Networked multiple-input-multiple-output for optical wireless communication systems

Abstract

With the escalation of heterogeneous data traffic, the research on optical wireless communication (OWC) has attracted much attention, owing to its advantages such as wide spectrum, low power consumption and high security. Ubiquitous optical devices, e.g. light-emitting diodes (LEDs) and cameras, are employed to support optical wireless links. Since the distribution of these optical devices is usually dense, multiple-input-multiple-output (MIMO) can be naturally adopted to attain spatial diversity gain or spatial multiplexing gain. As the scale of OWC networks enlarges, optical MIMO can also collaborate with network-level operations, like user/AP grouping, to enhance the network throughput. Since OWC is preferred for short-range communications and is sensitive to the directions/rotations of transceivers, optical MIMO links vary frequently and sharply in outdoor scenarios when considering the mobility of optical devices, raising new challenges to network design. In this work, we present an overview of optical MIMO techniques, as well as the cooperation of MIMO and user/AP grouping in OWC networks. In consideration of the challenges for outdoor OWC, key technologies are then proposed to facilitate the adoption of optical MIMO in outdoor scenarios, especially in vehicular ad hoc networks. Lastly, future applications of MIMO in OWC networks are discussed.

This article is part of the theme issue ‘Optical wireless communication’.

1. Introduction

To meet the ever-growing demand for wireless network access, optical wireless communication (OWC) has become a promising technology to provide high data rate service with wide spectrum and low-power consumption, where an intensity modulation and direct detection (IM/DD) scheme is commonly adopted [1,2]. From the transmitter side, energy-efficient light-emitting diodes (LEDs) are adopted as access points (APs), where signals are modulated on the intensity of lights. From the receiver side, photodiodes (PDs) or cameras could detect the illumination of LEDs and then decode the information. Since optical beams are usually directional and could not penetrate through opaque blocks, OWC could realize high spatial reuse ratio, security-guaranteed transmission, and high-precision positioning [3]. Owing to the dense deployment of LEDs in daily life and various embedded optical detectors, multiple-input-multiple-output (MIMO) can be naturally adopted in OWC networks, which exploits the spatial characteristics of wireless channels to improve the network throughput. Since IM/DD schemes require that the transmitted signals must be real and positive, traditional MIMO techniques designed for radio frequency (RF) communications could not be applied directly. Besides, since the power of reflected optical paths is usually limited compared with its line-of-sight (LOS) counterpart, OWC channels are prone to high correlation, which is detrimental to the performance of optical MIMO [4].

In [5–8], several optical MIMO techniques, including repetition coding (RC), spatial multiplexing (SMP) and spatial modulation (SM) were illustrated to improve the quality of service for a single user in the OWC network. It was experimentally demonstrated that more than 1 Gbps data rate can be achieved by a 3 × 3 optical MIMO system [7]. For multi-user MIMO (MU-MIMO), where the data for different users are transmitted simultaneously, inter-user interference alignment is also crucial [9]. Given the estimated channel state information (CSI) at the transmitter (CSIT), optical precoding and decoding schemes were developed to reduce the inter-user interference under optical power constraints [10–13]. A successive interference cancellation (SIC) scheme was also investigated [14,15]. When CSIT is not available, several blind interference alignment (BIA) schemes at the user side are proposed [16,17].

When the scale of OWC networks increases or the distribution of APs and users becomes dense, the cooperation of MIMO and network-level operations, like user/AP grouping, is vital. On the one hand, as the number of APs and users increases, the complexity of interference alignment methodology increases dramatically, which impedes the practical implementation of optical MU-MIMO systems. However, via user/AP grouping, the whole network can be divided into several subnetworks to form small MU-MIMO systems, which enhances its scalability. On the other hand, the number of users being served at the same time/frequency block should be restricted by the number of available APs in order to cancel the inter-user interference at the transmitter side [11] and user grouping is commonly used to select the active users for each time/frequency block. Even when non-orthogonal multiple access is applied, user grouping is still influential to facilitate interference cancellation at the user side [18,19]. Both network-centric and user-centric formation of subnetworks were illustrated to decide user/AP grouping and link selection [20,21]. In addition, cell-free architecture was studied, which breaks the boundary of subnetworks and allows each user to connect multiple APs in its field-of-view (FOV) flexibly [22,23].

At present, the study of MIMO for OWC networks still focuses on indoor scenarios, whereas OWC for outdoor scenarios is attracting more and more attention, especially in vehicular ad hoc networks (VANETs), owing to its high spatial reuse ratio and low power consumption [2]. When considering the mobility of outdoor optical devices, many challenges have to be solved [2]. Firstly, since an optical wireless link is sensitive to the relative distance and directions of transceivers, it changes frequently and sharply if either the user or the AP moves at high speed. Secondly, frequent handover caused by optical link switches could degrade the network performance significantly. Therefore, how to integrate optical MIMO into VANET to improve network throughput and robustness should be investigated.

Our goal in this work is to firstly review the state-of-the-art optical MIMO and MU-MIMO techniques in OWC networks and then present a novel framework of optical MIMO in VANET. In §2, the system model of optical MIMO and several typical interference alignment schemes are presented. Different topologies of large-scale MIMO OWC networks are addressed in §3. Section 4 presents some key issues of MIMO in OWC networks and the existing solutions. The framework of optical MIMO in VANET is proposed to facilitate high-speed mobile scenarios in §5. Lastly, future work of MIMO in OWC networks is discussed in §6.

2. Optical multiple-input-multiple-output

(a). System model of optical multiple-input-multiple-output

An OWC network is composed of multiple LEDs, served as APs, and multiple users equipped with optical detectors, whereby MIMO can be naturally adopted. Assuming $|{\mathcal{N}}_t|$ APs are activated to serve $|{\mathcal{N}}_r|$ users at one specific time slot, the received signal for user $i\in {\mathcal{N}}_r$, which has N_p PDs is written as

$${\mathit{y}}_i={\mathit{H}}_i(\mathit{x}+\mathit{D})+{\mathit{z}}_i,$$ 2.1

where H_i is the $N_P\times |{\mathcal{N}}_t|$ channel matrix between user i and $|{\mathcal{N}}_t|$ APs, and x is a $|{\mathcal{N}}_t|$-dimensional vector denoting the transmitted signal. D is the $|{\mathcal{N}}_t|$-dimensional vector of DC bias, which guarantees that APs operate in their linear transfer range. z_i represents the additive noise, with average power of σ². In regard to x, MIMO transmission schemes can be classified into two types, i.e. combined transmission (CT) or vectored transmission (VT). For CT schemes, APs convey the same signals in order to improve the reliability of the optical wireless link, also referred to as spatial diversity gain. For VT schemes, those APs could transmit multiple data streams simultaneously to attain the SMP gain. How to decouple the multiple data streams is discussed in the next section.

Frequency division duplexing is generally adopted in OWC networks, where an RF or infrared frequency band is used for uplink and a visible light frequency band is used for downlink [24,25]. Therefore, downlink channel estimation and uplink feedback is required if APs need CSI [26]. For different types of optical detectors, the channel matrix H_i could manifest different features. In general, there are two types of optical detectors, namely, non-imaging detectors and imaging detectors. A non-imaging detector is equipped with a non-imaging concentrator and a PD array [4]. The PD array can receive signals from all the APs in its FOV. To ensure the reliability of optical links, the FOV of a PD array could be relatively wide. However, when APs are close to each other, the channels between a PD array and these APs are similar, resulting in high channel correlation. An example of the channel matrix between a user with a 2 × 2 PD array and 4 APs is given by [8]

$${\mathit{H}}_{i,\text{ni}}=\left[\begin{array}{cccc}1.82& 1.720& 1.628& 1.720\\ 1.720& 1.820& 1.720& 1.628\\ 1.628& 1.720& 1.820& 1.720\\ 1.720& 1.628& 1.720& 1.820\end{array}\right]\times {10}^{-6}.$$ 2.2

For an imaging detector, a lens is added to project lights from different directions to different PDs in the array. Therefore, the correlation between channels from different APs can be reduced [8]. A thin-lens imaging detector can partially or completely separate different APs with small distortion, but has a narrower FOV in comparison to non-imaging detectors [27]. Hemispherical or fisheye lenses can enlarge the FOV of imaging detectors at the cost of larger space. When the locations of APs and PDs are the same as (2.2), the channel matrix with the hemispherical-lens imaging detector is given by Gupta & Chockalingam [8]

$${\mathit{H}}_{i,\text{hs}}=\left[\begin{array}{cccc}0& 0.018& 2.712& 0.018\\ 0.018& 0& 0.018& 2.712\\ 2.712& 0.018& 0& 0.018\\ 1.720& 1.628& 1.720& 0\end{array}\right]\times {10}^{-7}.$$ 2.3

It is apparent that the divergence of channels from different APs is increased with the aid of a lens. Moreover, the lens can be added at the transmitter side if LED array is deployed, to improve the channel divergence between LEDs in an LED array [28].

(b). Interference alignment

If there are multiple users in the user group ${\mathcal{N}}_r$, the transmitted signal x in (2.1) is related to the data for all those users. Accordingly, interference alignment is necessary to decode the data for a specific user.

(i). Precoding and decoding

When CSIT is available, linear precoding and decoding schemes could be used to reduce inter-user interference [9,10]. Specifically, precoding vectors are applied at the transmitter to transform users’ desired symbols to the transmitted signal x. At the user side, after subtracting the DC bias and applying the decoding vector, the N_d streams of decoded symbols for user i are formulated as

$$\begin{array}{rl}{\mathit{d}}_i={\mathit{u}}_i^T({\mathit{y}}_i-{\mathit{H}}_i\mathit{D})& ={\mathit{u}}_i^T{\mathit{H}}_i\mathit{x}+{\mathit{u}}_i^T{\mathit{z}}_i={\mathit{u}}_i^T{\mathit{H}}_i(\sum _{j\in {\mathcal{N}}_r}{\mathit{w}}_j{\mathit{s}}_j)+{\mathit{u}}_i^T{\mathit{z}}_i\\ & ={\mathit{u}}_i^T{\mathit{H}}_i{\mathit{w}}_i{\mathit{s}}_i+\sum _{j\in {\mathcal{N}}_r,j\ne i}{\mathit{u}}_i^T{\mathit{H}}_i{\mathit{w}}_j{\mathit{s}}_j+{\mathit{u}}_i^T{\mathit{z}}_i,\end{array}$$ 2.4

where ${\mathit{w}}_i\in {\mathbb{R}}^{|{\mathcal{N}}_t|\times N_d}$ and ${\mathit{u}}_i\in {\mathbb{R}}^{N_P\times N_d}$ are the precoding and decoding vectors for user i. s_i denotes the N_d streams of symbols for user i and the second term in the second line represents the interference incurred by other interfering users. Aggregating the received signals for all the users, (2.4) can be rewritten as

$$\mathit{d}={\mathit{U}}^T\mathit{H}\mathit{W}\mathit{s}+{\mathit{U}}^T\mathit{z},$$ 2.5

where $\mathit{d}={[{\mathit{d}}_1,{\mathit{d}}_2,\dots ,{\mathit{d}}_{|{\mathcal{N}}_r|}]}^T$ is a $|{\mathcal{N}}_r|N_d$-dimensional vector, $\mathit{H}={[{\mathit{H}}_1^T,{\mathit{H}}_2^T,\dots ,{\mathit{H}}_{|{\mathcal{N}}_r|}^T]}^T$ is a $(N_P|{\mathcal{N}}_r|)\times |{\mathcal{N}}_t|$ matrix, $\mathit{W}=[{\mathit{w}}_1,\dots ,{\mathit{w}}_{|{\mathcal{N}}_r|}]$ is a $|{\mathcal{N}}_t|\times (|{\mathcal{N}}_r|N_d)$ matrix and $\mathit{U}=[e_1\otimes {\mathit{u}}_1,\dots ,e_{|{\mathcal{N}}_r|}\otimes {\mathit{u}}_{|{\mathcal{N}}_r|}]$ is a $N_P|{\mathcal{N}}_r|\times |{\mathcal{N}}_r|N_d$ matrix. Besides, s and z are the vectors composed of s_i and z_i, respectively. e_i is the ith column of a $|{\mathcal{N}}_r|$-dimensional unit matrix and ⊗ denotes the Kronecker product of two matrices. Several criteria, including ZF, MMSE and SLNR, are commonly used for precoding and decoding design.

In general, the calculation of precoding and decoding vectors can be modelled as the optimization problem of a certain criterion under power constraints, given by

$$\begin{array}{rl}& \underset{\mathit{W},\mathit{U}}{min}f(\mathit{H},\mathit{W},\mathit{U},{\sigma }^2)\\ & \text{s.t.}P(\mathit{W})\le 0\end{array}\}$$ 2.6

The ZF scheme forces the interference term to be zero, namely, the interference term in (2.4) has to be zero [9]. Therefore, the optimization object can be set as $f(\mathit{H},\mathit{W},\mathit{U},{\sigma }^2)=\sum _{i\ne j}{I}_{-}(||{\mathit{u}}_i^T{\mathit{H}}_i{\mathit{w}}_{\mathit{j}}|{|}_F^2)$, where I₋(t) is an indicator function and takes the value of 0 when t ≤ 0 but takes the value of ∞ when t > 0. The MMSE scheme tends to minimize the mean squared error of the decoded signal which relates to the interference term and also the noise term. In particular, the mean squared error of the decoded signal for user i is formulated as ${\text{MSE}}_i=E_{\mathit{s},\mathit{z}}||{\mathit{d}}_i-{\mathit{s}}_i|{|}_F^2$ [10]. Thus, $f(\mathit{H},\mathit{W},\mathit{U},{\sigma }^2)=\sum _i{\text{MSE}}_i$.

SLNR for user i is defined as [12]

$${\text{SLNR}}_i=\frac{Tr\{{\mathit{w}}_i^T{\mathit{H}}_i^T{\mathit{H}}_i{\mathit{w}}_i\}}{Tr\{{\mathit{w}}_i^T({\sigma }^2\mathit{I}+\sum _{j\in {\mathcal{N}}_r,j\ne i}{\mathit{H}}_j^T{\mathit{H}}_j){\mathit{w}}_i\}},$$ 2.7

where Tr{ · } denotes the operation to calculate the trace of a matrix. Accordingly, $f(\mathit{H},\mathit{W},\mathit{U},{\sigma }^2)=\sum _i{\text{SLNR}}_i$ for SLNR-based precoding and decoding. Different from signal-to-interference-and-noise ratio (SINR), SLNR for a specific user is determined by its own precoding vector and independent of precoding vectors for other users, which could reduce the optimization complexity [11,12]. Accordingly, SLNR was regarded as an approximation of SINR to estimate the achievable data rate [29]. Sum user data rate was adopted as the optimization object in [13].

Regarding the power constraint, different methodologies are adopted for either multi-carrier or single-carrier modulations. When multi-carrier modulation, like orthogonal frequency division multiplexing (OFDM), is employed, the time-domain transmitted signal after inverse fast Fourier transformation (IFFT) is approximately subject to a Gaussian distribution [4]. Hence, to reduce the probability of the transmitted signal exceeding the linear transfer range of APs, the variance of the transmitted signal has to be constrained, namely, P(W) = E{diag(Wss^TW^T)}1 − P_t ≤ 0 [9]. When single-carrier modulation, like pulse amplitude modulation, is adopted, the time-domain transmitted signal is a finite and discrete random variable. At this time, the amplitude of the transmitted signal has to be limited, i.e. P(W) = |W|β1 − P_t ≤ 0 [10]. β denotes the maximum amplitude of users’ symbols and 1 denotes a vector with all elements as 1. |W| represents the element-wise absolute value of W.

The precoding and decoding vectors can be updated via alternate iterations in order to obtain the global or local optimal solutions to (2.6) [10]. For the decoding vector of optical networks, since there is no extra constraint, its calculation is the same as the conventional RF networks. For example, the decoding vector can choose, but not be limited to, maximum ratio combining, select best combining and equal gain combining schemes. However, the conventional precoding vectors cannot be applied directly owing to the power constraint in (2.6). Problem transformation and convex approximation methods were investigated [10,13], which have comparatively high complexity. A simpler scheme is to split the precoding matrix into two different parts, i.e. W = W₀(αI), where W₀ aims to reduce the inter-user interference and αI guarantees that the power constraint is satisfied [11]. For W₀, the power constraint can be omitted temporally to reduce the calculation complexity. Then, α is set to the maximum value which meets the power constraint [12].

(ii). Successive interference cancelation

If a user has multiple streams of symbols to decode or an uplink MIMO system is considered where APs should decode symbols from multiple users, SIC schemes can also be employed to remove the interference. Without loss of generality, SIC detection for a user that has multiple streams of symbols to decode is presented here. Similarly, a ‘precoding’ and ‘decoding’ matrix is employed at the transmitter and receiver, respectively,

$${\mathit{d}}_{i,\mathrm{SIC}}={\mathit{u}}_{i,\mathrm{SIC}}^T{\mathit{H}}_i{\mathit{w}}_{i,\mathrm{SIC}}{\mathit{s}}_i+\sum _{j\in {\mathcal{N}}_r,j\ne i}{\mathit{u}}_{i,\mathrm{SIC}}^T{\mathit{H}}_i{\mathit{w}}_{j,\mathrm{SIC}}{\mathit{s}}_j+{\mathit{u}}_{i,\mathrm{SIC}}^T{\mathit{z}}_i.$$ 2.8

Different from precoding and decoding schemes, which tend to make ${\mathit{u}}_i^T{\mathit{H}}_i{\mathit{w}}_i$ quasi-diagonal, the SIC schemes would make ${\mathit{u}}_{i,\text{SIC}}^T{\mathit{H}}_i{\mathit{w}}_{i,\text{SIC}}$ a lower-triangular or upper-triangular matrix. Thereafter, the elements in s_i can be decoded successively from top to bottom (for lower-triangular matrix) or from bottom to top (for upper-triangular matrix). Various algorithms have been proposed to obtain the triangular matrix, which aim to improve the detection accuracy or reduce the computing complexity [14,15].

(iii). Blind interference alignment

The performance of precoding and decoding relies on accurate CSIT, which requires downlink channel state estimation and uplink feedback. When the number of users and APs increases, the overhead of CSI feedback becomes high. A direct method to avoid inter-user interference without CSIT is to use frequency or time-domain orthogonal multiple access schemes, namely, all APs only serve one user in a time/frequency block. However, bandwidth efficiency will be degraded. Therefore, BIA schemes were proposed to eliminate the inter-user interference without CSI feedback and without the sacrifice of bandwidth efficiency [16,17].

In a MU-MIMO system adopting the BIA scheme, the supersymbol containing multiple users’ data is transmitted from APs. After that, each user switches among several receiving modes to cancel the inter-user interference and decode its desired symbols. The BIA scheme in [12] with 2 APs is addressed in detail, which could be extended to MU-MIMO systems with more APs. Specifically, for two APs and K users as shown in figure 1, one supersymbol consists of K + 1 blocks and the transmitted signal from two APs in the kth block is given by

$$\mathit{x}[k]=\{\begin{array}{ll}\sum _{j=1}^K{\mathit{s}}_j+\mathit{D},& k=0\\ {\mathit{s}}_k+\mathit{D},& 1\le k\le K\end{array},$$ 2.9

where s_j denotes the two-dimensional transmitting symbol for user j.

Figure 1.

(a–c) Illustration of BIA scheme with two APs. (Online version in colour.)

For each user, two receiving modes are employed, which can be realized by either divergent filters or PDs with different orientations. The schedule of two receiving modes for users is shown in figure 1c. In block 0, all the users select Mode 1. At the kth (k > 0) block, user k switches to Mode 2, while others stay in Mode 1. As a result, denoting ${\mathit{H}}_i^{[1]}$ and ${\mathit{H}}_i^{[2]}$ as the channel matrices for user i under two receiving modes, the received K + 1 blocks of signal for user i is given by

$${\mathit{y}}_i[k]=\{\begin{array}{ll}{\mathit{H}}_i^{[1]}(\sum _{j=1}^K{\mathit{s}}_j+\mathit{D})+{\mathit{z}}_i[k],& k=0\\ {\mathit{H}}_i^{[1]}({\mathit{s}}_k+\mathit{D})+{\mathit{z}}_i[k],& 1\le k\le K,k\ne i\\ {\mathit{H}}_i^{[2]}({\mathit{s}}_i+\mathit{D})+{\mathit{z}}_i[k],& k=i.\end{array}$$ 2.10

The CSI is known at user side and we have

$$\left[\begin{array}{c}{\mathit{y}}_i[0]-\sum _{k=1,k\ne i}^K{\mathit{y}}_i[k]+(K-2){\mathit{H}}_i^{[1]}\mathit{D}\\ {\mathit{y}}_i[i]-{\mathit{H}}_i^{[2]}\mathit{D}\end{array}\right]=\left[\begin{array}{c}{\mathit{H}}_i^{[1]}\\ {\mathit{H}}_i^{[2]}\end{array}\right]{\mathit{s}}_i+\left[\begin{array}{c}{\mathit{z}}_i[0]-\sum _{k=1,k\ne i}^K{\mathit{z}}_i[k]\\ {\mathit{z}}_i[i]\end{array}\right].$$ 2.11

As long as ${\mathit{H}}_i^{[1]}$ is not aligned with ${\mathit{H}}_i^{[2]}$, two elements in s_i can be decoded via (2.11). Defining degree of freedom (DoF) as the average number of independent symbols transmitted in a block [17], we find that DoF is equal to (2K/K + 1). As the number of users increases, DoF approaches the number of APs, which is also the upper bound of DoF for precoding and decoding schemes. Therefore, the bandwidth efficiency is guaranteed for the BIA scheme. The extended BIA scheme with more than 2 APs was addressed in [16].

3. Networked optical multiple-input-multiple-output

As the scale of OWC networks enlarges, the complexity of interference alignment will increase significantly if the whole network is modelled as a single MU-MIMO system. Therefore, it is preferred to divide the network into several subnetworks to form multiple small MU-MIMO systems. The following schemes have been proposed for subnetwork formation.

(a). Network-centric formation

Network-centric (NC) formation refers to the formation of optical attocells, where the location of APs is dominant [21]. As shown in figure 2a, an optical attocell is constituted by a group of APs within a rectangle or cellular region, as well as the corresponding user group under their coverage. In addition, a user on the cell edge has to connect to one attocell which can provide the best quality of service. As a result, the NC attocell usually has a fixed geometrical shape with clear cell edges.

Figure 2.

(a–d) Different OWC networks. (Online version in colour.)

In an NC attocell, CT or VT schemes can be adopted for multiple APs serving users simultaneously [20]. If there are more users than the number of APs in an attocell, user scheduling is also required. Since the interference from other attocells is non-negligible for users on the cell edge, cell partitioning and frequency reuse were investigated to eliminate the inter-cell interference (ICI), where the trade-off between bandwidth efficiency and SINR has to be evaluated carefully [30,31]. In order to mitigate the loss of bandwidth efficiency, both inter-user interference and ICI can be reduced via the precoding matrix for each attocell [32].

(b). Cell-free formation

For the NC attocell, since users’ distributions are not fully considered during the network formation, there might exist many cell-edge users, leading to severe ICI. In order to improve SINR for users, cell-free formation was proposed [22,23]. As shown in figure 2b, each user is allowed to connect to a group of APs within its FOV, which could provide the highest channel gains, and there is no restriction of cell edges anymore. As a result, the received signal power is enhanced and ICI is omitted. Besides, user fairness is also considered for cell-free formation in [22].

The CT scheme is usually adopted for cell-free formation [33]. Within each AP group, APs use the same resource blocks to serve the associated user, while different AP groups can choose either the same resource blocks or different resource blocks according to the inter-user interference strength. Graph theory was used to represent the inter-user interference, based on which users are scheduled in multiple resource blocks to ensure the interference-free transmission [34,35]. In [36], coalition formation game is applied for resource allocation of AP groups in order to avoid the inter-user interference.

(c). User-centric formation

When user density becomes high, some users might share most of the APs in their FOVs, which is referred to as users’ similarities. For example, when two users are adjacent to each other and have similar orientations, their connected APs are almost the same. For cell-free formation, in order to avoid inter-user interference, AP groups related to those adjacent users should occupy orthogonal resource blocks, leading to the reduced bandwidth efficiency. Therefore, user-centric (UC) formation was proposed [20,21]. In a UC cluster, a group of adjacent users will select a group of APs to connect with, as shown in figure 2c. Accordingly, the distribution of users other than APs dominates the formation of UC clusters [20]. Specifically, user groups are firstly generated according to users’ similarities, such as relative distances among users. In a specific user group, each user will choose an anchor AP, which can offer good channel quality and has not been selected by other users. Those anchor APs and some nearby idle APs would constitute the AP group to serve that specific user group, where VT and CT schemes can be adopted.

Since UC clusters are determined according to users’ similarities, the irrelevance between the channels for users from different UC clusters is increased compared with NC formation. Therefore, the inter-cluster interference can be reduced. Moreover, when a user group is treated as a unit, the interference avoidance schemes mentioned for cell-free formation can also be deployed to cancel the inter-cluster interference.

In figure 2d, the average user’s data rate for different network formation and MIMO transmission schemes are compared. It is illustrated that cell-free and UC formation are able to improve the network throughput compared with NC formation, thanks to the consideration of users’ similarities. Meanwhile, by comparing UC-VT and UC-CT, it can be seen that a VT scheme can achieve higher data rates since more users are served at a time. However, when interference from other MIMO subnetworks is strong, such as in NC attocells, a CT scheme might have better performance since the received signals from all the APs in a subnetwork are accumulated to combat the effect of interference. Accordingly, VT or CT schemes can be selected based on the interference strength and the number of active users in a subnetwork dynamically.

4. Challenges

MU-MIMO techniques could improve the OWC network throughput by exploiting spatial diversity or multiplexing gain. However, challenges arise when the network becomes dense.

(a). Multi-user multiple-input-multiple-output under high channel correlation

Since multi-path effects are marginal for optical links, the correlation between OWC channels could be high, which appears when the distribution of APs or users becomes dense. At this time, the OWC channel matrix would be ill-conditioned, resulting in the degraded performance of inter-user interference alignment.

When the VT scheme is adopted, the effective channel matrix after applying precoding vectors, i.e. HW, approaches a diagonal, block-diagonal or triangular matrix, where diagonal elements are the effective channels for different users. However, there exist apparent divergences among those effective channel gains if the OWC channel matrix is ill-conditioned, resulting in uneven user performance. To mitigate the performance loss of users having poor effective channels, power imbalance was proposed [12,37]. Besides, it is discovered that the channel correlation in frequency domain is lower than time domain, thanks to the introduction of phase differences [9]. Therefore, MU-MIMO-OFDM systems were proposed for OWC networks [9,38]. Moreover, [28,38,39] used lens at transmitters or receivers to separate signals from different APs in spatial domain. The lens could reduce the channel correlation due to its high spatial resolution. However, it suffers from the limited FOV and the increased cost. Filters were used at both transmitters and receivers to increase the divergence of optical channels in [17] and the detectors with angular diversity were deployed in [40]. In addition, since the interference term can actually be transformed to useful information if several users require the same data, adaptive precoding based on the knowledge of the transmitted symbols for users was proposed [41]. If the transmitted symbols for several users are identical, the interference among those users is regarded as useful information rather than interference in precoding and decoding design [41].

Besides, channel correlation might be reduced thanks to the surrounding environments and users’ movements. For example, when the surrounding obstacles intercept parts of the LOS paths between users and APs, the divergence between elements in the channel matrix could be increased, which reduces the channel correlation. Besides, when users have different orientations in movements, the channel divergence can also be improved. However, the blockages or user movements might also reduce the number of available APs at a time.

(b). User-AP association and resource allocation

When the number of users is larger than the available APs or the OWC channel correlation is still high after applying the schemes in the previous subsection, user-AP association and resource allocation should be investigated to guarantee the system performance, which includes intelligently deciding which group of users should be served by which group of APs and the efficient methodology to allocate power/time/frequency resources to user/AP groups. However, the number of possible options for user-AP association and resource allocation is extremely large, leading to the extremely high complexity to attain the optimal solution.

A user-centric user-AP association algorithm was proposed in [20]. For each time slot, a group of users that maximize the weighted sum rate after ZF precoding is selected. In this way, users that are highly correlated to each other will not be scheduled in one group. The weight for user i is defined as the inverse of its long-term average data rate, which is updated periodically to achieve the fairness among users. To reduce the complexity of user group selection, the relative distance between users and APs was used to evaluate the users’ data rates roughly [20,21]. Besides, the joint design of user-AP association and resource allocation over multiple successive time slots was proposed in [22], which is modelled as a network utility maximization problem and solved by the successive convex approximation scheme.

5. Optical vehicular ad hoc network

As shown in figure 3, VANET is a communication network of vehicles, road side units (RSUs) and regional controllers, which aims to improve transportation efficiency and provide internet services for users on the roads [2,42]. VANET includes vehicle-to-vehicle (V2V) and vehicle- to-infrastructure (V2I) wireless links, as well as wired links among RSUs and regional controllers.

Figure 3.

VANET network model. (Online version in colour.)

(a). Optical links in VANET

Owing to the ubiquitous deployment of lights and optical detectors on the roads, optical wireless links are introduced to support V2V and V2I communications with the benefits of wide spectrum, high spatial reuse ratio and low power consumption [2]. In general, vehicles are equipped with multiple lights and cameras for easy driving, and V2V optical links can be established naturally via these optical devices. Besides, light sources and pervasive cameras installed along the roads, denoted as RSUs, are capable of establishing V2I optical links with vehicles. Since lights on vehicles or RSUs are primarily designed for transportation systems, their distinct illumination characteristics should be carefully investigated in optical link design. For example, the headlamp on a vehicle should inform other drivers of the vehicle’s location constantly. Therefore, it would remain flickering for a relatively long period once it is turned on, during which the related V2V link could transmit massive Internet data or periodically broadcast traffic data. On the contrary, brake lights are only turned on when the vehicle is about to brake and the optical link will last just a short time, which could convey urgent data related to that brake action. For traffic lights, when the red light is switched on, vehicles in its coverage should stop moving and thus V2I links could benefit from the stable optical channels. When the green light is turned on, vehicles move across the intersection quickly and V2I links need to deal with the variations of wireless channels.

Since the coverage of an RSU for OWC is relatively small, the duration of optical V2I communications between a single vehicle and an RSU is limited. Inter-vehicle relay is expected to extend the service area of V2I communications. Therefore, we propose the optical-link-assisted vehicle cluster for inter-vehicle data exchange. Meanwhile, intelligent cooperation among vehicles in the cluster facilitates local data processing without the involvement of regional controllers. Specifically, an optical-link-assisted vehicle cluster is defined as a set of vehicles that are connected via one-hop or multi-hop optical links. Figure 4 depicts an example of the optical-link-assisted vehicle cluster, which can be represented by an undirected graph. The nodes denote the vehicles while the edges represent the optical V2V links. Since light beams are usually directional and cannot penetrate through blocks, the interference among optical V2V links can be easily avoided. In particular, the interference from non-adjacent links is blocked by vehicles, while the interference from neighbouring vehicles could be neglected in either spatial or frequency domains, e.g. using lens to separate signals from different lights. As a result, optical links in a cluster can be activated simultaneously with relatively low interference even when the vehicle density is high, which is a main advantage over its RF-link-assisted counterparts. However, outdoor optical links could be more vulnerable to various noises than RF links due to the effect of sunlight, snow, heavy dust and so on [2]. [43] proposed to improve the SNR by narrowing down the FOV and filters were used in [44]. Spread spectrum coding was also investigated to improve the robustness [2]. Besides, since optical links do not interfere with the conventional RF links, they could coexist and cooperate with RF-link-assisted counterparts to improve the reliability and efficiency of V2V links.

Figure 4.

Description of optical-link-assisted vehicle cluster. (Online version in colour.)

(b). Optical multiple-input-multiple-output in VANET

When considering multiple lights and detectors equipped on vehicles, optical links in VANET can be modelled as MIMO systems. However, as opposed to indoor scenarios, optical MIMO links vary frequently and sharply in VANET, leading to new challenges on channel information feedback and stable transmission. Therefore, we propose an optical MIMO structure for VANET in this subsection, which is classified into intra-cluster MIMO and cluster-RSU MIMO, respectively. Intra-cluster MIMO is designed for V2V links within optical-link-assisted vehicle clusters, while cluster-RSU MIMO is for links between vehicle clusters and RSUs.

(i). Intra-cluster multiple-input-multiple-output

In an optical-link-assisted vehicle cluster, one vehicle establishes V2V optical links with its neighbours. As shown in figure 4, vehicle B and vehicle C could receive signals from vehicle A. If vehicles are equipped with imaging detectors and could separate signals from different directions, multiple data streams can be transmitted in parallel by assigning them to different lights. For example, one tail-light on vehicle A transmits signals to vehicle B, while another tail-light transmits signals to vehicle C. Interference-free light allocation algorithm in [39] could divide the lights into disjoint sets based on CSIT in order to serve several users independently. Since V2V optical links change sharply and frequently owing to fast movement of vehicles, the association between light sets and receiving vehicles has to be updated quickly, which requires continuous and considerable CSI feedback to ensure the link quality.

In this paper, a dynamic multi-user transmission strategy is proposed and could adapt to the variations of optical links with the reduced feedback information. Denote the transmitting vehicle as T and the receiving vehicles as R₁, …, R_n. Firstly, sensors on T should monitor the surrounding environments which implies the quality of OWC channels. For instance, cameras could be used to capture the images of the surroundings. From the captured images at T, the fading and blurring effects due to fog, haze or quick relative movements between adjacent vehicles can be detected to indicate the quality of signals at receivers R₁, …, R_n. Secondly, R₁, …, R_n will feed back the necessary information including whether they could separate different lights of T and the indices of detected lights, which requires less bits than accurate CSI feedback. After that, taking into account the feedback from R₁, …, R_n, local sensing results and the remaining lighting time of lights, T could decide the active lights for transmission and the current transmission strategy. Specifically, if receivers can distinguish different lights of T and the visibility is higher than a threshold, T will split its active lights to disjoint sets according to [39] to serve R₁, …, R_n independently, where receiving vehicles could decode the desired signals directly without interference alignment. Otherwise, the lights on T should serve the receiving vehicles jointly and BIA schemes could be applied for interference alignment at the receiver side. After that receiver-light association is determined, according to the OWC channel quality, T can select either CT scheme to attain the diversity gain or VT scheme to attain the multiplexing gain. Similarly, for the inverse links from R₁, …, R_n to T, transmission strategy can be selected according to the environment sensing results and the reduced feedback of channel quality.

(ii). Cluster-road side unit multiple-input-multiple-output

A conventional RF-link-assisted vehicle cluster selects a vehicle as the cluster head to connect with RF base stations [45]. However, since the coverage of an RSU for OWC is relatively small, the duration of the optical V2I link between a moving vehicle and an RSU is limited. Therefore, it is difficult to complete data transmission for all the vehicles in a cluster merely through the optical link between a single cluster head and the RSU. Besides, owing to the limited coverage of RSUs for OWC, frequent handover could degrade the efficiency of V2I links.

To improve the communication duration with RSUs, a cluster-to-infrastructure (C2I) mode is proposed first, where vehicles in a cluster can be served jointly. In particular, an RSU would continue transmitting data that is targeted at the cluster as long as there are still vehicles, which belong to the cluster and are currently moving under its coverage. After the cluster receives data from the RSU, the data would be routed to target vehicles via V2V links within the cluster. As a result, the communication duration with an RSU is extended with the aid of intra-cluster data exchange.

In order to avoid frequent handovers, the prediction of vehicle mobility is used to facilitate C2I communications. As shown in figure 5, a regional controller is employed to manage these RSUs on the roadside. Based on the uplink information from vehicles and the detected data by sensors at the RSUs, the regional controller could forecast the movements of vehicles and then decide which RSUs should serve a specific cluster, in order to realize seamless C2I communications without complicated and frequent handovers. Besides, the RSUs within the coverage of a regional controller can cooperate to serve multiple vehicles to attain SMP or diversity gain.

Figure 5.

A diagram of the C2I communications. (Online version in colour.)

To reduce the reliance on CSI feedback, the regional controller can evaluate channel quality via environment sensing and vehicle monitoring, and then adjust the transmission strategy dynamically. In particular, according to the channel quality, receiver-light association (interference-free light allocation or BIA) and transmission scheme (VT or CT) could be decided.

(c). Intelligent sensing in vehicular ad hoc networks

The adaptation to frequent variations of V2V and V2I optical links originating from vehicle movements is crucial to efficient data communications in VANET. However, due to the lack of uplink/downlink reciprocity for OWC, CSI feedback could be a huge overhead in outdoor high-mobility scenarios. Since the multi-path effect is negligible, optical channel gains can be viewed as invariant unless the location of vehicles changes [19] and are highly related to the geographical positions of transceivers, as well as actual atmosphere conditions. Therefore, it is possible to estimate and forecast optical channels at the transmitter side merely based on environment sensing and limited feedback, which facilitates dynamic multi-user transmission strategy and seamless C2I communications.

To improve the accuracy of CSI estimation and prediction, deep learning methodology could be introduced. The optical channels in current and consecutive time slots are related to vehicles’ position, velocity, current traffic status, current time stamp, the day of the week, etc. Therefore, CSI and the corresponding traffic data, including the vehicle’s trace with timestamps, traffic status and environmental data from sensors are collected for neural network training. With these inputs, the weights in the neural network are updated to reduce CSI estimation error. Thereafter, the trained neural network is able to provide online channel estimation and prediction with the detected traffic data as the inputs. Moreover, the network weights will be adjusted online with the addition of new traffic data.

6. Future work

As the deployment of light arrays, displays and optical detectors becomes extremely dense, optical MIMO has the potential to improve the system performance and yield various new applications. Several future research directions are listed below.

• (1)Optical camera communication (OCC) in mobile scenarios: In dense OWC networks, high channel correlation might restrict the number of independent data streams. Therefore, OWC adopting imaging detectors, especially cameras, has attracted much attention recently due to its reduced channel correlation, which is denoted as OCC [46]. There are two types of OCC wireless links, i.e. LED-camera link and screen-camera link. For LED-camera link, the camera demodulates the transmitted data according to the brightness of LEDs on the captured images. For the screen-camera link, 2D signals are embedded on the images displayed on the screen. 2D barcode frames have been investigated to improve the throughput. However, most of the current work assumes that the positions of LEDs or displays on the received images are known, which might be impractical in mobile scenarios. Therefore, OCC with moving transmitters or receivers should be investigated in detail.
• (2)Multi-mode adaptive MIMO: Nowadays, various optical devices can be embedded at either transmitter or receiver. Therefore, multi-mode adaptive transmission and reception can be developed, in order to ensure system performance in various scenarios. For example, using the data collected by sensors and the feedback information, the transmitter can decide the number of users to serve, modulation schemes and interference alignment methods intelligently. At the user side, non-imaging PDs can be used when the channel correlation is low. Meanwhile, low frame rate cameras can be adopted to demodulate low-rate signals and estimate the position of transmitters. Then, high frame rate cameras could trace the lights for high-rate transmission.
• (3)Mobile crowd sensing: With the development of sensor-embedded smartphones, mobile crowd sensing has become a popular research topic, which is relevant to the positioning accuracy of mobile devices, sensing area, energy consumption and so on. Thanks to the dense deployment of energy-efficient lights and displays, optical MIMO should be introduced into mobile crowd sensing as a complement to RF networks, to either enhance the sensing area or reduce power consumption. Besides, optical networks could facilitate accurate positioning and provide additional direction/rotation information of devices with the aid of imaging detectors.

7. Conclusion

In this paper, we first present a general model of optical MIMO and MU-MIMO, based on which several interference alignment schemes are illustrated. As OWC networks become increasingly dense, different networked MIMO topologies are demonstrated and then compared. Key issues which affect the performance of dense optical MIMO are discussed. Moreover, to address the new challenges in outdoor scenarios, the framework of optical MIMO for VANET is proposed. Finally, future research directions of networked optical MIMO are provided.

Data accessibility

This article has no additional data.

Authors' contributions

All the authors contributed to the writing of the manuscript.

Competing interests

We declare we have no competing interest.

Funding

This work was supported in part by National Natural Science Foundation of China(grant no. 61871253), in part by Guangdong Optical Wireless Communication Engineering and Technology Center and in part by Shenzhen VLC System Key Lab(ZDSYS20140512114229398).