peak search technique.

B. BINARY RADIO TOMOGRAPHIC IMAGING
We define Q m ⊂ {1, 2, . . . , N }, where n ∈ Q m if the line between AP i m and MT j m crosses the pixel n. The relationship between x and q can be described as where ∨ and ∧ represent OR and AND operations, respectively. The binary RTI attempts to estimate x fromq, and from the above relationship, this problem can be formulated as a combinatorial optimization problem. In this study, we consider two methods to solve the binary RTI problem: a simple method and low rank approximation method. if y m = 0 then 4: for all n ∈ Q m do 5: x n := 0 6: end for 7: end if 8: end for 1) SIMPLE METHOD Algorithm 1 outlines the algorithm of the simple method, which is a type of greedy algorithms. Initially, all elements of x are set to one, which implies that there are objects in all pixels. If the path (i m , j m ) is identified as LOS (that is, q m = 0), x n for ∀n ∈ Q m are changed to x n = 0. Although this algorithm is very simple, pixels that are not included in any path are estimated to be one.

2) LOW RANK OPTIMIZATION METHOD
The low rank approximation method comprises optimization, filtering, and binarization. In optimization, the SLF is estimated from estimated path statesq. The estimated SLF includes impulsive noise, also known as salt-and-pepper noise in image processing. Specifically, there is a small number of pixels with values more than zero in areas that most pixels have zero values. The impulsive noise is discarded by filtering. Finally, the filtered SLF is binarized by comparing each pixel with threshold.

a: OPTIMIZATION
In the low rank optimization method, x n (n = 1, 2, . . . , N ) are relaxed to real values satisfying 0 ≤ x n ≤ 1. From (2), x n satisfies the following equations: We assume that A 2 is a rectangular area with W 1 × W 2 [m 2 ] and it is divided it into N 1 × N 2 pixels with a size of δ × δ [m 2 ]. We define Z = [z n 1 ,n 2 ] 1≤n 1 ≤N 1 ,1≤n 2 ≤N 2 as z n 1 ,n 2 = x n 1 +(n 2 −1)N 1 , i.e., Z is a matricization of x. We assume that Z is an approximately low rank matrix. For a givenq, Z can be estimated by using a nuclear norm optimization with total variation [41]:    = [φ i 1 ,i 2 ] 1≤i 1 ,i 2 ≤N 1 and = [ψ j 1 ,j 2 ] 1≤j 1 ,j 2 ≤N 2 are given by To discard impulsive noise, we apply a two dimensional median filter to the estimated SLF Z (LR) = [z (LR) n 1 ,n 2 ] 1≤n 1 ≤N 1 ,1≤n 2 ≤N 2 with the nuclear norm optimization (3). The median filtered SLF Z (Med) = [z (Med) n 1 ,n 2 ] is given by [42] z (Med) n 1 ,n 2 = median{z (LR) where W represents a window. In this study, we adopt the (3 × 3) window. The median filter is a non-linear filter and is beneficial for eliminating impulsive noise.

V. PERFORMANCE EVALUATION A. SIMULATION ENVIRONMENT
In this section, we evaluate the performance of the proposed binary RTI method with simulation experiments. Fig. 5 [6] adopted a simplified simulation model for factory environments, where only flat and slowly curved surfaces of scatters are supported. Moreover, the materials of the walls, floor, and ceiling are assumed to be perfect electrical conductors (PECs). In this study, we adopt a similar simplified model with simple shaped objects in the rectangular area, and assume that all the objects, walls, and ceiling are PECs, and the floor is concrete. MTs are randomly placed within the movable area in the figure and we set h MT = 2.0 [m]. Radio channels between APs and MTs are generated with EEM-RTM [44], which is a ray-launchingbased radio propagation simulator.
Note that the localization error affects the performance of the proposed method becauseθ LOS (i m , j m ) and τ LOS (i m , j m ) (m = 1, 2, . . . , M ) are computed from position r (MT) j m of MT j m , as described in section IV-A. However, in this study, we do not consider the localization error. More specifically, we assume an ideal situation where all MTs are perfectly localized. The reason is that the aim of this study is to demonstrate the basic performance of the binary RTI. In the future research, we will consider a joint localization and RTI method, which combines the binary RTI method with a localization algorithm. VOLUME 11, 2023 Table 2 presents the parameters for radio signals. For each received signal, we added a noise with power Bk B × T 0 × N F , where B represents the bandwidth of the signal, k B = 1.381 × 10 −23 , T 0 = 290 K, and N F = 9 dB. We implement the proposed RTI method using MATLAB R2022b [45].
Note that we do not compare the performance of the proposed binary RTI method with other RTI methods because to the best of our knowledge, there are no RTI methods with binarized SLFs. Instead, we compare two approaches for the binary RTI method, i.e., the simple and low rank approximation methods.

1) PERFORMANCE OF LOS/NLOS IDENTIFICATION
We first evaluate the performance of the LOS/NLOS identification method with 2D MUSIC. The number T of received signals to compute a correlation matrix R is set to T = 30. The LOS/NLOS identification is conducted for N all = 6000 AP-MT pairs of an AP and MT, where MTs are randomly placed within the area. Fig. 6 presents examples of the MUSIC spectrum P (dB) MUSIC (θ, τ ) = 10 log 10 P MUSIC (θ, τ ) for LOS (Fig. 6a) and NLOS (Fig. 6b) environments. In both figures, there are peaks which corresponds to AoAs and ToAs of multipath components. The red lines represents (θ LOS (i m , j m ),τ LOS (i m , j m )). In Fig. 6a, we observe that there is a peak at the same AoA and ToA as the red line, which means that there is a peak at (θ LOS (i m , j m ),τ LOS (i m , j m )) in the case of the LOS environment. Therefore, we can identify LOS/NLOS by comparing the spectrum at (θ LOS (i m , j m ),τ LOS (i m , j m )) with threshold P th .
Let N LOS and N NLOS denote the number of LOS and NLOS paths, respectively, where N LOS + N NLOS = N all , and N FP and N FN denote the number of NLOS paths identified as LOS paths and the number of LOS paths identified as NLOS paths, respectively. We define the false positive rate FPR and false negative rate FNR as Additionally, we also observe that FPR for N A = 2, 4, 8 are almost the same and FNR are slightly increased with N A . Therefore, in the following simulation results, we set N A = 2. We evaluate the performance of the SLF estimation methods for P (dB) th = 20 and 30. When P (dB) th = 20, both FPR and FNR are smaller than 10 −1 . On the other hand, when P (dB) th = 30, FPR is smaller than 10 −2 , but FNR is larger than 10 −1 .

2) PERFORMANCE OF SLF ESTIMATION
We conduct the simple and low rank approximation methods by randomly selecting M = 700 AP-MT pairs. Fig. 8 presents SLFs estimated with the simple method. Figs. 8a and 8b correspond to the SLFs for P (dB) th = 20 and 30, respectively. By comparing Figs. 5 and 8, we observe that the simple method can estimate the SLF. However, the estimated SLF includes impulsive noise because some pixels are not included on any measurement path. We also observe that the estimated SLF for P (dB) th = 30 includes impulsive noise in more pixels than that for P (dB) th = 20. The reason is that when P (dB) th = 30, more false negative errors are included in the LOS/NLOS identification, as illustrated in Fig. 7. Specifically, many LOS paths are identified as NLOS paths.
Estimated SLFs with the low rank optimization method with P (dB) th = 20 are presented in upper subfigures of Fig. 9, where Figs. 9a, 9b, and 9c correspond to Z (LR) , Z (Med) , and Z (Bin) , respectively. We set γ = 0.1 for the nuclear optimization. We observe that Z (LR) is similar to the SLF in Fig. 8a, which is an estimated SLF by the simple method. However, the impulsive noise can be reduced via median filtering because the SLF is relaxed to real values. As depicted in Fig. 9b, almost all pixels with impulsive noise are discarded in Z (Med) . Fig. 10a presents the empirical probability density function (EPDF) of Z (Med) . As illustrated in the figure, EPDF is a bimodal distribution, where the lower clump corresponds to pixels without any objects and the higher clump corresponds to pixels that may include physical objects. Therefore, we can apply the Otsu's threshold selection, to binarize the pixels. Fig. 9c presents the binarized SLF Z (Bin) . We observe that the low rank approximation method can obtain a finer SLF than the simple method.
Estimated SLFs with the low rank optimization method with P (dB) th = 30 are presented in lower subfigures of Fig. 9, where Figs. 9d, 9e, and 9f correspond to Z (LR) , Z (Med) , and Z (Bin) , respectively. Since the LOS/NLOS identification with P (dB) th = 30 exhibits a higher false negative rate and the nuclear optimization reduces the rank of Z (LR) , Z (LR) in Fig. 9d includes more pixels with smaller non-zeros values than in Z (LR) in Fig. 9a. Therefore, although impulsive noise can be removed by median filtering, Z (Med) in Fig. 9e also includes pixels with smaller values than Z (Med) in Fig. 9b. The result affects the performance of binarization. Fig. 10b presents the EPDF of Z (Med) for P (dB) th = 30, which is a bimodal distribution as Z (Med) for P (dB) th = 20. However, because it is a more spread distribution, it is difficult to discriminate the two clumps with an adequate threshold. Therefore, as shown in Fig. 9f, most of the pixels are decided to be zero.

VI. CONCLUSION
In this study, we have investigated SLF estimation in factory environments, where there are several metallic objects, metallic walls, and a metallic ceiling, which cause a severe multipath fading channel. To estimate the SLF in such a severe environment, we proposed the binary RTI method, where elements in a SLF are binarized. The simulation results demonstrate that the binary RTI method can estimate the SLF by combining it with the 2D MUSIC-based LOS/NLOS identification. We have evaluated the estimated SLFs for threshold parameter P  VOLUME 11, 2023 Since the purpose of this study is to propose the idea of the binary RTI method and evaluate its basic performance, certain unresolved issues remain in this research: • Although we adopt the 2D MUSIC method, there have been some techniques for LOS/NLOS identification [46], [47]. The LOS/NLOS identification is a crucial and difficult research topic that should be investigated by considering these existing techniques.
• In the LOS/NLOS identification, we assumed that MTs are perfectly localized by a localization scheme, such as a LiDAR-based localization technique. However, this is not cost-effective because additional hardware for LiDAR is required. We will consider localization techniques based on radio signals for the binary RTI method.
• We have two methods to estimated SLFs: the simple greedy method and the low-rank optimization method. The former method is simple; however, it cannot completely remove impulsive noise in the estimated SLF. On the other hand, the latter method can obtain a finer SLF than the former method; however, it requires a significant computational cost especially for the nuclear optimization. To implement a more cost-effective and accurate estimator, we need to investigate other approaches.
• The estimated binarized SLF can be adopted for designing wireless networks in factory environments such as relay node placement techniques [48].
• More sophisticated network designs can be realized if 3D SLFs are obtained. To do so, the binary RTI problem should be formulated in the 3D space.
We will address these technical issues in our future research.