Prediction and Communication Co-design for Ultra-Reliable and Low-Latency Communications

09/06/2019 ∙ by Zhanwei Hou, et al. ∙ The University of Sydney Beijing University of Technology 0

Ultra-reliable and low-latency communications (URLLC) are considered as one of three new application scenarios in the fifth generation cellular networks. In this work, we aim to reduce the user experienced delay through prediction and communication co-design, where each mobile device predicts its future states and sends them to a data center in advance. Since predictions are not error-free, we consider prediction errors and packet losses in communications when evaluating the reliability of the system. Then, we formulate an optimization problem that maximizes the number of URLLC services supported by the system by optimizing time and frequency resources and the prediction horizon. Simulation results verify the effectiveness of the proposed method, and show that the tradeoff between user experienced delay and reliability can be improved significantly via prediction and communication co-design. Furthermore, we carried out an experiment on the remote control in a virtual factory, and validated our concept on prediction and communication co-design with the practical mobility data generated by a real tactile device.

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I Introductions

I-a Backgrounds and Motivations

Ultra-reliable and low-latency communications (URLLC) are one of the new application scenarios in 5G communications [2]. By achieving ultra-high reliability (e.g., to

packet loss probability) and ultra-low end-to-end (E2E) delay (e.g,

 ms), URLLC lays the foundation for several mission-critical applications, such as industrial automation, Tactile Internet, remote driving, virtual reality (VR), and tele-surgery [14, 40, 8]. How to achieve two conflicting requirements on delay and reliability remains an open problem.

To improve reliability, several technologies have been proposed in the existing literature and specifications, such as K-repetition [1], frequency hopping [31], large-scale antenna systems [38], and multi-connectivity [23]. With these technologies, different kinds of diversities are exploited to improve reliability at the cost of more radio resources. On the other hand, to reduce latency in the air interface, the short frame structure was proposed in 5G New Radio (NR)[19], and fast uplink grant schemes were proposed to reduce access delay [28, 13]. However, there are some other delay components in the networks, such as delays in buffers of devices, computing systems, backhauls, and core networks. As a result, the user experienced delay can hardly meet the requirements of URLLC. Novel concepts and technologies that can reduce the user experienced delay and improve overall reliability (i.e., total packet losses and errors in different parts of the system) are in urgent need.

To tackle these challenges, we aim to meet the requirements of URLLC by jointly optimizing prediction and communication. The basic idea is to predict the future system states at the transmitter, such as locations and force feedback, and then send them to the receiver in advance. In this way, the user experienced delay can be reduced significantly. For example, if the E2E delay is  ms and the prediction horizon is  ms, then the user experienced delay is  ms. However, predictions are not error-free, and long prediction horizon will lead to a large prediction error probability. Intuitively, there is a trade-off between the user experienced delay and the overall reliability. To satisfy the two conflicting requirements of URLLC, we need to jointly optimize the prediction and communication systems. Specifically, in this paper, we will address the following questions: 1) how to characterize the tradeoff between user-experienced delay and overall reliability with prediction and communication co-design? 2) Is it possible to satisfy the requirements of URLLC by prediction and communication co-design? 3) If yes, how to maximize the number of URLLC services that can be supported by the system?

The above questions are challenging to answer since multiple components of delay and errors are involved in prediction and communication systems. As such, we need a prediction and communication co-design framework which takes different delay components and errors into account. Moreover, the complicated constraints on the user experienced delay and the overall reliability are non-convex in general, and hence it is very difficult to find the optimal solution.

I-B Our Contributions

The main contributions of this paper are summarized as follows:

  • We establish a framework for prediction and communication co-design, where the time and frequency resource allocation in the communication system and the prediction horizon in the prediction system are jointly optimized to maximize the number of devices that can be supported in the system.

  • We derive the closed-form expressions of the decoding error probability, the queueing delay violation probability, prediction error probability, and analyzed their properties. From these results, the tradeoff between user experienced delay and overall reliability can be obtained.

  • We propose an algorithm to find a near optimal solution of the optimization problem. The performance loss of the near optimal solution is studied and further validated via numerical results. Besides, we analyze the complexity of the algorithm, which linearly increases with the number of devices.

Furthermore, to evaluate the performance of the proposed method, we compared it with a benchmark solution without prediction. Simulation results show that the tradeoff can be improved remarkably with prediction and communication co-design. In addition, an experiment is carried out to validate the accuracy of mobility prediction in practical remote-control scenarios.

The rest of this paper is organized as follows: In Section II, we review the related literature. The system model is presented in Section III. The co-design of prediction and communication is proposed in Section IV. Numerical and experimental results are presented in Section V, and conclusions are drawn in Section VI.

Ii Related Work

Ii-a Communications in URLLC

There are some existing solutions to reduce latency in communication systems for URLLC [19, 35, 28, 13, 25]. With the 5G New Radio (NR) [19], the notion of “mini-slot” is introduced to support transmissions with the delay as low as the duration of a few symbols. The queueing delay is analyzed and optimized in [35], where the tradeoff among throughput, delay and reliability was studied. To reduce the access delay in uplink transmissions, a semi-persistent scheduling (SPS) scheme was developed in [28]. A grant-free protocol was proposed in [13] to further avoid the delay caused by scheduling requests and transmission grants. With the preemptive scheduling scheme in [25], the short packets with high priority can preempt an ongoing long packet transmission without waiting for the next scheduling period. With this scheme, the scheduling delay of short packets is reduced.

To improve the reliability for the low latency communications, different kinds of diversities were introduced [1, 31, 38, 23]. In [1], K-repetition was proposed to avoid retransmission feedback. The basic idea is to send multiple copies of each packet without waiting for the acknowledgment feedback. Considering that the required delay is shorter than channel coherence time, frequency hopping was adopted in [31] to improve reliability. In [38], a Lyapunov optimization problem was formulated to improve the reliability with guaranteed latency, where spatial diversity was used to improve reliability. In [23], interface diversity was proposed to achieve URLLC without modifications in the baseband designs by providing multiple communication interfaces. However, by introducing diversities, the reliability is improved at the cost of low resource utilization efficiency.

This tradeoff between delay and reliability has been exhaustively studied in communication systems [39, 4, 32, 5]. To reduce the transmission delay, the blocklength of channel codes is short, and the decoding error probability is nonzero for arbitrary signal-to-noise ratio (SNR). The fundamental tradeoff between transmission delay and decoding error probability in the short blocklength regime was derived in [39]. The tradeoff between the queueing delay and the delay bound violation probability was studied in [4]. To achieve a lower delay bound, the violation probability increases. Moreover, grant-free schemes can help reduce latency, but introduce extra packet losses due to transmission collisions. How to achieve ultra-high reliability with grant-free schemes was studied in [5]and it is shown that the proposed stop-and-wait protocol can achieve outage probability.

Ii-B Predictions in URLLC

To achieve satisfactory delay and reliability in URLLC, different kinds of predictions have been studied in the existing literature [37, 34, 11, 18, 20, 36].

In [37], the predicted control commands were sent to the receiver and waiting in the buffer. When a control command is lost in communications, predicted commands in the receiver’s buffer will be executed. The length of predictive control commands was optimized to minimize the resource consumption. The idea of model-mediated tele-operation approach was mentioned in [34]. By predicting the movement or the force feedback, the user experienced delay can be reduced. In both [37] and [34], prediction errors were not considered, and whether we can achieve ultra-high reliability in the systems remains unclear.

Different from command or mobility predictions in control systems, predicting some other features of traffic or performance of communications is also helpful. In [11], based on the predicted traffic state, a bandwidth reservation scheme was proposed to improve the spectral efficiency of URLLC. By exploiting the correlation among different nodes, the behavior of different users can be predicted [18]. Then, by reserving resources according to the predicted behavior, the access delay can be reduced. A fast hybrid automatic repeat request (HARQ) protocol was proposed in [20], prediction is used to omit some HARQ feedback signals and successive message decodings, so that the expected delay can be improved by to compared with standard HARQ. In [36], the outcome of the decoding was predicted before the end of the transmission. With the predicted result, there is no need to wait for the acknowledgment feedback, and thus the E2E delay can be reduced.

Iii System Model

Fig. 1: Illustration of network structure.

As shown in Fig. 1, we consider a joint prediction and communication system, where mobile devices send packets to a receiver, which could be data center, controller, or tactile device. The function of the receiver depends on specific applications. In remote driving [14], a human driver can remotely control a vehicle based on the feedback from various sensors installed on the vehicle. In factory automation [40], sensors update information to the controller to perform better closed-loop control, or to a data center for monitoring or fault detection. In Tactile Internet [8], force and torques are sent to a tactile device to render the sense of touch, and thus can enable haptic communications. The packets generated by each device may include different features, such as the location, velocity and acceleration of a device in remote driving or industrial automation, or the force and torques in Tactile Internet.

The receiver can be deployed at a mobile edge computing (MEC) server or a cloud center. In our framework, we consider a general wireless communication system, where mobile devices send packets to a cloud center via wireless links, backhauls, and core networks. The framework is also suitable for an MEC system, where the delays and packet losses in backhauls and core networks are set to be zero [30].

Iii-a User Experienced Delay

Time is discretized into slots. The duration of each slot is denoted as . Let be the state of the th device in the th slot, where is the number of features. The state of the th device that is received by the receiver in the th slot is denoted as . In traditional communication systems, each device sends its current state to the data center. Let (slots) be the th device’s end-to-end (E2E) delay in the communication system. If the packet that conveys is decoded successfully in the th slot, then , and the user experienced delay is . For clarification, the key notations are listed in Table I.

Notation Description
number of mobile devices
number of features in a state
number of copies transmitted in -Repetition
duration of each time slot
end-to-end(E2E) delay in communication system
end-to-end(E2E) delay in communication system
prediction horizon of the th device
delay experienced by the th device
queueing delay of the th device
transmission delay of the th device
decoding delay of the th device
delay in backhauls and core networks of the th device
transmission duration of each copy in -Repetition of the th device
delay requirement
prediction error probability of the th device
queueing delay bound violation probability of the th device
packet loss probability of the th device
decoding error probability of the th device
expected decoding error probability of the th device
overall reliability of the th device
reliability requirement
state of the th device in the th slot
predicted state of the th device in the th slot
received state of the th device in the th slot
transition noise of the th device in the th slot
difference between real state and predicted state of the th device in the th slot
state transition matrix of the th device
effective bandwidth of the th device
average packet arrival rate of the th device
bandwidth of the th device
fraction of time and frequency resources for data transmission
transmit power of the th device
noise power spectral density
SNR of the th device
large-scale channel gain of the th device
small-scale channel gain of the th device

SNR loss due to inaccurate channel estimation

inverse function of the Q-function
number of antennas at the AP
TABLE I: Index of Key Notations

where is the bandwidth, represents the transmit power, denotes the noise power spectral density, represents the received SNR, denotes the large-scale channel gain, is the small-scale channel gain, is the SNR loss due to inaccurate channel estimation, [39], is the inverse function of the Q-function, and is the decoding error probability. The blocklength of channel codes is . When the blocklength is large, (2) approaches the Shannon capacity.

Fig. 2: Illustration of prediction and communication co-design.

As shown in Fig. 2, to improve the user experienced delay, each device predicts its future state. is denoted as the prediction horizon. In the th slot, the device generates a packet based on the predicted state . After slots, the packet is received by the data center. Then, we have , which is equivalent to . Therefore, the delay experienced by the user is .111If is smaller than , is negative. This means that the receiver can predict the states of devices. In this paper, we only consider the scenario that .

Remark 1.

It is worth noting that the states of adjacent slots could be correlated. Thus, source coding schemes that compress the information in multiple slots can achieve higher compression ratio. On the other hand, channel coding schemes that encode the packets to be transmitted in multiple slots into one block, can achieve higher reliability. However, both of them will lead to a longer decoding delay. To achieve ultra-low latency, in this paper we assume that the source coding and channel coding in the th slots only depend on and the data to be transmitted in this slot.

Iii-B Delay and Reliability Requirements

The delay and reliability requirements are characterized by a maximum delay bound and a maximum tolerable error probability, and . It means that should be received by the data center before the th slot with probability .

To satisfy the delay requirement, the user experienced delay should not exceed a maximal delay bound, i.e.,

(1)

In the considered communication system, the E2E communication delay includes queueing delay , transmission delay , decoding delay , and delay in backhauls and core networks .

Thus, the constraint in (1) can be re-expressed as follows,

(2)

where , .

The overall reliability depends on prediction errors and packet losses in communications. In the control system, if the difference between the actual state of the device and the received state does not exceed a required threshold, the user cannot notice the difference. For example, in Tactile Internet, the minimum difference of the force stimulus intensity that our hands can percept is referred to as just noticeable difference (JND) [9]. We define the difference between and as , where . The JND of this system is denoted as . Then, the prediction error probability is given by

(3)

Even if is accurate enough, it will be useless if it is not received by the data center before the th slot. Denote the queueing delay bound violation probability and the packet loss probability of the th device as and , respectively. Then, the overall reliability of the device can be expressed as follows,

(4)

To achieve ultra-high reliability, all of , and should be small (i.e., less than ). Thus, (4) can be accurately approximated by , and the reliability requirement can be satisfied if

(5)

Iv Tradeoffs in Prediction and Communication Systems

In this section, we first consider a general linear prediction framework, and derive the relation between the prediction error probability and the prediction horizon in a closed form. Then, we characterize the tradeoff between communication reliability and E2E delay for short packet transmissions in a closed form. Based on the analysis, we further study how to maximize the number of URLLC services that can be supported by the system.

Iv-a State Transition Function

We assume that the state of the th device, , changes according to the following state transition function [15]

(6)

where , , is the state transition matrix and , , is the transition noise. We assume that is constant, and thus it can be obtained from measurements or physical laws. The elements of

are independent random variables that follow Gaussian distributions with zero mean and variances

, respectively.

Remark 2.

This model is widely adopted in kinematics systems or control systems [15, 16]

. Here we consider a general prediction method for a linear system. This is because for non-linear system, the relation between the prediction horizon and the prediction error probability can hardly be derived in a closed-form expression. To implement our framework in non-linear systems, data-driven prediction methods such as neural networks should be applied. These methods do not rely on system models, and will be considered in our future work.

According to (6), the state in the th slot is given by

(7)

Iv-B Prediction Horizon and Prediction Error Probability

Inspired by Kalman filter, we consider a general linear prediction method

[15]. Based on the system state in the th slot, we can predict the state in the th slot according to following expression,

(8)

From (8), we can further predict the state in the th slot,

(9)

After steps of prediction, the difference between and can be derived as follows,

(10)

The th element of is given by

(11)

where is the element of at the th row and the th column.

Since the state transition noises follow independent Gaussian distributions, and is a linear combination of them, follows a Gaussian distribution with zero mean. The variance of is denoted as , which is given by

(12)

Therefore, can be derived as follows,

(13)

where

is the cumulative distribution function (CDF) of

, and is the CDF of standard Gaussian distribution with zero mean and unit variance.

By substituting (13) into (3), can be expressed as follows,

(14)

From the expression in (14), we can obtain the following property of .

Lemma 1.

strictly increases with the prediction horizon .

Proof.

Please see Appendix A. ∎

Lemma 1 indicates that a longer prediction horizon leads to a larger prediction error probability. This is in accordance with the intuition. For example, predicting the mobility of a device in the next  ms will be much harder than predicting the mobility in the next  ms.

Iv-C Queueing Delay Bound Violation Probability

To derive the queueing delay bound violation probability, , we can use the concept of effective bandwidth [32]. Effective bandwidth is defined as the minimal constant service rate of the queueing system that is required to ensure the maximum queueing delay bound and the delay bound violation probability [6].222To analyze the upper bound of the delay bound violation probability, a widely used tool is network calculus [3]. However, with network calculus, one can hardly obtain a closed-form expression of the delay bound violation probability. Since we are interested in the asymptotic scenarios that is very small, effective bandwidth can be used [6].

The number of packets generated in each slot depends on the mobility of the device and the random events detected by the device. According to the observation in [7], packet arrival processes in Tactile Internet are very bursty. To capture the burstiness of the packet arrival process, a switched Poisson process (SPP) can be applied [11] 333In standardizations of 3GPP, In standardizations of 3GPP, queueing models are not specified since they depend on specific applications.

. A SPP includes two traffic states. In each state, the packet arrival process follows a Poisson process. The average packet arrival rates are different in the two states, and the SPP switches between the two states according to a Markov chain. With the traffic state classification methods in

[11], the AP knows the average packet arrival rate in the current state, (packets/slot). According to [32], the effective bandwidth of the Poisson process is given by

(15)

which is the minimal constant service rate required to ensure and . Since the transmission delay of each packet is fixed as , to guarantee the queueing delay violation probability, the following constraint should be satisfied,

(16)

Then, the queueing delay violation probability can be derived as

(17)

where

(18)

where is the “” branch of the Lambert W-function, which is defined as the inverse function of . The derivations of (17) and (18) are given in Appendix B.

With the expressions in (17) and (18), we can obtain the following property of .

Lemma 2.

strictly decreases with the queueing delay when and are given.

Proof.

Please see Appendix C. ∎

Lemma 2 indicates that with the same packet arrival process and service process, the queueing system with a smaller queueing delay bound requirement has a larger queueing delay violation probability. The intuition is that for a given CDF of the steady state queueing delay, the queueing delay violation probability decreases with the queueing delay bound.

Iv-D Packet Loss Probability in Transmissions

With predictions, the communication delay can be longer than the required delay bound (e.g.,  ms). As such, retransmissions or repetitions becomes possible. To avoid feedback delay caused by retransmissions, we apply -Repetitions to reduce the packet loss probability in the communication system, i.e., the device sends copies of each coding block no matter whether the first few copies are successfully decoded or not [1]. The transmission duration of each copy is denoted as . Then, we have . Some time and frequency resources are reserved for channel estimation at the AP. The fraction of time and frequency resources for data transmission is denoted as . To avoid overhead and extra delay caused by channel estimation at the device, we assume the device does not have channel state information (CSI). The impacts of CSI and training pilots on the achievable rate have been studied in the short blocklength regime [26, 24, 22, 10]. If more resource blocks are occupied by pilots, the accuracy of the estimated CSI can be improved. However, the remaining resource blocks for data transmission reduces. How to allocate radio resources for pilots and data transmissions is a complicated problem and deserves further study. By assuming CSI is not available at the transmitters, our approach can serve as a benchmark for future research.

For the transmission of each copy, we assume that the transmission duration is smaller than the channel coherence time and the bandwidth is smaller than the coherence bandwidth. This assumption is reasonable for short packet transmissions in URLLC. Then, the achievable rate in the short blocklength regime over a quasi-static SIMO channel can be accurately approximated by the following normal approximation [39]444The bounds of the decoding error probability can be obtained by using saddlepoint method [17], which is very accurate but has no closed-form expression. Since the gap between the normal approximation and practical coding schemes is around  dB [33], it is accurate enough for our framework.,

(19)

where is the bandwidth, represents the received SNR, [39], is the inverse function of the Q-function, and is the decoding error probability. The blocklength of channel codes is . When the blocklength is large, (19) approaches the Shannon capacity 555The results in [27] indicate that if Shannon capacity is used in the analyses, the delay bound and delay bound violation probability will be underestimated. Thus, the requirements of URLLC cannot be satisfied..

According to (19), the expected decoding error probability of each transmission over the SIMO channel is given by [39]

(20)

where is applied, denotes the large-scale channel gain, is the small-scale channel gain, represents the transmit power, is the SNR loss due to inaccurate channel estimation, denotes the noise power spectral density, and is the distribution of the instantaneous channel gain. For Rayleigh fading channel, we have , where is the number of antennas at the AP. From the approximation in [29]666As validated in [29], the approximation in (21) is accurate, especially when the number of antennas is large or the packet loss probability is small., can be accurately approximated by

(21)

where , is the number bits in each coding block, , , , , , and .

After repetitions, the packet loss probability in the communication system is given by

(22)

From (22), we can obtain the following property of .

Lemma 3.

When is given, strictly decreases with the repetition time .

Proof.

When is given, is fixed. According to (22), decreases with since . ∎

Lemma 3 indicates that there is a tradeoff between the transmission delay and the reliability in communications. -Repetition can be used to improve the transmission reliability at the cost of increasing the transmission delay.

V Prediction and Communication Co-design

In the above tradeoff analyses, we obtained closed-form relations between each delay component (or prediction horizon) and its corresponding packet loss factor in terms of prediction, queueing and wireless transmission, respectively. Based on the above analyses, the tradeoff between the overall reliability and prediction horizon is revealed. As such, we could formulate the optimization problem in the following subsection.

V-a Problem Formulation

To maximize the number of devices that can be supported by the system, we optimize the delay components, prediction horizon, and bandwidth allocation of wireless networks. The optimization problem can be formulated as follows,

(23)
s.t. (23a)
(23b)
(23c)
(23d)
(23e)
(23f)
(23g)

where (23a) is the constraint on total bandwidth, (23b) is the constraint on user experienced delay, (23c) is the constraint on reliability. (23d) is obtained by substituting (18) and (16) into (17), (23e) is obtained from (21) and (22), and (23f) is obtained by substituting (12) into (14).

Problem (23) is not a deterministic optimization problem since the numbers of optimization variables and constraints depend on the number of users, which is not given. In addition, some optimization variables are integers and the constraints in (23c), (23d), and (23e) are non-convex. Thus, it is very challenging to solve this problem.

V-B Algorithm for Solving Problem (23)

To solve the problem (23), we first find the minimal bandwidth required for each user to ensure its delay and reliability requirements, i.e., . By minimizing the bandwidth allocated to each user, the total number of users that can be supported with a given amount of total bandwidth can be maximized. Without the constraint on total bandwidth, the problem (23) can be decomposed into multiple single-user problems:

(24)
s.t. (25)

To solve the above problem, we need the minimal bandwidth that is required to ensure a certain overall reliability. We denote it as . However, deriving the expression of is very difficult. To overcome this difficulty, we first minimize for a given . Then, we find the minimal required bandwidth that can satisfy via binary search.

When is given, the minimal overall error probability can be obtained by optimizing in solving the following problem,

(26)
s.t.

For mathematical tractability, we set . According to [32], this simplification leads to negligible performance loss. We will first prove and decreases with in the Proposition 1 when .

Proposition 1.

and decrease with when .

Proof.

Please see Appendix D. ∎

Proposition 1 reveals the relation between the reliability of the queueing system (or the reliability of the wireless link) and the prediction horizon. With this relation, the number of independent optimization variables can be reduced.

It can be recalled that increases with . Thus, together with Proposition 1, the optimal solution is obtained when the equality in (27) holds, which is

(27)

Moreover, for a given value of , the values of and that satisfies and (27) can be obtained via binary search. Therefore, we only need to optimize in problem (26). The optimal solution and the minimal overall reliability in this simplified scenario are denoted as and , respectively.

Unfortunately, the simplified problem is still non-convex. As such, we will propose an approximated solution as follows. According to Lemma 1, increases with , and we have proved and decreases with in Proposition 1. A near optimal solution can be obtained when . Since the optimization variables are not integers, may not hold strictly. To address this issue, we can use binary search to find that satisfies when , and when . The corresponding reliability is denoted as . The overall reliability achieved by this near optimal solution is denoted as .

The performance gap between the near optimal solution and optimal one is analyzed in the following Proposition 2.

Proposition 2.

The gap between and is less than , where is the reliability achieved by the optimal solution.

Proof.

Please see Appendix E. ∎

Proposition 2 shows that the gap between the near optimal overall reliability and the optimal one is bounded by the value of the optimal overall reliability. Since the optimal overall reliability is in the order of , the gap is very small.

The required minimal bandwidth to guarantee the overall reliability can be obtained from the following optimization problem,

(28)
s.t. (28a)

Since the packet loss in the communication system decreases with bandwidth, the optimal solution of problem (28) is achieved when the equality in (28a) holds. Thus, the minimal bandwidth can be obtained via binary search. The algorithm to solve problem (24) is summarized in Table II.

V-C Discussions on Implementation Complexity and Optimality

The original optimization problem is decomposed into single-user problems. To solve each single-user problem, we search the required bandwidth and optimal prediction horizon in the regions and , respectively, where and are the upper bounds of bandwidth and prediction horizon. Therefore, the complexity of the proposed algorithm is around .

The performance loss of the near optimal solution relative to the global optimal solution results from simplification and the differences between and . According to the analysis in [32] and Proposition 2, the performance loss is minor. We will further validate the performance loss with numerical results.

0:  User-experienced delay requirement , reliability requirement , user number , average packet arrival rate , each packet duration , slot duration , bandwidth of each subcarrier , upper bound of bandwidth , upper bound of prediction horizon , transmit power , user location transition noise , initial noise , threshold , .
0:  The minimal bandwidth to ensure URLLC for the th user.
1:  .
2:  .
3:  Binary search in a range of and obtain .
4:  while  do
5:     if  then
6:         .
7:     else
8:         .
9:     end if
10:     .
11:     Binary search in a range of and obtain .
12:  end while
13:  return  .
TABLE II: Algorithm to solve (24)

Vi Performance Evaluation

In this section, we evaluate the effectiveness of the proposed co-design method via simulations and experiments.

Vi-a Simulations

In the simulations, we consider a one-dimensional movement as an example to evaluate the proposed co-design method. With this example, we show how the proposed method helps improving the tradeoffs among latency, reliability and resource utilizations (i.e., bandwidth and antenna). For comparison, the performance achieved by the traditional transmission scheme with no prediction is provided. The simulation parameters are listed in Table III. In all simulations, SNRs are computed according to . The path loss model is , where is the distance from the th device to the AP and is the shadowing. The shadowing

follows log normal distribution with a zero mean and a standard deviation of

. To ensure the reliability and latency requirements, we consider the worst case of shadowing  dB (i.e., ), which is defined as the probability that the delay and reliability of a device can be satisfied [29].

For the one-dimensional movement, the state transition function in (6) can be simplified as follows [15],

where , , and represent the location, velocity and acceleration in the th slot, respectively, is the Gaussian noise on acceleration, and is given by

(29)

which follows Newton’s laws of motion. In predictions, the standard deviation of the transition noise of acceleration is  m/s, and the required threshold is = m. The standard derivatives of the initial errors of location, velocity and acceleration are set to be  m,  m/s, and  m/s, respectively. In practice, the values of initial errors depend on the accuracy of observation and residual filter errors [15].

Parameters Values
Maximal transmit power of a user  dBm
Single-sided noise spectral density  dBm/Hz
Information load per block b  bits
Average packet arrival rate  packets/second
Slot duration  ms
Transmission duration  ms
Delay of core network and backhaul  ms
TABLE III: Simulation Parameters [2]

Vi-A1 Single-user scenarios

In single-user scenarios, the distance between the user and the AP is set to be  m. To evaluate the proposed co-design method, the prediction horizon is optimized to obtain the minimal overall error probability.

Fig. 3: Joint optimization of predictions and communications: the packet loss probability in communications, the prediction error probability , and the over error probability are drawn as functions of prediction horizon .

Under the given delay requirement (i.e.,  ms), the packet loss probability in communications , the prediction error probability , and the overall error probability are shown in Fig. 3. To achieve target reliability, the bandwidth is set as  KHz and the number of antennas at the AP is set to be . It should be noted that the reliability depends on the amount of bandwidth and the number of antennas, but the trend of the overall reliability does not change.

In Fig. 3, the communication delay and prediction horizon are set to be equal, i.e., . In this case, user experienced delay is zero. The results in Fig. 3 show that when the E2E communication delay  ms, i.e., less than the delays in the core network and the backhaul , it is impossible to achieve zero latency without prediction. When  ms, the required transmission duration increases with prediction horizon . As a result, the overall error probability, , is first dominated by and then by . As such, first decreases and then increases with . The results in Fig. 3 indicate that the reliability achieved by the proposed method is with  ms,  ms,  ms and . The optimal solution obtained by exhaustive search is . The gap between above two solutions is , which is very small.

Fig. 4: Comparison of reliability-delay tradeoff curves between co-design and no predictions with different bandwidth and numbers of received antennas .

In Fig. 4, the proposed co-design method is compared with a baseline method without prediction. When there is no prediction, the user experienced delay equals to communication delay. The results in Fig. 4 show that when the requirement on user experienced delay is less than  ms, it cannot be satisfied without prediction. When the required user experienced delay is larger than  ms, the reliability achieved by the co-design method is much better than the baseline method. In other words, by prediction and communication co-design, the tradeoff between user experienced delay and overall reliability can be improved remarkably. Particularly, in the case and  KHz, to ensure the same reliability , the user experienced delay can be reduced by  ms and zero-latency can be achieved by the proposed co-design method.

Vi-A2 Multiple-user scenarios

In multiple-user scenarios, we will consider two scenarios: the distribution of large-scale fading of the mobile devices is available/unavaibale. In the first scenario, the distances from devices to the AP are uniformly distributed in the region