1. Introduction

The demands for enhancing the performance of wireless communications continue to grow, as many applications with the data transmission rate of terabits per second (Tbps) are ready to be deployed, such as virtual reality (VR), augmented reality (AR), and high-quality three-dimensional (3D) display. Visible light communications (VLC), as one of the potential technologies for the sixth generation (6G) wireless communication networks, can provide broader bandwidths to satisfy the increasing demands [1,2]. Also, VLC can offer advantages of free-license, electromagnetic immunity, energy efficiency, and data security [3].

However, the disadvantage of fast attenuation limits its applications, and indoor short-range communication becomes the main application scenario. Based on the standardization of IEEE 802.15.7r1, reference channel models of indoor VLC are described and presented [4]. In general, there are likely to be multiple light sources within a small area, and these light sources can provide communication services simultaneously. Multiple-input multiple-output (MIMO) and relay-assisted (cooperative) technologies are emerging techniques that can improve spectrum efficiency and communication reliability for communication systems with multiple sources. Compared with MIMO, relay-assisted communication owns superiorities in deployment flexibility and has been used in long-term evolution (LTE) systems [5].

For VLC, deploying relay nodes for communications can achieve better reliability and broader link coverage [6]. There are two main types of relay-assisted communications: full-duplex (FD) and half-duplex (HD) relaying. While HD relaying is preferred in radio frequency (RF) systems to avoid coupling of transmitted and received signals, FD provides a higher spectrum efficiency and can easily be used in VLC systems. It is revealed that the line-of-sight (LOS) components are at least 7dB higher than the diffuse components via light reflections from surfaces in the room [7]. Further research demonstrates that considering only the LOS components in VLC systems can be a reasonable approach to simplify channel models. Therefore, FD relaying can be much easier to be deployed in VLC systems than in RF systems because loop interference caused by reflection components is at low levels [8]. Previous works have considered realizing multi-hop transmission among ceiling lights by FD relaying methods [9,10]. Researchers have explored orthogonal frequency division multiplexing (OFDM) based VLC with FD relaying to improve spectrum efficiency [11]. However, an elongated cyclic prefix (CP) is needed in OFDM-based systems because signals through direct and relay links create a broader delay spread in the time domain. To reduce the length of CP and enhance the spectrum efficiency, we introduce orthogonal time frequency space (OTFS) into VLC systems with FD relaying.

Unlike OFDM, OTFS is a two-dimensional (2D) modulation scheme that multiplexes symbols over the delay-Doppler domain [12]. The OTFS waveforms capture a high-resolution delay-Doppler radar image of the channels. Therefore, the modulated symbols remain orthogonal to one another at the receiver. This feature makes it better for combating inter-carrier interference (ICI) and inter-symbol interference (ISI) over the delay and Doppler spread channels. In an FD relay-assisted VLC system, different propagation paths lead to a delay spread at the receiver. Thus, a CP, longer than the delay spread, is required to avoid ICI and ISI caused by the multi-path effects. However, the length of the CP for the relay system might be too long and decrease the spectrum efficiency. Compared with OFDM, OTFS can effectively reduce the percentage of CP in data streams and improve spectral efficiency. To effectively combat ISI and ICI caused by delay spreads, the required length of CP in a relay-assisted system with OFDM and OTFS are the same. But the number of information bits in a single OTFS symbol is much more than that of an OFDM symbol because OTFS spreads information symbols over a 2D domain. Therefore, we utilize this advantage of OTFS to enhance the spectral efficiency of FD relay-assisted VLC systems. Details of spectral efficiency comparison are presented in Section 3.

In this paper, we apply OTFS into a VLC system with FD relaying for the first time. Unlike OTFS in RF communications, the signals of VLC should be positive real numbers, so we develop DCO-OTFS to meet the requirement. In the proposed DCO-OTFS based VLC system with FD relaying, DCO-OTFS symbols can retain orthogonality over delay-Doppler channels and mitigate ICI and ISI caused by delay spread of the FD relaying system. We establish the channel model of the proposed DCO-OTFS based VLC system with FD relaying and discuss the modulation and demodulation methods. Then, we compare the spectrum efficiency and data transmission rate of DCO-OTFS and DCO-OFDM systems in the simulations.

The rest of the paper is organized as follows. In Section 2, the channel model of the relaying VLC system is described. The modulation and demodulation methods of DCO-OTFS are presented in Section3. Section 4 compares the spectrum efficiency and data rate performance of DCO-OTFS and DCO-OFDM in the relaying VLC system. Finally, we give conclusions in Section 5.

2. Channel model

We establish a typical FD relaying-based indoor VLC system as shown in Fig. 1. There is a light source in the middle of the room ceiling, and ${\textrm{N}_u}$ users are in the room. Each user device has a light-emitting diode (LED) as a transmitter and a photodiode (PD) as a receiver. We assume that the norm vectors of the LED and PD of each user are in the same direction. In this system, only one user device requires data transmission from the light source at a time slot. Other user devices support communications as relay nodes that capture additional optical power of the light source and re-transmit the acquired signals to the target user device.

 

Fig. 1. A typical FD relaying-based indoor VLC system.

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2.1 Channel propagation gain

We consider the LOS components from the LEDs to the PDs in the FD relaying-based indoor VLC system. It is assumed that the half-power semi-angle of each LED is ${\Phi _{1/2}}$, and the field-of-view (FOV) semi-angle of each PD is $\Psi $. Therefore, the channel propagation gain can be expressed as:

We suppose that the coordinates of the light source, the destination user device, and other users are ${{\mathbf k}_S}$, ${{\mathbf k}_D}$, and ${{\mathbf k}_{{R_i}}}$, respectively. ${{\mathbf n}_S}$, ${{\mathbf n}_D}$, and ${{\mathbf n}_{{R_i}}}$ ($i = 1,2, \cdots ,{N_u} - 1$) denote the normalized norm vectors of the source, destination, and other users. Therefore, the distance between the light source and the user destination can be written as ${d_{S \to D}} = {\|{{{\mathbf k}_D} - {{\mathbf k}_S}} \|_2}$. Similarly, the distance from the light source to the relay nodes is ${d_{S \to {R_i}}} = {\|{{{\mathbf k}_{{R_i}}} - {{\mathbf k}_S}} \|_2}$. The distance from the relay nodes to the destination is denoted as ${d_{{R_i} \to D}} = {\|{{{\mathbf k}_D} - {{\mathbf k}_{{R_i}}}} \|_2}$. For the direct path, the PD of the destination captures the signals transmitted from the light source, and the emergence and incidence angle of this link can be expressed as ${\alpha _{S \to D}} = \arccos (({{\mathbf k}_D} - {{\mathbf k}_S})\cdot {{\mathbf n}_S}/{d_{S \to D}})$ and ${\beta _{S \to D}} = \arccos (({{\mathbf k}_S} - {{\mathbf k}_D})\cdot {{\mathbf n}_D}/{d_{S \to D}})$, respectively. For the ${i_{th}}$ relay path, the relay node first obtains the signals, and the corresponding emergence and incidence angles are ${\alpha _{S \to {R_i}}} = \arccos (({{\mathbf k}_{{R_i}}} - {{\mathbf k}_S})\cdot {{\mathbf n}_S}/{d_{S \to {R_i}}})$, and ${\beta _{S \to {R_i}}} = \arccos (({{\mathbf k}_S} - {{\mathbf k}_{{R_i}}})\cdot {{\mathbf n}_{{R_i}}}/{d_{S \to {R_i}}})$. Then, the relay node re-transmits the waveforms to the destination user, and the emergence and incidence angles are written as ${\alpha _{{R_i} \to D}} = \arccos (({{\mathbf k}_D} - {{\mathbf k}_{{R_i}}})\cdot {{\mathbf n}_{{R_i}}}/{d_{{R_i} \to D}})$, and ${\beta _{{R_i} \to D}} = \arccos (({{\mathbf k}_{{R_i}}} - {{\mathbf k}_D})\cdot {{\mathbf n}_D}/{d_{{R_i} \to D}})$. Therefore, the channel propagation gain of the direct path is ${h_{S \to D}} = H({\alpha _{S \to D}},{\beta _{S \to D}},{d_{S \to D}})$. The channel gains of the ${i_{th}}$ relay path are ${h_{S \to {R_i}}} = H({\alpha _{S \to {R_i}}},{\beta _{S \to {R_i}}},{d_{S \to {R_i}}})$ and ${h_{{R_i} \to D}} = H({\alpha _{{R_i} \to D}},{\beta _{{R_i} \to D}},{d_{{R_i} \to D}})$. If both ${h_{S \to {R_i}}}$ and ${h_{{R_i} \to D}}$ are more than zero, the ${i_{th}}$ relay node is used for communications. So ${\rm I} = \{{i|{h_{S \to {R_i}}}\cdot {h_{{R_i} \to D}} > 0} \}$ contains indices of the activated relay nodes in the system.

2.2 Delay spread

The distance difference between the direct link and the relay links creates a delay in the time domain. Also, the processing time at the relay nodes enlarges the delay spread further. We assume that the processing delay caused by each relay node is ${\tau _p}$, so the delay of the ${j_{th}}(j \in {\rm I})$ relay path can be expressed as:

The delay spread caused by the relay paths can probably have an immense impact on high-rate communication system. Suppose that the duration of one symbol is $\tau $ in the time domain, the ratio of CP length will be more than $\max ({\tau _j})/\tau $ ($j \in {\rm I}$) to alleviate ICI and ISI. If the maximum delay of different relay paths is wide or the duration of one transmitted symbol is short, adding CP to combat ICI and ISI will lead to a considerable loss of spectral efficiency.

2.3 Signal noise ratio (SNR) of the system with Gaussian noise

We consider the FD relaying-based indoor VLC system with adding white Gaussian noise (AWGN). In the system, ${P_S}$ denotes the electrical power transmitted by the light source. $SN{R_0}$ is defined as the ratio of the received power to the AWGN power at the destination node without relaying paths. When the variance of the adding noise is $\sigma _0^2$, it can be defined as:

The transmitted power of the activated relay nodes are ${\eta _j}{P_S}$ ($j \in {\rm I},{\eta _j} > 0$), where ${\eta _j}$ ($j \in {\rm I}$) are constants in the system. Therefore, the received power of the destination user device is expressed as:

In the system, the relay nodes receive the signals sent from the light source, then amplify the waveforms at the power of ${\eta _j}{P_S}$ and transmit the amplified waveforms to the destination. This relaying mode is called amplify-and -forward (AF). Moreover, we assume that receivers at the relay nodes are with AWGN of the same power $\sigma _0^2$ as the destination. The noise at the relay nodes will be transmitted to the destination node. Accordingly, the total noise power brought by the receiver of the destination node and the re-transmit noise from the relay nodes can be derived as:

Then, the SNR value of the received signals at the destination can be expressed as:

3. Methods

3.1 DCO-OTFS modulation and demodulation

OTFS modulates symbols in the delay-Doppler domain to maintain orthogonality among modulated symbols over time and frequency selective channels. That means OTFS can avoid ICI and ISI caused by multiple paths and Doppler effects [12,13]. In the FD relaying-based indoor VLC systems, multiple-path leads to immense delays at the receiver and increases the size of the required CP for DCO-OFDM based system. Therefore, we introduce a variant of OTFS for FD relaying-based VLC system. Figure 2 illustrates the block diagram of a DCO-OTFS-based VLC system. In DCO-OTFS, the information bits are modulated in the delay-Doppler domain with $N$ points along the delay axis and $M$ points along the Doppler axis. Similar to the traditional DCO-OFDM, DCO-OTFS uses the property of Hermitian symmetry to generate waveforms with real numbers and adds direct current (DC) to realize positive optical signals. The modulated DCO-OTFS symbols satisfy Eq. (7), where $n = 0,1, \cdots ,N$.

The inverse symplectic Fourier transform (ISFFT) can convert the delay-Doppler representation signal to a time-frequency representation signal as shown in (8), where $n^{\prime} = 0,1, \cdots ,N$ and $m^{\prime} = 0,1, \cdots ,M$.

Then, the time-frequency domain signal is transformed by inverse fast Fourier transform (IFFT) to the time domain as a $N \times M$-dimensional DCO-OTFS signal. The signal is consisted of M multicarrier symbols with N subcarriers and can be represented as:

In Eq. (9), $m^{\prime} = 0,1, \cdots ,M - 1$ and $n = 0,1, \cdots ,N$. Due to the Hermitian symmetry process, all values of x are real numbers. Only one CP is added to avoid ICI and ISI. By adding DC bias, the optical signal can be transmitted by a LED. At the receiver, the PD captures the received optical waveform and removes DC components and CP. The obtained sequence y has $N \times M$ points and is then transformed to the time-frequency domain signal by FFT. The time-frequency domain signal can be expressed as:

The symplectic fast Fourier transform (SFFT) converts ${Y_{t - f}}$ to the delay-Doppler domain signal

After the DCO-OTFS demodulation, message passing (MP) algorithm-based detection is used to restore the QAM symbols, and the MP detector is described in the following subsection. Finally, the QAM demodulator recovers the output bits.

 

Fig. 2. Block diagram of a DCO-OTFS based VLC system.

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Compared with DCO-OFDM-based systems, DCO-OTFS modulation does not lead to a significant increase in computational complexity. In DCO-OFDM-based systems, NM points in the time domain are generated by IFFT, and the complexity of modulation is O(MNlogN) [14]. In DCO-OTFS-based systems, NM points in the time domain are generated by ISFFT, and the complexity is O(MNlog(MN)).

3.2 Message passing detection

Message passing (MP) algorithm based on sparse factor graph has been applied to channel estimation, channel decoding, and signal detection in wireless communications. For signal detection, a type of MP algorithm called expectation propagation (EP) only conveys a few statistics and reduces the computational complexity of the detector [15]. The MP algorithm in this paper is similar to the algorithm in [16], where the posterior probability distribution of the received QAM symbols is approximated by a Gaussian distribution function. The mean and variance of the Gaussian distribution function are passed and adjusted through several iterations until the stopping criteria is achieved. The MP algorithm outputs the decision on transmitted symbols $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over X} $ that satisfies Eq. (12), where ${a_k} \in {\rm A}$ represents constellations of the transmitted QAM symbols, $l$ denotes the iteration number, and $p_{i,j}^{(l)}({a_k})$ is the approximated posterior probability.

3.3 Spectrum efficiency

The proposed FD relaying-based DCO-OTFS VLC system has an obvious advantage of reducing the costs of adding CP. In this subsection, we compare the spectrum efficiency of the proposed DCO-OTFS system with the traditional DCO-OFDM system. We assume that the modulation bandwidth of the channel described in Section 2 is W. For DCO-OTFS, there are $N$ points along the delay axis and $M$ points along the Doppler axis. For DCO-OFDM, there are $N$ points along the frequency axis. Therefore, each DCO-OTFS symbol contains $NM$ points in the time domain, and each DCO-OFDM symbol contains $N$ points. A cyclic prefix is added to the transmitted symbol to alleviate the influence caused by ICI and ISI, and the duration of the CP should be more than the maximum delay spread. Accordingly, CP with $\left\lceil {\mathop {\max }\limits_{j \in {\rm I}} {\tau_j}\cdot 2W} \right\rceil$ points are added to each DCO-OTFS symbol and each DCO-OFDM symbol to avoid ISI and ICI caused by the multi-path delay. Therefore, the spectral efficiency of the proposed DCO-OTFS system is derived as:

In the proposed DCO-OTFS system, M can be large enough to increase the value of the third term in formula (13), which leads to a higher spectrum efficiency than the DCO-OFDM systems.

4. Simulation results and discussions

We do simulations over the channel model mentioned in Section 2. The performance of DCO-OTFS is compared with DCO-OFDM in the FD relaying-based VLC system. In the simulations, N_u=5 users are in the room. The positions and directions of their transmitters and receivers are listed in Table 1. These parameters are chosen randomly and will not influence the following qualitative conclusions. We assume that only one user requires communication services, and others work as relay nodes. The power coefficient satisfies ${\eta _j} = 1$ ($j \in {\rm I}$) in the system, and the used bandwidth is 500MHz. Parameters of DCO-OTFS and DCO-OFDM scheme are N=128 and M=128.

Table 1. Parameters of light source and users in the system

View Table

Figure 3 shows the BER performance of the relaying VLC system with DCO-OTFS and DCO-OFDM. The input bits are modulated to 64-QAM symbols, and the processing delay at relay nodes is 10nanoseconds (ns). The simulation results imply that the proposed FD relaying-based DCO-OTFS VLC system performs better than the relaying system with the traditional DCO-OFDM. The BER performance of the DCO-OTFS scheme without adding CP is about $3 \times {10^{ - 3}}$ when the SNR value exceeds 15dB. To further enhance the BER performance, a cyclic prefix should be added to each OTFS symbol. When a 1/800 CP is added, the duration of CP is close to the maximum delay spread of the relay system, and the BER performance of the proposed FD relaying-based DCO-OTFS VLC system is significantly improved. The spectral efficiency of the system with 1/800 CP is 5.90bits/s/Hz. As shown in the simulation results, increasing the length of CP further has a limited effect on improving BER performance. On the contrary, the spectral efficiency of DCO-OFDM with 1/10 CP is 5.36bits/s/Hz. Increasing the breadth of CP to 1/4 can enhance the bit error rate (BER) performance of DCO-OFDM, but it still performs worse than the proposed DCO-OTFS scheme and impairs spectral efficiency. If the length of CP is reduced to 1/11 or less, the BER performance deteriorates severely because the CP is too short to combat the ICI and ISI in the system.

 

Fig. 3. BER performance of both DCO-OTFS and DCO-OFDM in the proposed FD relaying-based VLC system.

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Figure 4 presents the spectral efficiency of the DCO-OTFS and DCO-OFDM VLC systems when the BER value is $3 \times {10^{ - 3}}$ (below the hard-decision forward error correction (FEC) threshold of $3.8 \times {10^{ - 3}}$ [17]). The results illustrate that DCO-OTFS achieves a higher spectral efficiency over channels with different SNR values. When the SNR value is 20dB, the achieved spectral efficiency of DCO-OTFS is about 8.2bits/s/, while that of DCO-OFDM with 1/10 CP is about 6.6bits/s/Hz. DCO-OFDM systems with less length of CP perform much worse. Because the added CP is too short to combat ICI and ISI in the RD relaying systems.

 

Fig. 4. Spectral efficiency of the FD relaying-base VLC with DCO-OTFS and DCO-OFDM.

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The processing delay at relay nodes influences the delay spread in the proposed FD relaying-base VLC system. In a practical relay-assisted VLC system, the processing delay will be different when using circuits with different light sources, photodiodes, and signal amplifiers. Moreover, the transmission delay for receiving a complete packet has impact on the processing delay. Thus, the processing delay varies in different relay-assisted systems. To study the relationship between the processing delay and BER performance of the proposed system, we do simulations over channels with various processing delays at relay nodes. Figure 5 shows the simulation results of the spectral efficiency when the processing delays are 10ns, 50ns, and 100ns, respectively. The rise of the processing delay has little impact on the spectral efficiency of the DCO-OTFS system. However, when the processing delay is increased from 10ns to 50ns, the spectrum efficiency of the DCO-OFDM system drops intensely. The increased delay spread exceeds the duration of the cyclic prefix added to OFDM symbols, so the DCO-OFDM system fails to combat ICI and ISI. The results indicate that the proposed DCO-OTFS-based FD relaying VLC system performs better and is more stable when the processing delay increases.

 

Fig. 5. Spectral efficiency when the processing delay is 10ns, 50ns, and 100ns.

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5. Conclusions

Indoor visible light communication with full-duplex relaying makes more use of the power at the light source to enhance the performance of the communication system yet suffers from the spectrum efficiency loss. In this paper, we propose a DCO-OTFS based relay-assisted visible light communication system. The analysis and simulation results point out that the proposed method can achieve higher spectral efficiency than the traditional DCO-OFDM scheme. When the delay spreads increase, the proposed DCO-OTFS system performs better and more robust than the traditional DCO-OFDM system. This work shows an example of a DCO-OTFS system with fixable delay spreads, and the results initially verify the validity of the proposed method. The delay spreads of relay paths are determined by the users’ locations and will be different when the distributions of the user locations are changed. Thus, the delay spread should be a random variable when the users change their locations in practical scenarios. Simulations over channels, where delay spreads are set randomly, will be implemented in our future works. We will also consider the ad-hoc networks using different relay locations. In a visible light ad-hoc network, there is no base station. All users can transmit original data streams to others. Idle users can be activated as relay nodes to assist data transmission. DCO-OTFS-based visible light ad-hoc networks have the advantages of increasing received signal power, realizing non-line-of-sight communications, and enhancing spectral efficiency.