Machine learning based optimization for vehicle-to-infrastructure communications

Accepted Manuscript Machine learning based optimization for vehicle-to-infrastructure communications Wei Xiang, Tao Huang, Wanggen Wan

PII: DOI: Reference:

S0167-739X(18)31832-6 https://doi.org/10.1016/j.future.2018.10.047 FUTURE 4552

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Future Generation Computer Systems

Received date : 31 July 2018 Revised date : 8 October 2018 Accepted date : 23 October 2018 Please cite this article as: W. Xiang, et al., Machine learning based optimization for vehicle-to-infrastructure communications, Future Generation Computer Systems (2018), https://doi.org/10.1016/j.future.2018.10.047 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Machine Learning Based Optimization for Vehicle-to-Infrastructure Communications Wei Xianga , Tao Huanga,∗, and Wanggen Wanb a College

of Science and Engineering, James Cook University, Cairns, QLD 4878, Australia b Institute of Smart City, and School of Communication and Information Engineering, Shanghai University, Shanghai 200444, China

Abstract In this paper, we study wireless communications in vehicle-to-infrastructure communications. In certain situations, multiple vehicles within a local range need to exchange information via a common roadside infrastructure. Example scenarios include busy intersections, and a driver with the knowledge of information from other vehicles can make safer decisions. Fast and reliable communications are essential in such use cases. We consider two different system models in this paper. In the first model, we consider the case where both the base station and vehicles are equipped with a single antenna. In the second model, we discuss the case where multiple antennas are installed on both the base station and vehicles. We show how the system can be optimized in both models. We then discuss how machine learning can be adopted in both models to realize the optimized system performance. Keywords: Vehicle-to-infrastructure, Internet of Vehicles, signal-antenna system, multi-antenna system, machine learning, information exchange

1. Introduction In recent years, more and more vehicles are purchased and used by families and individuals as basic daily transportation tools. Taking Australia as an example, according to the Australian Bureau of Statistics [1], there are 775 motor vehicles per 1000 people by January 2017. With the continuous growth in the number of vehicle ownership, driving safety becomes an important concern for the public. Among all types of vehicle collisions, intersection collisions are the most common. Typical crashes at an intersection include: traffic turning at an intersection and crash into incoming traffic, vehicle driver speeding at the yellow traffic light and crashing into vehicles traveling in the other direction, and vehicles crashing into crossing pedestrians. Usually these type crashes are fatal, because usually one of the vehicles involved in these types of crashes are often at high speed. These types of crashes can be actively avoided, if drivers are aware of the driving conditions of all the other vehicles. ∗ Corresponding author: Dr. Tao Huang, Email: [email protected], Address: A2.227, College of Science and Engineering, James Cook University, Cairns,QLD 4878, Australia. This work was supported in part by the National Natural Sciences Foundation of China under Grant 61628102.

Preprint submitted to Special Issue on Advanced AI for Multimedia Communications and Processing in IoVNovember 1, 2018

Figure 1: Example scenario at an large intersection. An intersection normally has complex traffic flows from four distinct directions. Vehicle drivers can make better and safer riving decisions, if he or she knows information such as location and speed in real time with minimum latency from the other vehicles also present in the intersection in question.

The development of the Internet of Vehicles (IoV) can greatly help drivers or even autonomous cars to make improved decisions at intersections so as to avoid potential crashes. The IoV is a special case of the Internet of Things (IoT). One special characteristic is that the movement of vehicles is limited by defined transportation infrastructure as well as defined traffic rules [2]. This characteristic can benefit the design and helps optimize the wireless communication between vehicles and road-side infrastructure. For example, in [3], the authors studied the integration of vehicle mobility prediction and machine learning based channel quality estimation. This study shows that the data transmission process can be significantly improved by scheduling vehicles’ data transmission time by predicting their expected position. In this case, a vehicle will only transmit data when the channel is in good condition. Also the work in [4] reveals that the channel condition can be exploited in the actual transmission context to improve the data transmission efficiency. Another important channel measurement metric termed the signal-to-noise ratio can be used to indicate the transmission hot-spot so as to achieve reliable data transmission [5]. Recently, an innovative scheme dubbed the Cognitive Internet of Vehicles (CIoV) was proposed in [6]. The motivation of this work is that the health status of a driver contributes significantly to the safety of both self and other drivers. The aim of the CIoV is to enhance transportation safety and network security by mining effective information from both the physical and network data spaces. The work in [7] proposed an SDN-based approach to develop a safetyoriented vehicular controller area network. The transportation safety is guaranteed by driver fatigue detection and emotional recognition. Further, the work in [8] applied cognitive computing to edge computing. Deep learning for the IoT has been introduced to the edge-computing environment. In addition, a novel offloading strategy was proposed to optimize the performance of IoT-based deep-learning applications with edge computing. Motivated by the reported studies in the literature, this paper focuses on scenarios where 2

machine learning can be employed to optimize the vehicle-to-infrastructure communications, and where all vehicles in a local network need to exchange information with all the other vehicles in the same network. We first survey two information exchange models , i.e., the single antenna system and the multiple antenna system. The objective of optimization is to improve the system sum rate. Note that in the multi-antenna system, we optimize the system degrees of freedom (DoF), which is a parameter indicating the system rate capacity. The remainder of the paper is organized as follows. The single antenna model and its optimization is discussed in Section 2. In Section 3, we study the multi-antenna system model and its optimization process. The integration of machine leaning in both models is discussed in Section 4, followed by concluding remarks drawn in Section 5. 2. Model I: Single-antenna Systems 2.1. Model Overview We firstly consider the model, where each vehicle is only equipped with a single antenna, and the local base station is also only equipped with one antenna. The complete information exchange among the users is performed via the multi-access and broadcast phases, as illustrated in Figs. 2 and 3. K vehicles exchange their information via the relay, and there is no direct link among the users [9]. In this system model, we incorporate physical-layer network coding. In the literature, physical-layer network coding has been shown to be able to significantly boost network throughput. To illustrate a use case of physical-layer network coding, we consider a two-vehicle network, where the two vehicles exchange information through a common relay. In the uplink phase, the two vehicles transmit their messages simultaneously to the common relay. For a BPSK modulated system, the message symbol transmitted from the two vehicles can be represented by x1 ∈ {−1, +1} and x2 ∈ {−1, +1}. The relay receives a superimposed signal. For ease of exposition, the AWGN channel is assumed, and the signal received at the relay can be written as y = x1 + x2 + n, where n is the additive white Gaussian noise with zero mean and power spectrum density N0 . After it receives the superimposed signal, the relay decodes a network coded message, which is a function of the messages from the two vehicles. In this BPSK modulated example, the superimposed message space is {−2, 0, +2}. When the superimposed message is 0, it means that the two message symbols transmitted from the two vehicles are different. By contrast, when the superimposed message is −2 or +2, it means that the two message transmitted from the two vehicles are identical. Therefore, in this BPSK modulated system, the relay can map the superimposed symbol with value 0 to −1, and map the superimposed symbol with value −2 or +2 to +1. Note that a mapping decision boundary should be computed for this system, and different mappings can be used. The relay then broadcasts this network coded message to the two vehicles, each of which can recover the other’s message by removing its own message from the network coded message. More details on physical-layer network coding can be referred to [10, 11, 12, 13]. In this model, we investigate the case, where two vehicles transmit simultaneously in one time in the multi-access phase as shown in Fig. 2. It is assumed that the local base station knows all the channel state information of all the users. When the base station receives the superimposed signal from each pair of vehicles, it computes their corresponding network coded messages. In the broadcast phase, the base station broadcasts the computed messages to the users as shown in Fig. 3. After the vehicle receives all the network coded messages from the base station, the relay can retrieve all the other vehicles’ messages by canceling its own message. In the following, we will focus on users’ transmission in the multi-access phase. 3

h1 Vehicle 1

hK

h2

hK-1 h3

Vehicle 2

Vehicle 3

Vehicle K

hl

h4

Vehicle K-1

Vehicle l

Vehicle 4

Figure 2: System model for the multi-access phase in uplink transmission. In this model, only two vehicles transmit simultaneously at one time in the multi-access phase. The solid arrows represent the transmitting vehicle pair, and the dashed arrows indicate silent vehicles.

h1 Vehicle 1

hK

h2

hK-1 h3

Vehicle K

hl

h4

Vehicle 2

Vehicle K-1

Vehicle 3

Vehicle 4

Vehicle l

Figure 3: System model for broadcast phase in downlink transmission. The broadcasted messages can be received by all the K vehicles.

In order to ensure the recovery of all the other vehicles’ messages by any vehicle, a Kvehicle system requires at least K − 1 pair-wise uplink transmissions in the multi-access phase. The number of downlink transmissions in the broadcast phase is the same as the number of uplink transmissions in the multi-access phase. The channel is assumed to be block fading, , indicating that the channels among the vehicles and the base station remain unchanged during the multi-access and broadcast phases. 2.2. Performance Measurements In this system, we employ nested lattice codes to illustrate the optimization procedure. It has been shown in [14, 15] that by employing nested lattice codes, the relay can easily decode the modulo sum of the messages rather than decoding the individual messages, as the addition of two users’ messages is still a lattice point in the same lattice structure. Our system model employs pair-wise transmission from the users to the relay. A subset Λ0 of Λ is dubbed a sublattice of Λ if and only if it is R-module. Given an R-lattice Λ and a sublattice Λ0 of Λ, the quotient group Λ/Λ0 naturally forms a partition of Λ. For a lattice network code (LNC), the message space is W = Λ/Λ0 , which can also be regarded as R-module [16]. The encoding and decoding of an LNC involves a lattice quantizer. Given a lattice Λ, its lattice quantizer is a mapping DΛ : Cn → Λ, which sends a point x ∈ Cn to a nearest lattice 4

Figure 4: Example of an Eisenstein integer based lattice code over GF(4), where different colors illustrate the partition of this LNC.

point in Λ in the sense of the Euclidean distance. That is, DΛ (x) , argminλ∈Λ kx − λk

(1)

where bold letters are used to represent row vectors. The encoder of an LNC E(·) maps each coset λ + Λ0 ∈ Λ/Λ0 to a coset leader. Given a message w ∈ W, the encoder can be written as: x = E(w).

(2)

Note that the image of the encoding function is also referred to as the constellation of the LNC. We illustrate an example of a lattice code over GF(4), as shown in Fig. 4. This example lattice is based on the Eisenstein integer [17]. On this lattice, we can construct a field structure of Z[ω]/2Z[ω]. The four cosets in Z[ω]/2Z[ω] are labeled by differently shaped points, as shown in Fig. 4. The message space of the LNC over GF(4) in this example is W = γ(Z[ω]/2Z[ω])n , where γ is a scaling factor to control the transmission power. Different colors in Fig. 4 illustrate the partition of the LNC. More detailed discussion on this GF(4) based LNC can be found in [18]. Given a transmission vehicle pair ( j, k) in the multi-access phase, let the message for vehicle j be w j and its transmitted signal be x j = E(w j ), with an average power constraint 1n E[||E(w j )||2 ] ≤ P. The received signal at the relay is y( j,k) = h j x j + hk xk + n

(3)

where n is a complex circularly-symmetric additive white Gaussian noise vector with zero mean and power spectrum density N0 . Denote by a = [a j , ak ] denote the computation vector for the vehicle pair ( j, k), a j , ak ∈ Λ and a j , ak < Λ0 . The goal for the base station is to decode an R-linear combination of transmitted message w( j,k) = a j w j + ak wk .

(4)

This computation is based on a scaled version of the received signal αy. Define ϕ as the natural projection mapping from Λ onto Λ/Λ0 via ϕ(λ) = λ + Λ0 . The decoder of the LNC can be 5

described by

ˆ ( j,k) = D(αy|h, a) = ϕ(DΛ (αy)) w

(5)

where h = [h j , hk ]. It is shown in [14] that the optimum scaling factor is the minimum mean square error (MMSE) coefficient given by αMMSE =

ahH ρ (1 + ||h||2 ρ)

(6)

where ρ is the SNR defined as P/N0 , and subscription H denotes the Hermitian transpose. For a computation vector a, the corresponding computation rate is [14, 15]   H 2 !−1   ρ|ah |  C + 2 (7) R j,k (h, a) = log2  ||a|| − . 1 + ρ||h||2  2.3. Optimization objective

As previously discussed, we consider pair-wise transmission scheduling in this system. The easiest way to schedule vehicles in this system is a sequential order. Given a system with K vehicles labeled from 1 to K, the i-th time slot of the multi-access phase, the scheduled transmission vehicle-pair is (i, i + 1). The received signal at the base station is y(i,i+1) = hi xi + hi+1 xi+1 + n.

(8)

Then the base station computes the R-linear combination of the transmitted message for vehiclepair (i, i + 1) as w(i,i+1) = ai wi + ai+1 wi+1 . (9) There will be a total of K − 1 time slots in the multi-access phase. For ease of exposition, in the following, symbols h and a are omitted in the notation of the computation rate for each pair of vehicles. Each vehicle’s transmission rate for this transmission scheduling scheme is    RC if l = 1     1,2 C C Rl <  (10) min{R , R } if l = 2, · · · , (K − 1)  l−1,l l,l+1    C R if l = K K−1,K

where Rl is the transmission rate for vehicle l, and RCj,k is given in (7). The explanation of (10) is as follows. Vehicle 1 only transmits in time slot 1 with user 2, so we have R1 < RC1,2 . Vehicle L only transmits in time slot K − 1 with user K − 1, so we have RK < RCK−1,K . For vehicle l ∈ {2, 3, · · · , K − 1}, it transmits in the (l − 1)-th and l-th time slots, with the previously scheduled vehicle and next scheduled vehicle respectively. So we have Rl < min{RCl−1,l , RCl,l+1 }. The sum-rate for the uplink can be expressed as Rsum =

K X l=1

6

Rl .

(11)

2.4. Optimized pair-wise transmission Conventional pair-wise transmission is simple to design. However, it does not consider the effect of the time-varying fading channel. We now present an improved pair-wise transmission for this system. The essential idea is that in each time slot, a pair of vehicles, which has the maximum computation rate, are selected for transmission. In order for the vehicle to recover all the others’ messages from K−1 network codewords forwarded from the relay, the scheduled userpairs in K − 1 time slots should be linearly independent of each other. The following algorithm describes how to select the vehicle-pair for transmission. Algorithm 1: Improved pair-wise transmission 1. The users are labeled from 1 to K; 2. For time slot 1, we select vehicle pairs l1 and l2 such that (l1 , l2 ) = arg max{RCl1 ,l2 |l1 , l2 ∈ {1, · · · , K}, l1 < l2 }

(12)

where RCl1 ,l2 is given in (7). Note that for each vehicle pairs (l1 , l2 ), the computation rate RCl1 ,l2 should also be maximized by choosing optimal a = [al1 , al2 ]. This can be effectively achieved via the Gaussian reduction algorithm [15]; 3. We form a row vector of length K s1 = [0 · · · 0 1 0 · · · 0 1 0 · · · 0] ↑ l1

↑ l2

(13)

where s1 [l1 ] = s1 [l2 ] = 1 and s1 [l] = 0, l ∈ {1, · · · , K}, l , l1 , l , l2 . Note that this row vector is binary, which is referred to as the pair-wise user selection vector (PSV); 4. For time slot 2, we select vehicle pairs l3 and l4 such that s.t.

(l3 , l4 ) = arg max{RCl3 ,l4 |l3 , l4 ∈ {1, · · · , K}, l3 < l4 }

(14)

s2 = [0 · · · 0 1 0 · · · 0 1 0 · · · 0] and s2 , s1 ;

(15)

↑ l3

↑ l4

5. We now define the following set  i      X  F (s1 , s2 , · · · , si ) =  κt st , κt ∈ {0, 1}    

(16)

t=1

where the summation is modulo-2 addition. This set forms an i-dimensional subspace over binary field, which is spanned by the binary PSVs s1 , s2 ,· · · , si ;

6. For the i-th time slot, 2 < i ≤ K − 1, we select the pair of vehicles, such that s.t.

( j, k) = arg max{RCj,k | j, k ∈ {1, · · · , L}, j < k}

(17)

si < F (s1 , s2 , · · · , si−1 ).

(18)

The constraint in (18) ensures that the PSV of the vehicle-pair selected in the i-th time slot do not fall in the subspace spanned by s1 , s2 , · · · , si−1 . That is, new message will be received by the base station in the i-th time slot; 7

Figure 5: Users’ sum-rate for the Z[i]-based LNC.

7. The procedure terminates after K − 1 selections. After K − 1 vehicle-pair selections, a pair-wise transmission scheduling matrix is constructed as follows S = [s1 s2 · · · sK−1 ]T (19)

where T denotes the transpose operation. This matrix has a rank of K − 1 due to the constraints (15) and (18) during the selection process. This ensures that a vehicle can decode all the other vehicles’ messages after having received these K − 1 network coded messages. By employing this improved pair-wise transmission scheme, the transmission rate for vehicle l must be less than the minimum computation rate, of which the l-th vehicle was scheduled for transmission. That is, (20) Rl < min{RCj1 ,l , RCj2 ,l , · · · , RCl,k1 , RCl,k2 , · · · } where 1 ≤ j1 , j2 , · · · ≤ l − 1, and l + 1 ≤ k1 , k2 , · · · ≤ K. The vehicles’ sum-rate can be expressed as K X Rsum = Rl . (21) l=1

This improved pair-wise scheduling scheme can be further extended to schedule more than two vehicles to transmit in each time slot, so as to take the advantage of the compute-and-forward scheme for multi-user systems. 2.5. Numerical results We compare the vehicles’ average uplink sum-rates between the conventional pair-wise transmission schemes and improved pair-wise transmission for the 3-vehicle and 4-vehicle cases.

8

Figure 6: Users’ sum-rate for the Z[ω]-based LNC.

In the simulation, we consider the sum-rate for the Gaussian integer Z[i]-based and Eisenstein integer Z[ω]-based LNCs with three and four vehicles, respectively. A Gaussian integer is a complex number that its real and imaginary√parts are both integers. It can be represented by Z[i] = {a + bi|a, b ∈ Z}, where i = −1. The norm of a Gaussian integer can be calculated as a2 + b2 . A Z[i]-based LNC is hypercube shaped. An Eisenstein in√ teger can be written as Z[ω] = {a + bω|a, b ∈ Z}, where ω = −1+2 −3 . The norm of an Eisenstein integer is a2 + b2 − ab. A Z[ω]-based LNC is hexagonal shaped. In this work, we consider the message space W = F13  Z[i]/βZ[i]  Z[ω]/γZ[ω], where β = 2 + 3i and γ = 4 + 3ω. In this case, we have EZ[i] (W) = {0, ±1, ±i, ±(1 + i), ±(1 − i), ±2, ±2i} and EZ[ω] (W) = {0, ±1, ±ω, ±(1 + ω), ±(1 − ω), ±(1 + 2ω), ±(2 + ω)}. The Rayleigh fading channel is assumed in our simulation. At each SNR, the average sum-rate is computed base on 105 channel realizations. Fig. 5 and 6 show the sum-rate for the Gaussian integer Z[i]-based and Eisenstein integer Z[ω]-based LNCs with three and four vehicles, respectively. It is shown that the improved pair-wise transmission scheme is capable of considerably improving the sum-rate compared to its conventional counterpart. For example, for the 4-vehicle system, a 2 bits/s/Hz improvement is observed at the SNR of 30 dB, while a 1.25 bits/s/Hz improvement is achieved for the 3-vehicle system. Larger improvements can be achieved at higher SNRs. 3. Multi-antenna Systems 3.1. System Overview We now extend the previous system from the single-antenna to multi-antenna scenario. Similar to the preceding model, K vehicles exchange information with the aid of a common base station. The system model is similar to the single-antenna system studied in the preceding section. The main difference lies in the uplink transmission. Due to the fact that both the vehicles and base station are equipped with multiple antennas, the vehicles can communicate with the 9

hK

h1 Vehicle 1

h2

hK-1 h3

Vehicle 2

Vehicle 3

h4

Vehicle K

hl

Vehicle 4

Vehicle K-1

Vehicle l

Figure 7: A multi-antenna system, in which each vehicle wants to learn all the messages in the system. The difference between the single-antenna and multi-antenna systems lies in whether or not simultaneous transmission by all the vehicles is possible by means of signal spacial multiplexing.

base station by means of signal spacial multiplexing, as illustrated in Fig. 7. Each vehicle is equipped with M antennas, and the relay with N antennas. Each round of information exchange consists of two phases, namely, an uplink phase and a downlink phase. In the uplink phase, all users transmit to the relay simultaneously using a common frequency band. In the downlink phase, the relay broadcasts to the users. We now discuss in more detail the uplink and downlink transmission of this multi-antenna system. Assume that the uplink phase consists of T u channel uses. In the tu -th channel use, the received signal vector yR (tu ) at the base station is given by yR (tu ) =

K X i=1

Hi (tu )xi (tu ) + nR (tu ), tu = 1, · · · , T u

where Hi (tu ) ∈ CN×M denotes the channel matrix from vehicle i to base station R, xi (tu ) is the transmitted signal from vehicle i, and nR (tu ) is an additive circularly-symmetric Gaussian noise vector drawn from CN(0, σ2 I). The transmission power of each user is limited to P. Let xi = [xTi (1) · · · xTi (T u )]T , i = 1, · · · , K, and Hi = diag{Hi (1), · · · , Hi (T u )}   0  Hi (1) 0    ..  . =  0 . 0   0 0 Hi (T u )

Then, the signal received by the base station in the uplink phase can be compactly written as yR = Hx + nR

(22)

where H = [H1 · · · HK ], x = [xT1 · · · xTK ]T , yR = [yTR (1) · · · yTR (T u )]T , and nR = [nTR (1) · · · nTR (T u )]T . We now consider the downlink transmission which, without loss of generality, consists of T d channel uses. In the td -th downlink channel use, the received signal at vehicle i, i = 1, · · · , K, is yi (td ) = Gi (td )xR (td ) + ni (td ), td = 1, · · · , T d

where Gi (td ) ∈ C M×N denotes the channel matrix from the base station to vehicle i, and ni (td ) is an additive circularly-symmetric Gaussian noise vector drawn from CN(0, σ2 I). The transmission power of the base station is limited to P. 10

Let xR = [xTR (1) · · · xTR (T d )]T . The received signal of vehicle i in the T d downlink channel uses is written as yi = Gi xR + ni , i = 1, · · · , K (23)

where Gi = diag{Gi (1), · · · , Gi (T d )}, yi = [yTi (1) · · · yTi (T d )]T , and ni = [nTi (1) · · · nTi (T d )]T . Upon receiving yi , each vehicle i decodes the messages from all the other vehicles, i.e., b x1 , · · · ,b xi−1 ,b xi+1 , · · · ,b xK , with the knowledge of the self-message xi . It is assumed that all the entries of the uplink/downlink channel matrices are independently drawn from a continuous distribution. This ensures that all the channel matrices are of full rank, e.g., rank(Hi (tu )) = min{M, N}, with probability one. 3.2. Performance Metrics

In a multi-antenna system, the degrees of freedom (DoF) is an important metric to understand its capacity behavior. Denote by ρ = σP2 the signal-to-noise raito (SNR). Let Ri (ρ) be the rate (per channel use) of user i at SNR ρ, i = 1, · · · , K. Define the decoding rate of user i as R˜ i (ρ) , PK PK ˜ i0 =1,i0 ,i Ri0 (ρ), i = 1, · · · , K, and define the sum-rate per channel use as R(ρ) , i=1 Ri (ρ). A sum-rate of R˜ i (ρ) is said to be achievable if each user i decodes the messages from all the other K − 1 users with vanishing error probability. Then, an achievable DoF per channel use is defined as R(ρ) ∆ . (24) d = lim ρ→∞ log ρ The maximum of d in (24) over all achievable schemes is referred to as the DoF capacity. For single-user MIMO channel with M inputs and N outputs, the capacity growth rate can be shown to be min(M, N)log(SNR). Towards this end, the degrees of freedom d is the maximum multiplexing gain of a generalized MIMO system. We first consider a system with fixed uplink/downlink time allocation, i.e., T u and T d are fixed. For the K-vehicle half-duplex multi-antenna system, the DoF capacity can be shown to be: #   K M 1    min{(K − 1)MT , MT }, ∈ 0, (25a) u d    T N K−1    !    K M 1 d = min{NT , MT }, ∈ , 1 (25b)  u d   T N K−1       K M    min{NT u , NT d }, ∈ [1, ∞) . (25c) T N  i 1 As can be seen from the above equation, in the case of M N ∈ 0, K−1 , the DoF is bottlenecked at the user side. This is because (25a) depends on the user’s antenna number M, but not on the relay’s antenna number N. In this case, increasing the number of antennas at the relay does not help further increase the system DoF capacity. On the other hand, in the case of M N ∈ [1, ∞), Eqn. (25c) suggests that the DoF depends on N instead of M, implying that the DoF is bottlenecked at the relay. In this case, increasing the number of antennas at the  user does not help further 1 ∈ increase the system DoF capacity. In the remaining case of M N K−1 , 1 , Eqn. (25b) that the DoF depends on both M and N. We also see that the DoF depends on the uplink/downlink time durations T u and T d .

11

3.3. Optimized DoF We now consider optimizing the uplink/downlink time allocation with the objective of maximizing the DoF of the system in Eq. (25). Given the total time duration T , this problem is formulated as maximize

d

(26a)

subject to

Tu + Td = T

(26b)

T u ,T d

where d is given in (25). The DoF capacity with optimal uplink/downlink time allocation is given by #   M 1    (K − 1)M, ∈ 0, (27a)    N K−1    !    K MN M 1 dmax =  , ∈ ,1 (27b)    M + N N K −1       KN M    , ∈ [1, ∞) . (27c) 2 N The corresponding optimal uplink/downlink time allocation is #   1 M 1    , ∈ 0,    K−1 N K−1    !   M Tu  M 1 =  , ∈ , 1   Td  N N K−1       M    1, ∈ [1, ∞) . N

(28a) (28b) (28c)

Note that T is selected such that T u and T d in (28) are integers. As can be observed from the above equation, the optimized DoF depends on the antenna ratio. The optimal time allocation i for uplink and downlink are also dependent on the antenna M 1 ratio. In the case of N ∈ 0, K−1 , the optimum DoF is bottlenecked at the user side. In this case, increasing the number of antennas at the relay does not help further increase the system optimum DoF capacity. On the other hand, in the case of M N ∈ [1, ∞), the optimum DoF is bottlenecked at the relay. In this case, increasing the number of antennas at the user does not  help further M 1 increase the system optimum DoF capacity. In the remaining case of N ∈ K−1 , 1 , the optimum DoF depends on both M and N. We now consider the DoF gain achieved by the uplink/downlink time allocation, as compared with the equal time allocation. By letting T u = T d = T2 in (25), the DoF capacity with equal time allocation is shown to be  KM M    , ∈ (0, 1) (29a)    2 N deq =    KN M    , ∈ [1, ∞) . (29b) 2 N Define the DoF gain ∆d , dmax − deq , where dmax is given in (27). We can now quantify the 1 relative DoF gain by evaluating d∆deq . For K = 3, the relative DoF gain is 33.33% at M N = 2 , and for 12

4.5N

Maximized DoF with optimal time allocation DoF with equal time allocation

K= 9

4N

DoF per channel use

3.5N 3N K= 6 2.5N 2N 1.5N

K= 3

1N 0.5N M/N achieves the maximal DoF gain 0 0

0.2

0.4

0.6 M/N

0.8

Figure 8: DoF capacity of the system versus the antenna ratio

M N.

1

1.2

The number of vehicles is set to K = 3, 6, 9.

√ K ≥ 4, the relative DoF gain is 41.42% at M 2 − 1. A significant DoF capacity improvement N = is attainable by the optimal time allocation scheme. For asymptotic cases where there is a large number of vehicles (i.e., K → ∞ and where the base station has a much larger number of antennas than the vehicle’s M N → 0), the relative DoF ∆d gain deq can achieve the maximum of 100% 1− ∆d = Mlim deq N →0 N →0 1 +

lim M

M N M N

= 100%.

An intuitive explanation is as follows. When K → ∞, the optimal time allocation is given by Tu M M M T d = N in (28b) for any N ∈ (0, 1). In conjunction with the condition of N → 0, one can see that the optimal time allocation strategy is to allocate almost all the time for downlink transmission, which leads to a DoF gain of 100%, as compared with equal time allocation. 3.4. Numerical Results Now we present numerical results to demonstrate the improvement in the optimized DoF. We show the DoF with different numbers of vehicles. Fig. 8 compares the DoF per channel use with K = 3, 6, and 9. As can be seen from the figure, the total DoF per channel use increases with the number of users. The antenna configuration that achieves the maximal DoF gain for each K is marked in Fig. 8. Fig. 9 shows the DoF capacity against the number of vehicles K for given 1 2 M antenna ratios of M N = 3 , 3 and N ≥ 1. Fig. 9 suggests that the optimized DoF is a piecewise M linear function of K when N < 1, which is also inferred in (27a) and (27b). Furthermore, as can be observed from Fig. 9, the DoF gain increases with the value of K when M N < 1. In the M event that N ≥ 1, (27c) shows that the optimized DoF is a linear function of K, and equal time allocation becomes optimal for all integers K ≥ 2. 13

5N 4.5N

Maximized DoF with optimal time allocation DoF with equal time allocation

DoF per channel use

4N 3.5N

M/N t 1

3N 2.5N 2N

M/N = 2/3

1.5N 1N 0.5N M/N = 1/3 0 2

3

4

5

6 K

Figure 9: DoF capacity of the system with various antenna ratios 1 2 M is set to M N = 3 , 3 , and N ≥ 1.

7 M N

8

9

10

versus the number of vehicles K. The antenna ratio

4. Machine Learning Integration 4.1. Machine Learning Problem In this section, we discuss how the machine learning paradigm can be adopted to optimize the aforementioned two systems. In the first single-antenna system, the objective is to maximize the system sum rate. The system sum rate can be significantly improved by scheduling each vehicle in consideration of their channel condition. Towards this end, the base station needs to obtain the knowledge of the channel condition of each vehicle in the system. In the multi-antenna system, the goal is to maximize the system DoF. In this system, we improve the system DoF by scheduling the uplink and downlink transmissions base on the number of antennas and the number of vehicles in the system. With the knowledge of the channel condition of each vehicle in the system, the data exchange rate can be maximized with the optimized DoF. Therefore, the challenge is to measure the channel condition in real time. In reality, the system can measure the channel condition of each vehicle in real time through an additional signaling process. Thus additional transmission overheads at the protocol level is required. The induced latency due to the signaling overhead may not acceptable in our system. Time is a critical factor for information exchange at traffic intersections, so that all drivers at a traffic intersection are fully aware of the intensions of all the other vehicles at the same intersection in real-time. Previous studies in [3, 4, 5] have shown that the channel condition in each location around a given base station can be pre-collected and studied with the aid of machine learning. 4.2. Machine Learning Algorithms Two machine learning algorithms are employed to optimize the two systems aforementioned. The first one is linear regression, while the other one is the convolutional neural network. The linear regression algorithm is used to predict the channel conditions. The linear regression model is widely used for forecasting new values based on independent predictors. Usually, 14

the first step in a regression analysis is to hypothesize the structure of the relationship between the input attributes and the target. At a traffic intersection, each vehicle experiences its own channel condition, depending on its location and surrounding objects, which include buildings, plants, vehicles, and pedestrians. The channel condition can also be affected by weather conditions, such as cloud conditions, raining days, etc.. These factors need to be used in the machine learning training process as the input attributes, and the target is the channel condition in each location at the traffic intersection. After the training process, the system will be able to learn the channel conditions of each vehicle at the intersection. With the predicted channel condition, the base station at the intersection can schedule the transmission immediately, without the transmission overhead in the signaling and channel condition measurement process. For vehicles in critical positions, e.g., about entering the intersection, the base station can instruct these vehicles to pre-code its messages based on the predicated channel conditions. Another machine learning algorithm used in the system is convolutional neural network (CNN), which is a class of deep and feed-forward artificial neural networks that have been wildly used for image classification in real time video feeds [19]. At a traffic intersection, cameras can be deployed to evaluate the current environment, such as the numbers of vehicles and pedestrians, by applying the CNN algorithm to the real-time video stream. These image classification results can be fed to the linear regression algorithm as part of the input attributes for predicting the channel condition of each vehicle. 5. Conclusion In this paper, we studied inter-vehicle communications, where multiple vehicles exchange information through a common base station. This is a common on-road scenario at large intersections, where drivers take better and safer control of their vehicles if they know the condition of their surrounding vehicles. Two system configurations were considered, namely the single-antenna and multi-antenna systems. The objective is to optimize the system data transmission rate and the capacity. We showed the method to achieve the maximum performance of the system. Significant performance improvements were demonstrated through the presentation of simulated results. We discussed how machine learning can be integrated to the system to facilitate the system optimization. In particular, we discussed the application of the linear regression and convolutional neural network approaches in the system. The integration of the linear regression and convolutional neural network algorithms can optimize the system without inducing additional signaling overheads. In vehicle communications, delay is critical for information exchange among nearby vehicles. Applying the machine learning paradigm to optimize wireless communications systems can effectively mitigate the delay experienced in conventional systems. References [1] http://www.abs.gov.au/AUSSTATS/[email protected]/Lookup/9309.0Main+Featu- res131%20Jan%202017?OpenDocument [2] F. Yang, S. Wang, J. Li, Z. Liu, and Q. Sun, “An overview of internet of vehicles,” in China Communications, vol. 11, no. 10, pp. 1-15, Oct. 2014. [3] B. Sliwa, T. Liebig, R. Falkenberg, J. Pillmann, and C. Wietfeld, “Efficient Machine-type Communication using Multi-metric Context-awareness for Cars used as Mobile Sensors in Upcoming 5G Networks,” in Proc. 2018 IEEE 88th IEEE Vehicular Technology Conference (VTC-Fall), Chicago, USA, Aug. 2018. [4] N. Bui, M. Cesana, S. A. Hosseini, Q. Liao, I. Malanchini, and J. Widmer, “A survey of anticipatory mobile networking: Context-based classification, prediction methodologies, and optimization techniques,” IEEE Communications Surveys and Tutorials, vol. 19, no. 3, pp. 1790-1821, Apr. 2017.

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[5] C. Ide, B. Dusza, and C. Wietfeld, “Client-based control of the interdependence between LTE MTC and human data traffic in vehicular environments, IEEE Transactions on Vehicular Technology, vol. 64, no. 5, pp. 1856-1871, May 2015. [6] M. Chen, Y. Tian, G. Fortino, J. Zhang, and I. Humar “Cognitive internet of vehicles” Comput. Commun., pp. 58-70, May 2018, doi:10.1016/j.comcom.2018.02.006. [7] Y. Zhang, M. Chen, N. Guizani, D. Wu, and V. C. Leung, SOVCAN: Safety-oriented vehicular controller area network, IEEE Commun. Mag., vol. 55, no. 8, pp. 94-99, Aug. 2017. [8] M. Chen, and V. Leung, “From cloud-based communications to cognition-based communications: a computing perspective,” Computer Commun., vol. 128, pp. 74-79, Sep. 2018. [9] D. G¨und¨uz, A. Yener, A. Goldsmith, and H. Poor, “The multi-way relay channel,” in Proc. IEEE International Symposium on Information Theory (ISIT), Seoul, Korea, July 2009, pp. 339-343. [10] S. Zhang, and S.-C. Liew, “Channel coding and decoding in a relay system operated with physical-layer network coding,” IEEE J. Sel. Areas Commun., vol. 27, no. 5, pp. 788-796, Jun. 2009. [11] S. Zhang, S.-C. Liew, and P. P. Lam, “Hot topic: Physical layer network coding,” in Proc. 12th ACM International Conference on Mobile Computing and Networking (MobilCom), Los Angeles, CA, Sep. 2006, pp. 358-365. [12] T. Huang, T. Yang, J. Yuan and I. Land, “Design of Irregular Repeat-Accumulate Coded Physical-Layer Network Coding for Gaussian Two-Way Relay Channels,” in IEEE Transactions on Communications, vol. 61, no. 3, pp. 897-909, March 2013. [13] T. Yang, I. Land, T. Huang, J. Yuan and Z. Chen, “Distance Spectrum and Performance of Channel-Coded PhysicalLayer Network Coding for Binary-Input Gaussian Two-Way Relay Channels,” in IEEE Transactions on Communications, vol. 60, no. 6, pp. 1499-1510, June 2012. [14] B. Nazer, and M. Gastpar, “Compute-and-forward: harnessing interference through structured codes,” IEEE Transactions on Information Theory, vol. 57, no. 10, pp. 6463-6486, Oct. 2011. [15] C. Feng, D. Silva, and F. R. Kschischang, “An algebraic approach to physical-layer network coding,” IEEE Transaction on Information Theory, vol. 59, no. 11, pp. 7576-7596, Nov. 2013. [16] J. H. Conway, and N. J. A. Sloane, Sphere Packings, Lattices and Groups, 3rd ed. New York: Springer-Verlag, 1999. [17] Q. T. Sun, J. Yuan, T. Huang and K. W. Shum, “Lattice Network Codes Based on Eisenstein Integers,” in IEEE Transactions on Communications, vol. 61, no. 7, pp. 2713-2725, July 2013. [18] Q. T. Sun, T. Huang and J. Yuan, “On lattice-partition-based physical-layer network coding over GF(4),” IEEE Commun. Letters, vol. 17, no. 10, pp. 1988-1991, Oct. 2013. [19] N. Sharma, V. Jain, and A. Mishra,“An Analysis Of Convolutional Neural Networks For Image Classification,” Procedia Computer Science, vol 132, pp. 377-384. 2018.

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Dr. Taoo Huang is currently a post-doctorral research h fellow at James Cookk University, Cairns, Australia. He reeceived hiss PhD froom the School S of Electrical Engineering and mmunications, University of Neew South Wales, W Syd dney, Austrralia, in 20 016. He Telecom receivedd his M. Eng. E (Advaanced) degrree in Senssor System m Signal Prrocessing from fr the Universsity of Adeelaide, Adelaide, Austtralia, in 20 007. He received his B. Eng. deegree in Electronnic and Innformation Engineeriing from Huazhong Universityy of Scien nce and Technollogy, Wuhaan, China, in 2003. Drr. Huang waas an Endeaavour Austrralia Cheun ng Kong Researcch Fellow (22014), awarrded by the Commonw wealth Goveernment of A Australia. He H was a recipiennt of the Auustralian Po ostgraduate Award, and d the Engin neering Ressearch Awarrd at the Universsity of New w South Waales. Dr. Huuang was a co-recipieent of a Besst Academiic Paper Award of IEEE Wireless W Com mmunicatioons and Neetworking Conference C (WCNC), Cancun, Mexicoo in 2011. Dr. D Huang was w a seniorr engineer, technical t au uthority, andd project leaad at the EMS SA ATCOM Paacific, Adellaide, Austrralia (2007--2009). He was w a reseaarch assistan nt at the Universsity of New w South Wales W (20144-2016). Hee was a viisiting reseearch fellow w at the Institutee of Networrk Coding, Chinese Unniversity off Hong Kon ng, Hong K Kong, Chinaa (2014). His reseearch intereests include wireless coommunicatio ons, Interneet of Thingss, machine learning, l and dataa analytics.  

 

Professsor Wangge en Wan  recceived  his  PPhD  degree e  in  informa ation  engin eering  from m  Xidian  Universsity, China,  in 1992. Fro om 1991 too 1992, he w was a visitin ng scholar w with the Co omputer  Engineeering  Deparrtment,  former  Minsk  Radio  Engiineering  Insstitute,  Belaarus,  the  USSR.  U He  was  a  postdocto oral  researcch  fellow  with  the  Informatio on  and  Coontrol  Engineering  ment of Xi’aan Jiao‐Tongg Universityy, China, fro om 1993 to 1995. From m 1995 to 1 1997, he  Departm was an  associate p professor w with the Elecctronic and d Informatio on Engineerring Department of  nd was prom moted to prrofessor in 1 1998. He waas a visitingg scholar  Shanghai Universitty China, an with  th he  Electricaal  and  Elecctronic  Eng ineering  Department  of  Hong  KKong  Unive ersity  of  Sciencee  and  Techn nology,  Clear  Water  B Bay,  China,  from  1998 8  to  1999.  He  was  a visiting  professor and secttion head aat the Multiimedia Inno ovation Cen nter of Hongg Kong Polyytechnic 

Universsity, Hung Hom, China, from 2000  to 2004. Since 2004, h he has beenn with the School of  Commu unication  and  Informaation  Enginneering,  Sh hanghai  Un niversity,  Chhina,  wherre  he  is  currently a professsor, dean off the Internaational Office, directorr of the Insttitute of Sm mart City,  and pro ogram leadeer of the Circuit and Syystems Dep partment. He is a fellow w of the IET T and an  IEEE  seenior  memb ber.  He  hass  been  co‐cchairman  fo or  many  intternational   conference es  since  2008. H His research h interests include dataa mining, siignal processing, and ccomputer ggraphics.  He is a ccoauthor off approximaately 200 accademic pap pers. 

  Professsor Wei Xia ang is the Foundation F Professor and a Head off Discipline Electronic Systems S

and Inte ernet of Thiings Engine eering at Ja ames Cook University. The IoT deegree is the e first of its kind d in Austtralia. He is a Felloow of the IET (FIE ET), a Felloow of En ngineers Australiia (FIEAust), and a Sen nior Membe r of the IEEE E (SMIEEE). During 2004 and 2015, 2 he was w an Asso ociate Profe essor with the t School of Mechanical and Electriccal Engineerring, Univerrsity of Soutthern Quee ensland, Too owoomba, A Australia. He H was a co-recip pient of thrree Best Paper Award ds at 2015 5 WCSP, 2011 2 IEEE WCNC, an nd 2009 ICWMC C. He has been awarded severral prestigio ous fellows ship titles. He was named a Queenssland Intern national Fellow (2010-2 2011) by th he Queensland Governnment of Australia, A an Ende eavour Ressearch Fello ow (2012-20 013) by the Commonw wealth Goveernment of Australia, A a Smarrt Futures Fellow F (201 12-2015) byy the Quee ensland Go overnment oof Australia a, and a JSPS In nvitational Fellow F jointlly by the Au ustralian Ac cademy of Science S andd Japanese Society for Pro omotion of Science (2 2014-2015).. In 2008, he was a visiting sccholar at Nanyang N Techno ological University, Sin ngapore. Du uring Oct. 2010 and Mar. 2011,, he was a visiting scholarr at the Univversity of Mississippi, O Oxford, MS, USA. During Aug. 20012 and Ma ar. 2013, He wass an Endea avour visiting associa ate professo or at the University U oof Hong Ko ong. His researcch interestss are in th he broad area of co ommunications and i nformation theory, particularly coding and signal processing g for multime edia commu unications ssystems.      

In this paper, we study wireless communications in vehicle-to-infrastructure communications. In certain situations, multiple vehicles within a local range need to exchange information via a common roadside infrastructure. Example scenarios include busy intersections, and a driver with the knowledge of information from other vehicles can make safer decisions. Fast and reliable communications are essential in such use cases. We consider two different system models in this paper. In the first model, we consider the case where both the base station and vehicles are equipped with a single antenna. In the second model, we discuss the case where multiple antennas are installed on both the base station and vehicles. We show how the system can be optimized in both models. We then discuss how machine learning can be adopted in both models to realize the optimized system performance.