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This work explores and evaluates the effect of diffuse light reflection on the accuracy of indoor localization systems based on visible light communication (VLC) in a high reflectivity environment using a received signal strength indication (RSSI) technique. The effect of the essential receiver (Rx) and transmitter (Tx) parameters on the localization error with different transmitted LED power and wall reflectivity factors is investigated at the worst Rx coordinates for a directed/overall link. Since this work assumes harsh operating conditions (i.e., a multipath model, high reflectivity surfaces, worst Rx position), an error of ≥ 1.46 m is found. To achieve a localization error in the range of 30 cm under these conditions with moderate LED power (i.e., P = 0.45 W), low reflectivity walls (i.e., ρ = 0.1) should be used, which would enable a localization error of approximately 7 mm at the room’s center.
© 2015 Optical Society of America
1. Introduction
VLC has gained popularity in recent years as a supplement to radio frequency (RF) technology. VLC offers many advantages such as free license bandwidth (BW), an available infrastructure, no interference with surrounding RF circuits, privacy and security [1].
In addition to its primary function as a lighting source, VLC also plays an important role as a communication source. Thus, one of the major considerations that must be taken into account is preventing one function from dominating the other. The use of light emitting diodes (LEDs) as a lighting source can fulfill this criterion and guarantee system efficiency for both functions. LEDs have an extended lifetime, low power consumption, high lighting efficiency, and can be modulated at higher data rates than conventional lighting sources [2].
VLC is used in a variety of applications, including high bit-rate data broadcasting within homes and offices. It is preferable in electromagnetic interference (EMI) sensitive environments like aircraft and hospitals, where the use of RF technology is inappropriate or harmful [3, 4]. Video streaming is possible by virtue of the huge transmission speed of VLC, as previously reported [5], where a 1-Gb/s VLC link was achieved that used a commercial phosphorescent white LED and common avalanche photodiode Rx. Traffic control systems also use VLC to enable vehicle-to-vehicle and infrastructure-to-vehicle communication to increase both the safety and efficiency of the transportation systems [6]. VLC also shows a remarkable response in short-range underwater data transmission [3, 7].
Another interesting research area and promising application of VLC is indoor localization in large buildings like hospitals, railway stations, and shopping malls [3]. Accurate indoor localization is critical for numerous applications, including indoor navigation, location-based services (LBS), asset tracking, autonomous robot control, and personal services [8, 9].
A global positioning system (GPS) is commonly used in outdoor positioning because it provides the maximum coverage capability. However, it has low accuracy in indoor positioning, with an average of meters, which is unsatisfactory [10]. Other systems designed for this purpose can achieve accuracies in the range of a few centimeters, including infrared (IR), ultra-sound, radio frequency identification (RFID), wireless local area network (WLAN), Bluetooth, ultra-wideband (UWB), magnetic, and audible positioning systems [11, 12]. Unfortunately, the performance of these systems is limited by electromagnetic interference, low security, complexity, and the need for additional infrastructure [12, 13]. For these reasons, localization systems based upon VLC are proposed and will be the backbone of this work.
Several algorithms are used to find the target position, including scene analysis, proximity detection, fingerprinting, and triangulation [10]. Triangulation is the most widely used algorithm in indoor VLC localization systems because it provides the optimum performance from the points of view of both accuracy and design [10]. Triangulation uses the geometric properties of a triangle to estimate the target location by measuring the distance from multiple reference points [10]. Distance measurement can be accomplished using RSSI, time of arrival/time difference of arrival (TOA/TDOA), or angle of arrival (AOA) method [14].
RSSI systems are the most popular and are characterized by simplicity and low cost because most of the existing communication devices are capable of measuring the RSS [14]. The RSSI technique requires a knowledge of: 1) the properties of the optical channel, and 2) power of the optical Tx to obtain the target position. The literature shows that numerous VLC localization systems that use RSSI have been proposed and modified [13, 15–20]. It should be mentioned that nearly every study that considered RSSI-VLC localization systems assumed the special case (line-of-sight (LOS) link) during analysis.
In one study [15], the 3D coordinates of the target were calculated using a traditional trilateration process, followed by a compensation process using an angle-gain profile with an error of less than 3 cm. Another system was proposed that used multiple optical Rxs with different orientations to receive the same location code from a single Tx and found the target position with an error of less than 1.5 cm [13]. Jeong et al. investigated the performance of the RSSI technique when the Tx and Rx normal axes were not aligned. They treated this situation by adjusting the measured distance using a normalization process, and the achieved error was about 1.6 cm [20]. An asynchronous indoor positioning system based on VLC was presented that did not require the synchronization of the distributed Txs. It had errors of 17.25 cm assuming direct sunlight exposure and 11.2 cm when indirect sun-light exposure was assumed [17]. Finally, a novel method of frequency assignment was presented for frequency reuse in indoor localization systems based on carrier allocation [18].
As previously mentioned, most of the published studies assumed an LOS model for simple analysis and realization. However, in practical settings, a portion of the light is reflected from different surfaces/objects, and non-line-of-sight (NLOS) communication exists between the Tx and Rx [21, 22]. Although there are systems that have achieved good accuracies experimentally based on LOS communication [15, 20], this is not always the case because the performance of a VLC system dramatically changes with the surrounding environment as a result of reflected light and time delay [22]. In other words, an experimental VLC system can achieve a remarkable localization performance under specific environmental conditions (i.e., surrounding reflections have a minor effect), whereas when it is evaluated in another environment, it shows noticeable error in the localization process. As an example, in [22], the reflected power was only about 6% of the total received power assuming plastic walls, whereas it rose to about 39% in the case of plaster walls. This behavior has a great impact on RSSI systems because the range measurement is directly related to the received signal strength. Therefore, ignoring the diffuse reflection will cause measurement errors, and the accuracy achieved can be severely reduced. Thus, a multi-path model is more appropriate, and NLOS components must be included for accurate localization in different environments.
A few studies have investigated RSSI-VLC localization systems with an NLOS link. In [23], the author calculated the upper accuracy limitation of the RSSI algorithm by deriving the Cramer–Rao bound (CRB). For simplicity, they used the sphere model during analysis and assumed that the channel gain was almost flat under a frequency of 10 MHz. They concluded that the influence of multipath reflections on the CRB could be ignored when the modulation speed was far smaller than the channel cutoff frequency.
In this work, a novel RSSI-VLC localization system based on an LOS/NLOS model is simulated and evaluated using the most common scenario (three bounces) from different surfaces. The evaluation process is completed by investigating the effects of different Tx and Rx parameters on the localization accuracy at the coordinates with the worst operation. The parametric study assumes different power values and surface reflectivity factors.
This paper is organized as follows. Section 2 describes the indoor optical wireless channel model for the LOS, multipath model, signal-to-noise ratio (SNR) expression and shows the positioning algorithm. The simulation results and evaluation process for the localization error are presented in section 3, and section 4 contains the conclusion of this work.
2. LOS/NLOS system model, design, parameters, and specifications
2.1 Directed optical channel model and positioning technique
The received optical power Pr in a LOS link can be expressed by [16]
where Pt is the average transmitted power, R0(φ) is the radiant angle intensity at radiation angle φ with respect to the Tx normal, d0 is the Euclidean distance between the Tx and the Rx, and θ is the angle of incidence with respect to the Rx normal, as depicted in Fig. 1. Aeff is the effective signal collection area and is given by [21]where A is the detector’s physical area, Ts(θ) is the optical filter gain, g(θ) is the concentrator gain, and FOV is the Rx’s field of view. The emission from an LED can be reasonably modeled as a Lambertian emission [21]. Thus, R0(φ) can be expressed as [21]where m is the mode number of an LED, and its value indicates the Tx directivity. It is related to φ1/2, the Tx semi-angle at half-power by [21]Then, the optical power received from a directed channel can be written as [21]Let the normal axes of an LED and Rx be parallel, as shown in Fig. 1. Then, Eq. (5) can be written as [23]where h is the vertical distance between the LED and photodiode (PD). The output electrical power from the PD is equal towhere R is the PD responsivity. The output electrical power from the PD can be written asThe distance between the LED and the Rx can be obtained usingThe Rx position can be estimated by finding the distance between the Rx and at least three Txs using the trilateration process [16]. The equations used for trilateration are as follows:where xi, yi, and zi are the coordinates of the ith LED, and xR, yR, and zR are the coordinates of the Rx to be estimated [16]. Subtract the second and third equations from the first equation given in Eq. (10). Because the LEDs are installed at the same height (z1 = z2 = z3), the two equations that result can be expressed in matrix form [16]:This basic form can be solved using the linear least squares method [24].2.2 Non-directed optical channel model
In an indoor environment, light undergoes multiple reflections between different surfaces/objects before reaching the Rx. Thus, Pr must be extended to include the effect of the NLOS components.
Although light suffers from both specular and diffusive reflections, most reflections are typically diffusive in nature. Therefore, we assume that the interior materials and indoor fixtures are purely diffusive [21]. The radiation intensity pattern emitted by a differential element of an ideal diffuse reflector is independent of the angle of the incident light. It is further assumed that each element has a Lambertian radiation pattern [25].
Assuming that the walls, floor, and ceiling are composed of small area segments (dA) with Lambertian characteristics, the optical power from all the segments reaching the Rx after k bounces from an LED can be described using [22]
where Nref is the total number of reflections, L represents the path-loss terms for each path, and denotes the power of the reflected rays after 𝑘 bounces. The integration is performed with respect to the surface S of all the reflectors. The PD detects light whose angle of incidence is less than the Rx FOV. A complete set of formulas to find these parameters (i.e., L and ) are given in [22].The following two observations are made at this point in the discussion. First, Pdiffuse is not directly proportional to d0 exclusively as in the directed link case, instead it also varies with other distances (d1 to dk + 1), where d1 is the distance between the LED and the first segment, and dk + 1 is the distance between the kth segment and the PD, as depicted in Fig. 2. Accordingly, the calculated distance will not be the exact value of d0, as indicated in the previous section. Second, the received power increases due to the contribution of NLOS components, as described by Eq. (12). Consequently, it is possible to predict that the calculated distance will be smaller than the real one, as described by Eq. (9).
2.3 SNR modeling
RSSI localization systems are very susceptible to noise [14], which results in higher inaccuracies during distance estimation. In this work, the noise performance will be considered. The noise is Gaussian, with a total variance of N, which is given by [26]
Where is the thermal noise variance, and is the shot noise variance due to the background radiation, received signal, and dark current [23]. Finally, represents the inter-symbol interference (ISI) caused by the optical path difference. Thus, the electrical SNR is given by [26]The shot and thermal noise equations and parameters are calculated using the noise model and parameters listed in [23]. The parameter values are listed in Table 1. The effect of ISI can be ignored for two reasons. First, localization systems require low data rates for sending LED and system information [8, 17]. Second, ISI can potentially be encountered in large rooms (e.g., conference halls), where the differences in the optical paths become significant with respect to the symbol length [27], which is a case that is not considered here.
Table 1. Noise Parameter Values
2.4 System design, parameters, and specifications
This work assumes the famous configuration of a 5 × 5 × 3 m3 empty room, where multiple reflections occur between the plaster walls, ceiling, and floor. There are four LED lights that work together as an access point mounted at a height of 2.5 m, and each has a different frequency carrier to mitigate the effect of inter-cell interference [28]. The center positions of these ceiling lights are (1.25, 1.25, 2.5), (1.25, 3.75, 2.5), (3.75, 1.25, 2.5), and (3.75, 3.75, 2.5). The different LED parameters are listed in Table 2, using the values used in [25]. These values ensure both proper lighting and the communication process [25]. The user terminal is assumed to be at the desk level at a height of 0.85 m, as shown in Fig. 3. Intensity modulation and direct detection method is used due to the simple implementation of a low-cost Rx [28].
Table 2. Summary of Relevant Parameters
3. Simulation results and discussion
3.1 Introduction
This section contains the simulation results of the proposed work, starting with the power distributions for both cases (LOS/NLOS) in section 3.2, followed by the SNR distribution around the room in section 3.3. The localization error around the room is investigated considering the effect of diffuse reflection in section 3.4. Finally, the results of a localization error analysis under different Rx and Tx parameters are presented using various transmitted power values and wall reflectivity factors in sections 3.5 and 3.6, respectively.
3.2 Power distribution and normalized impulse response
The received power distribution at the desk level, including the LOS and 1st to 3rd reflection values, as well as their total, is shown in Fig. 4. The receiving surface is divided into small 20 × 20 cm segments, which form a grid. This distribution is produced by applying predefined parameter values to the mathematical model (Eqs. (5) and (12)).
Fig. 4 Received optical power due to (a) LOS path, (b) first reflection, (c) second reflection, (d) third reflection, (e) total diffuse power, and (f) overall link.
Based on this figure, the strongest LOS components are under the four lighting sources and gradually fall as the Rx moves to the four corners. The received power varies from 0.14 mW at the corner of the room to 0.64 mW under the ceiling lights along inside the room, as shown in Fig. 4(a). Adding the NLOS components will raise the total received power from 0.15 to 0.77 mW, as shown in Fig. 4(f). Most of the increased power due to the NLOS is concentrated near the walls because of the influence of reflection, as indicated in Fig. 4(b) to Fig. 4(e). Thus, an Rx located at the room’s corner will absorb the lowest LOS power and the strongest diffuse power, as indicated in Fig. 4(a) and Fig. 4(e).
Finally, at a corner of the room (0.2, 0.2, 0.85), the power from the LOS path is 0.19 mW, while the diffuse power received is 0.16 mW (about 45% of the total received power), which presents the maximum contribution to the total received power among all the positions.
Key information about the power received in the case of the LOS and overall (LOS and NLOS) scenarios extracted from Fig. 4 is presented in Table 3. This information includes the maximum, minimum, and average power values and their corresponding coordinates for the LOS and overall (LOS and NLOS) scenarios.
Table 3. Summary of Received Optical Power
Figure 5 shows the impulse response at Rx position (0.2, 0.2, 0.85), which is defined as the sum of the directed signals received from the lighting sources and reflected signals from different sources to an Rx positioned at this point. Rx position (0.2, 0.2, 0.85) is of interest because it represents the point at which the contribution of diffuse power is the maximum, as indicated in the previous discussion. Taking Δt = 0.2 ns as the bin width of the power histogram, the first peak is mainly due to the nearest LED light (1.25, 1.25, 2.5), and it contributes the major response to the impulse response. The other peaks are mainly due to direct paths from far LED lights and dispersed signals from reflected paths (i.e., walls, ceiling, and floor). Compared with the first peak, the far sources and dispersed signals contribute more delay to the impulse response because of elongated tail high-order reflections.
3.3 SNR distribution
Figure 6 shows the SNR distribution for the LOS/NLOS and the overall link for a quadrant of the room (since the room and lighting geometry are symmetrical). Noise parameters are listed in Table 1, based on the mathematical model described in section 2.3. The SNR has the same distribution as that of the received power for different cases, as illustrated in Fig. 4. The SNR due to the total received power is a slightly modified version of that for the LOS link because it represents the dominant link. The SNR becomes worse as the Rx moves from the center of the room toward the corner to reach its worst case (SNR = 32 dB). The SNR from the total received power is about 2.4 dB higher than that in the case where only the LOS components are assumed.
Fig. 6 SNR distribution across quadrant of room in case of (a) LOS, (b) diffuse, and (c) overall (LOS/NLOS) link.
3.4 RSSI localization error
The localization error is estimated at every possible Rx position at desk level in the case of the LOS link and overall link (LOS and NLOS) in Fig. 7 based on a trilateration process using the parameters listed in Table 2. To investigate the relation between the SNR and the localization error, Fig. 6 and Fig. 7 should be reviewed at the same time.
Fig. 7 Localization error distribution at different Rx positions due to (a) LOS link and (b) overall link.
For the LOS scenario, the main factor that controls the localization accuracy is the SNR, as will be discussed here. Figure 7(a) provides the relation between the SNR and localization error. Figure 6(a) shows that the best SNR lies at the room’s center. Thus, the minimum localization error obtained is at the room’s center (0.18 mm), as shown in Fig. 7(a). Figure 6(a) indicates that the minimum SNR achieved is at the room’s corner, which results in the worst localization error recorded (14.06 cm), as indicated by Fig. 7(a). In addition, one can observe from Fig. 6(a), that the SNR is enhanced as the Rx moves toward the room’s center. This behavior reflects the localization error in Fig. 7(a), which shows that the localization error decreases when the Rx is moving toward the room’s center.
The situation becomes more complex when dealing with the overall link (LOS/NLOS) because the diffuse power should be taken into consideration when exploring the relation between the SNR and localization error for the overall scenario. As seen in Fig. 4(e, f) and Fig. 6(c), at the room’s center, the diffuse reflection has a minor effect, while the SNR is at its maximum level. This leads to the minimum localization error at the room’s center (error = 6 cm), as shown in Fig. 7(b). As the Rx moves away from the room’s center, the localization error becomes significant, until it reaches its maximum value (1.52 m) at the worst operating coordinates (0.2, 0.2), as shown in Fig. 7(b). This result agrees with the discussion presented in section 3.2, which indicated that the maximum absorbed diffuse power lies at (0.2, 0.2), and Fig. 6(c), which shows that the minimum SNR occurs at the room’s corner. This analysis will focus on an Rx positioned at (0.2, 0.2, 0.85) because this represents the worst case scenario.
3.5 Performance evaluation of localization error with transmitted power
The effects of the Rx FOV, Rx noise BW, Rx height, and Tx semi-angle on the localization error at different transmitted LED power values are explored in the cases of the LOS link and overall link (LOS and NLOS). In the case of the LOS link (ρ = 0), the localization error recorded will be due to the noise effect only, and it indicates the upper accuracy limit on the overall link. To obtain the following behavior for both cases, the system configuration in section 2.4 and the noise parameters values given in Table 1 will be used, assuming that the Rx is positioned at (0.2, 0.2, 0.85), which represents the worst case scenario. As a general rule, the localization error is decreased with an increase in the transmitted power, as the noise contribution is decaying.
3.5.1 Effect of Rx FOV on localization error
For a correct trilateration process at all positions inside the room, the Rx must receive signals from at least three sources. When applied to the room configuration of this work, the Rx FOV must satisfy the following criterion:
where rSi is the ith LED position coordinates, and rR is the position coordinates of the Rx. The FOV at an Rx needs to be larger than 67.3°. Figure 8(a) shows the performance of the localization error with the transmitted optical power per LED for the LOS (FOV = 70°), while Fig. 8(b) shows the overall link case at different Rx FOV values.Fig. 8 Localization error values for different Rx FOV values at (0.2, 0.2, 0.85) for (a) LOS link and (b) overall link.
The results show that a larger FOV will produce a larger localization error, which is caused by the definition of the FOV, in which more diffuse power is absorbed. A small angle of acceptance provides a better performance because the diffuse power is decreased. However, even working with the smallest allowed FOV (FOV70°), the localization system has a very poor performance, as indicated in Fig. 8(b).
To investigate the large localization error difference between FOV = 75° and 80°, Table 4 is presented. Table 4 lists the amounts of diffuse power absorbed from the nearest three LEDs at the Rx position (0.2, 0.2). Two samples are taken from Fig. 8(b), with transmitted power per LED values of 0.1 and 0.5 W.
Table 4. Received Power Values from Nearest Three LEDs at Different Rx FOV Values
Based on Table 4, the difference between the amounts of diffuse power absorbed from the LEDs for the two samples at FOV = 70° and 75° is small. Thus, the localization error difference is also small. Based on Table 4, the amounts of diffuse power absorbed from the LEDs for the two samples at FOV = 75° and 80° are large. Thus, the localization error difference is also large. Finally, the values listed in Table 4 show that the amounts of diffuse power absorbed from the LEDs for the two samples at FOV = 80°, 85°, and 90° are close. Thus, the localization error difference is also small.
3.5.2 Effect of Rx noise BW on localization error
Figure 9(a) shows the performance of the localization error for the LOS link, while Fig. 9(b) shows the error in the case of the overall link at different Rx noise BWs. Based on these figures, we can make the following observations. First, for the LOS scenario (Fig. 9(a)), it is observed that for lower Rx noise BWs (less than 100 MHz), it is possible to obtain an error free positioning process, whereas this is not the case in the overall configuration scenario, where an error of 1.52 m is observed, as shown in Fig. 9(b). Second, for higher Rx noise BWs (larger than 100 MHz), the effect of noise becomes obvious in the case of the LOS link at lower transmitted power regions. Third, for very high noise BWs (i.e., BW 500 MHz), the performance of the localization system is extremely degraded, even for the LOS link at low LED power.
Fig. 9 Localization error for different Rx noise BWs at (0.2, 0.2, 0.85) for (a) LOS link and (b) overall link.
3.5.3 Effect of Rx height on localization error
The minimum distance (h) required for a correct trilateration process at any location can be calculated using Eq. (15). At FOV = 70°, the minimum distance is found to be 1.44 m (i.e., the maximum height allowed for the Rx is 1.06 m). At first glance, it seems that as the distance between the Tx and the Rx (h) decreases, the localization error should decrease. This fact was emphasized in [23]. Noting that, this behavior was carried out using a uniform ceiling lighting scenario, at which the ceiling lights were uniformly distributed around the room, even at the corners, with a narrow spacing between them, according to the Sparrow criterion [23].
Figure 10(a) shows the localization error near the room’s center (Rx lies between the lights), in a case that resembles uniformly distributed lighting using the configuration introduced in section 2.4, which shows a similar behavior.
Fig. 10 Localization error at different Rx heights due to (a) LOS link near center and (b) LOS link at corner (0.2, 0.2).
The previous discussion is no longer applicable for an Rx positioned at the room’s corner, as shown in Fig. 10(b). This performance is mainly caused by the Rx effective area (Aeff). As the Rx height increases at the corner, the incidence angle (θ) increases (Fig. 1). This decreases Aeff, as indicated by Eq. (2), which has the priority to control the power level at the room’s corner, especially from far sources, as shown by Eq. (5). Thus, the noise level will grow at higher Rx positions, and the localization error will increase. Figure 10(b) indicates that the largest error obtained is at the highest Rx position or equivalently at the lowest distance (h). It is apparent that the localization error at the center is much smaller than that at the corner, as indicated by Fig. 10(a) and (b), due to the SNR distribution (Fig. 6(a)).
Figure 11 shows the localization error due to the overall link. Its behavior is similar to that of the LOS link at the room’s corner (Fig. 10(b)), but the error is incredibly worse due to the effect of diffuse power.
3.5.4 Effect of Tx semi-radiation angle (θ1/2) on localization error
The performance of the localization error with the transmitted optical power for different Tx semi-angles (θ1/2) will be examined. For the LOS scenario (Fig. 12 (a)), it is observed that a worst case bound is found at θ1/2 = 30°, where the system falls and records an error of 2.2 m at 0.1 W. It can be noted that, for this scenario, a higher Tx semi-angle will result in a better localization accuracy, especially at a higher transmitted power. It is true that as the angle is minimized, the Tx directivity is increased, but at the expense of the Tx concentration area (Fig. 1). This work assumes distinct ceiling lights, where the concentration areas of the Txs are separate (directly under the source) and overlap at the room’s center. As the Rx moves to the corner, the overlapping area vanishes, as discussed and seen in Fig. 4(a). Thus, the noise is accumulated at the room’s corner, especially at lower Tx semi-angles, which decreases the localization accuracy. This result represents the inverse of that included in [23], because as previously stated, that study [23] assumed uniform lighting, where the Rx was always located at the concentration area of the adjacent Txs, even at the room’s corner.
Fig. 12 Localization error for different Tx semi-radiation angles at (0.2, 0.2) due to (a) LOS link and (b) overall link.
For the overall scenario shown in Fig. 12(b), an important observation is made at higher semi-angles (i.e., θ1/2 = 70° and 80°). At these values, an inverted behavior to that of the LOS is presented. This is caused by the nature of the reflections, which accumulate with an increase in the Tx semi-angle.
To investigate why the localization error at θ1/2 = 30° is the maximum, as shown in Fig. 12(b), the following discussion and Table 5 are presented. As the LED semi-radiation angle (θ1/2) becomes narrower, more power is concentrated in a limited area (Fig. 1). Thus, at low radiation angles, the Rx receives a good power level from the nearest LED (LED1) and low power from the other two LEDs (LED2 & LED3). This causes the percentage of the diffuse power received from LED2 & LED3 for the corresponding LOS to be very large. Thus, the localization error is very large in the case of a very low theta value (θ1/2 = 30°).
Table 5. Received Power Values from Nearest Three LEDs at Different Tx Semi-radiation Angles (θ1/2)
Table 5 verifies the previous discussion. It shows the amount of LOS received power and the corresponding amount of diffuse power absorbed from the nearest three LEDs at an Rx positioned at (0.2, 0.2), for an LED transmitted power of 0.1 W. The last column shows the ratio between the diffuse power and LOS power received from the three LEDs. Based on this, it is apparent that, at θ1/2 = 30°, the ratio is the smallest when receiving from LED1 compared to the other theta values (0.4), while the ratio is extremely large (8.71) when receiving from LED2 & LED3. Recall that, the trilateration requires the power received from three LEDs simultaneously. Thus, the localization error when operating at θ1/2 = 30° is the largest.
3.6 Performance evaluation of localization error with wall reflectivity
This section discusses the effects of the Rx FOV, Rx noise BW, Rx height, and Tx semi-radiation angle on the localization error, assuming different wall reflectivity factors. The Rx is positioned at (0.2, 0.2), which represents the worst case scenario. At first sight, the curves are increasing with the reflectivity as more diffuse power reaches the Rx, and thus the localization error is increased. The obtained result is consistent with the results obtained in section 3.5, as follows.
Figure 13(a) shows an increase in the localization error with a widening of the Rx FOV because more diffuse power is absorbed, as indicated in section 3.5.1.
Fig. 13 Localization error at different wall reflectivities when Rx is positioned at (0.2, 0.2) for different (a) Rx FOVs, (b) noise BWs, (c) Rx heights, and (d)Tx semi-radiation angles (θ1/2).
The Rx noise has a negative impact on the localization process, as illustrated in Fig. 13(b). As the noise BW increases, the error worsens. For low noise BWs (i.e., less than 100 MHz), the error is identical to the case in Fig. 9(b) and achieves an error of 0.36 m at a reflectivity of 0.1.
As the receiver height increases, the error increases, as explained in section 3.5.3. Figure 13(c) shows this result. The minimum recorded error is at an Rx positioned at the ground level (h = 2.5 m), recording an error of 0.34 m at a wall reflectivity of 0.1.
Figure 13(d) shows the localization error assuming different Tx semi-radiation angles (θ1/2). The localization error has the same behavior as illustrated in section 3.5.4. At a low reflectivity (ρ = 0.1), the behavior is similar to the LOS link previously studied (Fig. 12(a)), in which the error increases when the Tx semi-radiation angle becomes narrower. As the reflectivity increases, the diffuse power is accumulated, and the localization accuracy is severely reduced, especially at higher semi-radiation angles (i.e. θ1/2 = 70° and 80°) because more power is reflected. This situation is also emphasized in Fig. 12(b).
4. Conclusion
This work explored the effect of diffuse reflection (NLOS components) on an RSSI-VLC-based localization system in a high-reflectivity environment (i.e., plaster walls with ρ = 0.8), using a distinct distribution of ceiling lights in the famous 5 × 5 × 3 m3 room configuration. Calculations found that the mean error was 68 cm, while the worst operating coordinates lay at (0.2, 0.2, 0.85), which produced a localization error of 1.52 m.
Diffuse reflection had a great impact on the localization error. For example, at the worst operating coordinates, the localization error was estimated to be 2 cm in the case of LOS, whereas it increased to 1.52 m in the case that included the effect of multipath propagation under the following specifications: a transmitted LED power of 1 W, 60° half-power transmitting angle, Rx with 70° FOV, 400 MHz noise BW, and walls with a reflectivity of 0.8.
Because this work assumed a harsh localization operating environment (i.e., a multipath model, high reflectivity surfaces, and the worst operating Rx position), it was found that regardless of the Tx and Rx parameters, the lowest localization error was ≥ 1.46 m.
To achieve a localization error of around 30 cm with the previous conditions and moderate LED power (i.e., 0.45 W) when the Rx is positioned at the worst operating coordinates, low reflectivity walls (i.e., ρ = 0.1) should be used. The localization error was greatly enhanced (i.e., 7 mm) when moving away from the worst operating Rx position (room’s corner) toward the room’s center while maintaining low reflectivity walls.
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