Toward Smart Factories: Modelling Hybrid RF and VLC Communication Channels for IIoT Applications

Wireless network access has no end.  The development of IIoT devices will continue to increase demand for wireless access networks [1]. The ongoing transformation towards the industrial metaverse extends and expands the domain of communication beyond traditional IIoT applications. This transformation changes what can be connected and how we create and interact with Immersive Virtual Environments (IVE) compared to the current approach, under the line of advancement of technologies such as Artificial Intelligence (AI) [2]. The physical and digital realms merging, that's the heart of the industrial metaverse, and we’re seeing unprecedented collaboration, innovation, and interaction across boundaries of distance and discipline.

One crucial factor in taking this step is the improvement of communication between Programmable Logic Controllers (PLCs) and robots, to form independent and interoperable networks. These networks enable near-autonomous data sharing between things and virtual worlds with reduced or no human interaction [3].

Intelligent systems and devices that transfer, process, and respond to information in real-time are the key to this integration. Of these, Cobots shine as representative examples. Intended to work in collaboration with people in physical and virtual worlds, Cobots represent the integration of cyber-physical systems that can enhance the efficiency and safety of deployment [4]. Nevertheless, operating such platforms in regulated settings with strict data privacy and security requirements necessitate a more in-depth analysis of IIoT implementation tactics for compliance guarantee.

Wi-Fi, Bluetooth Classic, and Bluetooth Low Energy (BLE) technologies are commonly utilized in everyday applications. However, in indoor locations with a high density of mobile devices, the RF band will become saturated, and Wi-Fi users will frequently experience significant contention and interference.  To address this issue, new technologies like VLC can be employed. VLC is expected to become the next complementary medium for indoor high-speed Internet and IIoT applications [5]. It enables the usage of energy efficient lighting luminaries [6], particularly the Light Emitting Diodes (LEDs) as high-speed data Access Points (APs) offers a complement to RF, the bandwidth of light is virtually unlimited. Local power-line infrastructure can be used as backbone [7-9]. The deployment of VLC is an excellent solution for indoor environments such as high-security smart buildings where high-speed data is communicated via modulation [10].

An aggregated Wi-Fi/VLC system combining a Wi-Fi and a VLC link was previously demonstrated in the study [11]. The overall aim of the study [12] is not merely to point out the most effective communication protocols for Cobot interaction but also to establish a foundational framework for specific applications and spearhead future innovations in IIoT applications. The authors [13] concentrate on upgrading the traffic system for the Intelligent Transportation System (ITS). In the study [14], the authors describe a light fidelity (Li-Fi)/femtocell hybrid network system for indoor environments. In the study [15], an indoor hybrid system that combines Wi-Fi and VLC luminaires was developed. It employs (1) broadcast VLC channels to supplement RF communications, and (2) a handover mechanism between Wi-Fi and VLC to dynamically divide resources and improve system throughput.

A natural downlink is typically provided by lights installed on the ceiling. Therefore, the uplink remains one of the most significant challenges in VLC. Transmitting data via VLC toward the ceiling is generally considered impractical. It also causes discomfort. One of the solutions is to shift the VLC emitter and receiver from the ceiling to the walls, but this would also affect the interior design of the environment [16]. Li-Fi is a subclass or specialized implementation of VLC that allows for high-speed, two-way, networked wireless communication via visible light.

In this work, a hybrid communication system is proposed to solve the uplink problem: that is, to use RF as the uplink, and VLC and RF as the downlink. The authors focus mainly on the modelling of the optical wireless channel and the conventional radio-wave wireless channel for IIoT. It is highly expected that future smartphones will include a VLC transceiver. Therefore, a combined mathematical model that utilizes both the VLC and Wi-Fi channels simultaneously to achieve high-speed data transfer and support the evolving demands of industrial automation is proposed.

The remainder of this paper is organized as follows: In section 2, the proposed industrial environment modelling for smart manufacturing is described. In section 3, the Hybrid VLC/RF channel Modelling in Industry 4.0 is presented under Co-Channel Interference (CCI) and with Non-Co Channel Interference (N-CCI) Conditions. Section 4 discusses and evaluates the performance of the proposed system conducted BER analysis in OOK modulation, multi-user access, received power distribution, and hybrid VLC/Wi-Fi channels. Finally, a conclusion is given in section 5.

According to the study [18], the LED optical Line of Sight (LOS) channel is characterized by Eq. (1) as follows:

$H(0)_{\text {LOS }}= \begin{cases}\frac{m+1}{2 \pi d^2} A \cos ^m(\phi) \cos (\psi), 0 \leq \psi \leq \psi_c \\ 0, \quad\quad\quad\quad\quad\quad\quad\psi>\psi_c\end{cases}$                        (1)

where, $A$ denotes the active area of the photodiode, $\psi$ represents the incidence' angle relative to the receiver axis, $\psi_c$ defines the detector's Field of View (FOV), $d$ refers to the distance separating the transmitter and the receiver, and $\phi$ denotes the angle of irradiance measured relative to the transmitter's perpendicular axis. The Lambertian order $m$ is expressed as $m=\frac{-\ln 2}{\ln \left(\cos \phi_{\frac{1}{2}}\right)}$ where the half power angle of the LED is given by $\phi_{\frac{1}{2}}$.

The total optical power of i LEDs is given in Eq. (2):

$P_{r x, L O S}=\sum_{i=1}^{L E D s} P_{t x} H_{L O S}^i(0)$                      (2)

where, $H_{\text {LOS }}^i$ is $i-t h$ LED channel DC gain, $P_{t x}$ is the transmitted optical power from LED.

We utilize the same strategy for modelling optical wireless non-Line of Sight (NLOS) signals as used for the sphere model [16]. In a room, the first diffuse reflection of a widebeam optical source emits an intensity $I_1$ over the entire surface $A_{room}$, as described by Eq. (3).

$I_l=\rho_l \frac{P_{{totalLED}}}{A_{\text {room}}}$                     (3)

where, the reflectivity of the surface and the total power of all the LEDs are expressed by $\rho_1$ and $P_{\text {totalLED}}$, respectively.

The average reflectivity $<\rho>$ is defined by Eq. (4).

$<\rho>=\frac{1}{A_{\text {room }}} \sum_i A_i \rho_i$                        (4)

where, $<\rho>$ denotes the area-weighted reflectivity of the ceiling, walls, floor, and other objects in the room, with A_i representing their respective surface areas.

As a result, the total intensity is calculated in Eq. (5) by summing a geometric series.

$I=I_l \sum_{j=1}^{\infty}\langle\rho\rangle^{j-1}=\frac{I_l}{1-<\rho>}$                      (5)

Such as the reflections number is expressed by j.

Considering the receiver as a small surface element within the room, the NLOS received power $P_{\text {NLOS }}$ and its corresponding area $A_{r x}$ are provided in Eq. (6).

$P_{N L O S}=A_{i x} I$                    (6)

Therefore, the NLOS channel loss is defined by Eq. (7):

$\eta_{\text {NLOS }}=\frac{P_{\text {NLOS }}}{P_{\text {totalLED }}}=\frac{A_{r x}}{A_{\text {room }}} \frac{\rho_l}{1-\langle\rho\rangle}$                       (7)

3.1 Superposition of LOS and NLOS channels

The received power is given by:

$P_{r x}=\left(P_{L O S}+P_{N L O S}\right) * T_s(\psi)^* g(\psi)$                       (8)

Such as the gain of the optical filter and the gain of the optical concentrator are expressed by $T_s(\psi)$ and $g(\psi)$, respectively.

Therefore, according to Eq. (9), the gain of combined channel [19] is given as follows:

$H_{N L O S+L O S}(f)=H(0)_{L O S}+H_{N L O S}(f) e^{j 2 \pi f \Delta T}$                       (9)

where, $\Delta T$ is the delay between the onset of the NLOS signal and the LOS signal.

The gain of the optical concentrator $g(\psi)$ is given by [20]:

$g(\psi)= \begin{cases}\frac{\eta_c^2}{\sin ^2\left(\psi_c\right)}, & 0 \leq \psi \leq \psi_c \\ 0, & \psi>\psi_c\end{cases}$                   (10)

where, $\eta_c$ denotes the concentrator refractive index.

In this system, optical OOK-NRZ modulation is employed.

The block diagram of OOK system is illustrated in Figure 3.

3.png

Figure 3. Block diagram of OOK system

The OOK-NRZ modulation envelop is given by Eq. (11).

$p(t)=\left\{\begin{array}{cc}2 P_r & \text { for } t \in\left[0, T_b\right) \\ 0 & \text { elsewhere }\end{array}\right.$                   (11)

where, the average power is expressed by P_r and the bit duration is denoted by T_b.

3.2 Bit error rate (BER)

The probability of error is given as:

$P_e=p(1) \int_0^{i_{t h}} p(i / 1) d i+p(0) \int_{i_{t h}}^{\infty} p(i / 0) d i$                      (12)

where, the level of threshold is presented by i_th, P(1) and P(0) denote probabilities of ‘one’ and ‘zero’, while Eq. (13) defines the marginal probabilities.

$\begin{array}{r}p(i / 0)=\frac{1}{\sqrt{2 \pi \sigma^2}} \exp \left(\frac{-i^2}{2 \sigma^2}\right) \\ p(i / 1)=\frac{1}{\sqrt{2 \pi \sigma^2}} \exp \left(\frac{-\left(i-I_p\right)^2}{2 \sigma^2}\right)\end{array}$                      (13)

Assuming equally probable symbols, i.e., P (0) = P (1) = 0.5, the optimal decision threshold is given by i_th = 0.5I_p, leading to a simplified expression for the conditional probability of error:

$P_e=Q\left(\frac{i_{t h}}{\sigma}\right)$                       (14)

where, Marcum’s Q-function is expressed by Q (), it is the area under the Gaussian curve, it can be computed by Eq. (15).

$Q(x)=\frac{1}{\sqrt{2 \pi}} \int_x^{\infty} e^{-\alpha^2 / 2} d \alpha$                    (15)

When using a matched filter, the output noise variance is entirely governed by the power spectral density (PSD) of the input noise and the total energy of the filter’s impulse response. Consequently, if the input noise is additive white Gaussian noise (AWGN) with a double-sided PSD of N₀/2, the resulting noise variance at the output of the matched filter can be expressed using Eq. (16).

$\sigma^2=\frac{N_0}{2} \int_{t=0}^{T_b} r^2(t) d t$                       (16)

The standard deviation, noted by σ, can be computed using Eq. (17) and Eq. (18), while the average energy per bit E_b is given by Eq. (19).

$\sigma=\sqrt{\frac{N_0 E_p}{2}}$                     (17)

$P_{e_{-} b i t_{-} o O K}=Q\left(\sqrt{\frac{E_b}{N_0}}\right)$                       (18)

$E_b=\frac{E_p}{2}=2\left(R P_r\right)^2 T_b$                        (19)

In the case of OOK-RZ formatting, $E_b$ is increased by a factor of $\frac{1}{\gamma}$ according to Eq. (20) as follows.

$E_b=\frac{E_p}{2}=\left(2\left(R P_r\right)^2 T_b / \gamma\right)$                 (20)

The Signal-to-Noise Ratio (SNR) can be introduced as [21]:

$S N R_{\mu, r}(f)=\frac{\left|G_{\mu, \alpha}(f)\right|^2 P_R}{\sigma^2}$                     (21)

where, the subcarrier transmits power, the variance of additive white Gaussian noise (AWGN), and the channel gain are expressed by P_R, σ2, and G_μ,α(f), respectively. In VLC, for user μ and AP α, the Signal-to-Interference-plus-Noise Ratio (SINR) is expressed as [22]:

$S I N R_{\mu, r}=\frac{\left(\kappa P_{t x} H_{\mu, \alpha}\right)^2}{N_0 B+\Sigma\left(\kappa P_{t x} H_{\mu, e l s e}\right)^2}$                     (22)

Here, κ denotes the conversion optical to electrical efficiency at the receiver side; The noise power spectral density is represented by N₀[A²/Hz]; H_μ,α refers to the gain of the channel between the associated VLC AP and user μ; and H_μ,else denotes the gain of the channel between the interfering VLC AP and user μ; and the LED modulation bandwidth is expressed by B.

3.3 Radio frequency communication channel

Considering an indoor environment where emitters and receivers are more or less stationary, the wireless RF channel can be commonly characterized by [23]:

$h(\tau)=\sum_i a_i \delta\left(t-\tau_i\right)$                    (23)

where, $a_i$ and $\tau_i$ are the attenuation and propagation delay associated with the $i^{\text {th }}$ multipath component, respectively. $\delta$ is the data function.

According studies [24, 25] the indoor path loss in buildings was carefully studied. Although the same three mechanisms (reflection, diffraction, and scattering) are dominated in indoor and outdoor environments, indoor conditions are much more variable. For example, the signal does vary levels greatly in case of opened and closed doors. Also, the position of Wi-Fi antennas has an important impact on receiving signal.

We will only consider losses by hard partitions (e.g., concrete walls and floors which are part of the building structure). They have physical and electrical characteristics which will affect radio paths. For example [26], a concrete wall has been measured to have about 8-15 dB losses, while a concrete floor has a 10 dB loss. In addition, the external dimensions, the building materials and building technology determine losses between floors. The Floor Attenuation Factor (FAF) typically ranges from 13 to 45 dB [17].

Indoor path loss obeys the distance power law. According to the study [27], the loss model can be expressed using Eq. 24 in the case where walls are in a direct path between receiver and transmitter antennas.

$L(d)=L_0+10 n \log d+k F_1+\sum_{i-1}^M A_i$                       (24)

Such as $M$ denotes the partitions number between receiver and transmitter antennas, $A_i$ presents the attenuation factor for the $i^{\text {th }}$ partition, $L(d)$ indicates the path loss over distance $d$ from the transmitter, $L_0$ denotes the propagation attenuation of free space over a reference distance of $1 \mathrm{~m}, n$ is the pathloss exponent, $k$ presents the number of floors between transmitter and receiver antennas and $F_1$ is the single-floor propagation attenuation (floor loss factor).

3.4 Hybrid VLC-RF channel

Since noise components $Z_{v l c}$ and $Z_{r f}$ are independent, the information capacity of the total channel is expressed as in Eq. (25):

$\begin{gathered}C=\max _{p\left(x_{v l c}, x_{r f}\right): \Sigma_{j=1}^k p_j \leq p} I\left(X_{v l c}, X_{v f}, Y_{v l c}, Y_{r f}\right) \\ =\max _{\left\{p_j\right\} \text { s.t. } \sum p_j \leq p} \sum_{j=1}^k \frac{1}{2} \log \left(1+\frac{P_j}{\sigma_j^2}\right)\end{gathered}$                       (25)

Which is achieved if $\left(X_{v l c}, X_{r f}\right) \sim_{\aleph}\left(0 ; \operatorname{dig}\left(P_{v l c}, P_{r f}\right)\right)$.

Lagrange multipliers can be used to solve the power allocation problem since it simplifies to a typical optimization problem.

$\max _{P_j} \sum_{j=1}^k \log \left(1+\frac{P_j}{\sigma_j^2}\right)$                        (26)

subject to $\sum_{j=1}^k P_j=P,\left(P_j \geq 0\right)$                        (27)

where, $U$ is chosen subjected to $\sum_j P_j \leq P$. If channel $j$ is allocated, then its power will be $P_j=U-\sigma_j^2$; otherwise, $P_j=0$. Power is allocated to the channel with the lowest variance, and as the power budget grows, we fill the channels in order of increasing noise variances. At any given time, the total of noise variance and signal strength in the channels in use is $U$.

3.5 Total received power

The total received power is calculated by:

$P_{R T}(d B)=P_{R L E D}(d B)+P_{R R F}(d B)-\operatorname{Loss}_{R F}(d B)$                          (28)

The received RF power is calculated without including the VLC channel as given in:

$P_R(d B)=P_{R R F}(d B)-\operatorname{Loss}_{R F}(d B)$                        (29)

where, $P_{\text {RLED }}$ is the received power of the LED channel in Eq. (8); $P_{R R F}$ is the received power and $\operatorname{Loss}_{R F}$ is the total loss mentioned in Eq. (24). Referring back to Figure 2, Eq. (28) is used for the downlink, while Eq. (29) is used for the uplink.

3.6 Load balancing and dynamic handover

Due to the small coverage area of VLC LEDs, the movement of users can probably prompt handover. A handover happens when a user's serving AP switches between two nearby states.  In general, the handover overhead in an indoor environment is in the millisecond range, which is believed to be less than the state interval T_p [21]. The handover efficiency between two nearby states is defined according to Eq. (30) as follows:

$\eta_{i, j}= \begin{cases}{\left[1-\frac{t_{i, j}}{T_p}\right]^{+}} & , \quad i \neq j \\ & i, j \in C \\ 1, & i=j\end{cases}$                        (30)

Such as t_i,j presents the overhead of AP switch from AP_i to AP_j. The link data rate between AP α and user μ in state n with handover efficiency is given by Eq. (31).

$r_{\mu, \alpha}^{(n)}=\left\{\begin{array}{cc}\eta_{\alpha^{\prime} \alpha} R_0, & \alpha=0 \\ \eta_{\alpha^{\prime} \alpha}^{\prime} R_{\mu, \alpha}^{(n)}, & \alpha=1,2 \ldots N_c\end{array}\right.$                     (31)

where, R⁽ⁿ⁾_μ denotes the data rate of VLC, α′ presents the AP of user μ in the state n−1, η′ describes the handover efficiency from AP α′ to AP α, and R₀ gives the Wi-Fi throughput.

The load balancing algorithm used in each state is expressed using Eq. (32) as follows:

$\gamma_\beta(x)= \begin{cases}\log (x), & \beta=1 \\ \frac{x^{l-\beta}}{l-\beta}, & \beta \geq 0, \quad \beta \neq 1\end{cases}$                   (32)

where, the proportional coefficient is denoted by β. In particular, the maximal system throughput is reached when β = 0 and a linear utility function is realized; proportional fairness is attained when β = 1; and max-min fairness is attained when β → ∞ [21].

In this paper, we have developed a collaborative hybrid VLC/RF system and solutions through a MIMO structure. Improved data transmission in the system with the optical devices’ ultrahigh bandwidths and RF robustness in industrial environments that require secure and stronger data transfer.

The research considered some vital factors such as OOK modulation, BER analysis, and the received optical power distribution, multiuser access system, as well as the hybrid VLC/Wi-Fi network system. The performance of the system was enhanced using frequency reuse planning and Shannon spectral efficiency techniques.

The system gets practical use by using VLC downlink and RF uplink communications for applications involving Cobots and IIoT systems. The arrangement prevents visual discomfort from the source of lighting and increases system consistency at the same time. The results show that the hybrid VLC-RF system provides an effective solution to provide rapid and safe wireless communication in industrial environments in the smart age. Future work will focus on enhancing the robustness, scalability, and security of hybrid VLC/RF systems through advanced noise modelling, latency analysis, adaptive resource allocation, failure recovery, and experimental validation in realistic industrial environments.