A D2D-based Protocol for Ultra-Reliable Wireless Communications for Industrial Automation

A D2D-based Protocol for Ultra-Reliable Wireless Communications for Industrial Automation

Abstract

{IEEEkeywords}

Ultra-reliable communications, low latency, 5G, industrial automation, device-to-device (D2D) communications, machine-type communications, multicasting, beamforming, sparse optimization.

1 Introduction

Enhanced mobile broadband (eMBB), massive machine type communications (mMTC), as well as ultra-reliable and low latency communications (URLLC) are the three main use cases that the 5G technology must support [1]. Addressing the above requirements in 5G calls for new methods and ideas at both the component and architectural levels, which include massive multiple-input multiple-output (MIMO) [2, 3], millimeter wave (mmWave) communications [4], and cloud radio access network (C-RAN) [5] for eMBB, as well as fast yet precise user access schemes to support a massive number of devices for mMTC [6][8]. This paper, on the other hand, aims to tackle the latency and reliability issues for URLLC inspired by the urgent demand from industrial automation [9][13].

In a typical closed loop industrial control scenario, sensors and actuators are deployed in the area of concern in a desired topology. Periodically or based on the events, the sensors send their measurements to the central controller, which then makes decisions and sends them to the actuators for implementation. Although currently sensors and actuators are connected to the central controller via a wired configuration in most of the factories, the fourth industrial revolution on the roadmap, known as Industry 4.0, calls for a migration of the communication networks from wired to wireless for the purpose of increasing the flexibility and freedom in moving machinery and also reducing the expenditure for the infrastructure [9][13]. Such a transition, however, imposes challenging requirements in terms of latency as well as reliability for the wireless technologies since the factorial automation systems are highly sensitive to any signal delays or distortions. Current 4G roundtrip latencies are on the order of ms, and are based on the ms subframe time with necessary overheads for resource allocation and access. For mission-critical applications in industrial automation, the latency requirements on the control loop are in the tens of milliseconds. This pushes the latency requirement of 5G physical layer down to the order of ms, an order of magnitude faster than 4G, while demanding very high-reliability, e.g., or even higher, in order to support future wireless factorial automation.

To address such a challenge, this paper mainly focuses on the downlink URLLC in one cell (factory) of a cellular system, where the multi-antenna base station (BS) (the central controller) needs to send a small amount of information bits (command) to each user (actuator) within the latency requirement (ms). The core question this paper tries to answer is how to achieve the above goal with ultra-reliability in the sense that all the users can decode their messages with a very high probability.

Achieving URLLC with the conventional broadcasting strategy is difficult due to the recent trend of massive connectivity [6]. Specifically, in a massive connectivity scenario where the number of devices is larger than that of antennas at the BS, it can be difficult to transmit at an appreciable data rate to each user reliably, especially for the cell-edge users that suffer from strong inter-cell interference. Moreover, time-division multiple-access (TDMA) may not be a feasible strategy since the required signal-to-noise ratio (SNR) is extremely high when each user is only allocated to a fraction of the total transmission time for its transmission.

One key observation we make in this paper is that in practice, each task in the factory is in general assigned to a group of devices, e.g., robots or 3D printers, who work in close proximity to each other and thus can potentially form a device-to-device (D2D) network for pear-to-pear communications. It is envisioned that the communication within each D2D network is significantly more reliable than that from the BS to the users due to the much stronger channels between the users in the same group. To exploit the reliable D2D networks, this paper proposes a novel D2D-based two-phase transmission protocol as shown in Fig. 1, in which the BS sends the messages to the users in the first phase, while in the second phase, the users who have already decoded the messages successfully (defined as the leaders of the groups) help relay the information to the other users in the same groups that fail to receive their messages previously. Note that the reliability of the overall system highly depends on the reliability of the cell-edge users. Our proposed protocol can opportunistically activate the cell-edge users that do not suffer from strong inter-cell interference thanks to the channel fading and let these leaders help the other cell-edge users with low signal-to-interference-plus-noise ratio (SINR) to achieve high reliability in the second phase.

To enable the proposed relay strategy to work, the leaders of each group need to receive the entire messages for all the users in their group. This paper devises a multi-group multicasting technique in the first phase [14], in which user messages in each group are combined together as a single message and multicast to the leaders in the corresponding group. Such a message combination strategy typically results in a manageable multicasting rate, since in most URLLC scenarios each device only requires a very small amount of information bits within the latency requirement such that the summation of rates for all users in the same group is still reasonably small. Moreover, a substantially smaller number of users need to be activated in Phase I as compared to the broadcasting scenario since one group only needs one leader.

Since the users in the same group usually belong to the same factory, the incentive mechanism and security issue, which are quite challenging in practical D2D networks [15], are no longer key considerations in our investigated setup. Instead, leader selection in the first phase becomes the deciding factor of our protocol, since the groups without leaders cannot utilize the reliable D2D networks in the second phase. This paper aims to propose a dynamic leader selection based beamforming solution merely based on the instantaneous downlink channel state information (CSI) (without CSI of the D2D networks) such that after the first phase each group has at least one leader with a high probability.

1.1 Prior Work

The wireless inter-connection of the traditional manufacturing industries is a crucial goal for future wireless standards [9][13]. The current wireless techniques are not designed for the stringent reliability and latency requirements of the mission-critical applications. As a result, designing new techniques for URLLC is considered as an increasingly important goal for 5G [16, 17], with some initial efforts already being developed to deal with the latency and reliability issues for wireless technologies. For example, [18] provides a high-level discussion about the potential to utilize diversity, e.g., MIMO, convolutional codes, and hybrid automatic repeat request (HARQ) scheme [19] to achieve URLLC. Moreover, coordinated multi-point (CoMP) [20], deployment strategies such as the cell size [21], adaptive modulation and coding (AMC) [22], as well as reduced transmission time intervals and shorter symbol durations in orthogonal frequency-division multiplexing (OFDM) systems [23] are also investigated to improve the reliability of wireless communications. However, these works in general are built on the traditional wireless techniques that are mainly driven by the broadband communications and are often inefficient for URLLC. There is general consensus that some fundamental change in the transmission protocols is necessary to satisfy the stringent latency and reliability requirements imposed by the future wireless industrial automation [17].

A recent work [24] presents an interesting two-phase transmission protocol, namely Occupy CoW, for both the uplink and downlink URLLC, that makes use of cooperative relaying to reach very high levels of reliability, while maintaining a fixed cycle time of ms in a network of nodes. For the downlink communication, specifically, the BS combines all the users’ messages together and multicasts them to the users in the first phase, while the users that can decode the messages help relay them to the other users in the second phase. However, if there are too many users in the system, such a combination of all users’ messages may lead to a very high multicasting rate, resulting in too few leaders in the first phase. Our work builds upon the Occupy CoW protocol but differs in the sense that the geographic information of the users is utilized to divide them into groups: only the messages of each group is sent to the corresponding leaders, as each leader can subsequently help its neighbors. One obvious advantage of such a grouping strategy is a reasonable multicasting rate for each group, instead of a high multicasting rate for all the users.

It is also worth noting that the conventional approach for sending individual messages to users in the downlink is information broadcasting. In the case of a single-antenna BS, the joint power and admission control problem for such a setting is investigated in [25, 26], in which the number of users achieving their SINR targets is maximized in the event that not all of them can achieve their SINR targets (e.g., when the SINR feasibility condition for power control defined in [27] does not hold). However, the goal for URLLC is to provide reliable services to all the devices, rather than a portion of devices. As a result, our work can be interpreted as an attempt to enlarge the feasible SINR regime of the conventional power control and beamforming technique [27] by a utilization of the D2D network such that URLLC can be achieved in more challenging settings.

1.2 Main Contributions

The main contributions of this paper are summarized as follows.

First, this paper proposes a novel two-phase transmission protocol for URLLC based on the observation that devices in close proximity to each other can form one group of D2D network in which reliable communication is possible. Under our proposed protocol, the BS combines each group’s messages together and multicasts them to the corresponding groups in the first phase, while the users that decode the messages successfully, i.e., leaders, help relay the messages to the other users in the same group in the second phase. We point out that since reliable communication is possible in each D2D network, the core issue under our proposed protocol is the beamforming design in the first phase that aims to activate at least one leader in each group, on whom the other users can rely in the second phase.

Second, we formulate the leader selection based beamforming problem in the first phase from a sparse optimization perspective by introducing a set of auxiliary variables that indicate the gap between each user’s SINR and its SINR target. Such a formulation enables us to design the beamforming at the BS and select the leaders of each group jointly rather than separately. Moreover, leader selection results in a new and non-trivial sparsity pattern for the auxiliary variables since in each group at least one auxiliary variable should be zero (which implies zero gap between the SINR and SINR target and thus a leader). To achieve this desired sparsity pattern, we introduce a novel geometric-mean based penalty for the auxiliary variables of each group, which is minimized to zero when each group has at least one leader. Numerical results are provided to show that such a penalty guarantees a fair leader assignment among groups.

At last, we provide a comprehensive performance comparison between our proposed strategy and other existing ones, e.g., Occupy CoW [24] and traditional information broadcasting. For various schemes, the probability of URLLC is defined as the probability that all the users in the system receive their messages successfully within the delay requirement. It is shown by simulation that with inter-cell interference, only our proposed scheme is able to achieve a probability of URLLC above as the number of information bits to each user increases.

1.3 Organization

The rest of this paper is organized as follows. Section 2 describes the system model for URLLC; Section 3 introduces the D2D-based two-phase transmission protocol for URLLC; Section 4 describes the corresponding leader selection based beamforming design; Section 5 introduces some benchmark schemes; Section 6 provides the numerical simulation results pertaining to performance comparison between our proposed scheme and benchmark schemes. Finally, Section 7 concludes this paper.

2 System Model

Consider the downlink communication in one cell (factory) consisting of one BS (controller) and users (actuators) as shown in Fig. 1. It is assumed that the BS is equipped with antennas, and each user is equipped with one single antenna. It is further assumed that the users form disjoint groups based on their geographic locations, while the users in each group are in close proximity to each other. Let denote the set of users that belong to group , and its cardinality denote the number of users in this group, , respectively. Note that each user only belongs to one group, thus if , and .

The downlink channel from the BS to the th user in group is denoted by , , , while the channel from the th user in group to the th user in group is denoted by , . This paper adopts a block-fading model, in which all the channels follow independent quasi-static flat-fading within a block of coherence time, where ’s and ’s remain constant, but vary independently from block to block. For convenience, it is assumed that the coherence time and bandwidth of ’s are the same as those of ’s, which are denoted by second and Hz, respectively. It is further assumed that the downlink channels ’s are perfectly known by the BS, but the channels between the users ’s are not known by the BS. At last, we assume that for any user in group , it knows its downlink channel and the channels from other users to it, i.e., ’s, , for information decoding.

For ultra-reliable communications, let second denote the delay requirement for all the users, which in general is much smaller than the channel coherence time, i.e., . Furthermore, let and denote the set and number of information bits that need to be conveyed to the th user in group within the delay requirement, i.e., , respectively. The core question for ultra-reliable communications in this scenario can be thus summarized as follows: how to design a protocol such that each of the users can receive its messages with an extremely low decoding error probability within second?

3 Proposed Protocol for Ultra-Reliable Communications

In this section, we propose a D2D-based two-phase transmission protocol to achieve ultra-reliable communications for the users located in groups. We assume that is very strong if since the users in the same group are close to each other, but relatively weak otherwise. As a result, the users in the same group can form a D2D network in which the communications can be made reliable. Motivated by the above observation, the D2D-based two-phase transmission protocol is briefly outlined as follows: in the first phase with a duration of second, the BS combines each group’s messages together, i.e., with bits information, , and sends ’s to the corresponding groups simultaneously via multi-group multicasting; in the second phase with a duration of second, the users that decode the information successfully in the first phase can help relay the messages to the other users in the same group via the D2D network. Note that under the proposed protocol, each user not only decodes its own messages, but also receives its neighbors’ messages, since the successful users in Phase I need to relay other users’ messages in the same group in Phase II. In the following, we elaborate this protocol in details.

3.1 Phase I

In the first phase with a duration of second, let denote the combined symbol intended for all the users in group , which is modeled as a circularly symmetric complex Gaussian (CSCG) random variable with zero-mean and unit-variance, . Then, the transmit signal of the BS in Phase I is expressed as

 \boldmath{x}(I)=N∑n=1% \boldmath{w}(I)nsn, (1)

where denotes the transmit beamforming for the entire massages of group . Suppose that the BS has a transmit power constraint ; from (1), we thus have

 N∑n=1∥\boldmath{w}(I)n∥2≤PBS. (2)

The received signal of the th user in group in Phase I is expressed as

 y(I)k,n=\boldmath{h}Tk,n% \boldmath{x}(I)+z(I)k,n=\boldmath{h}Tk,n%\boldmath$w$(I)nsn+\boldmath{h}Tk,n∑j≠n\boldmath{w}(I)jsj+z(I)k,n,   k=1,⋯,Kn, ∀n, (3)

where denotes the superposition of the additive white Gaussian noise (AWGN) and the inter-cell interference at the th user in group in Phase I, with a power . The SINR of the th user in group in Phase I is then expressed as

 γ(I)k,n=|\boldmath{h}Tk,n\boldmath{w}(I)n|2∑j≠n|% \boldmath{h}Tk,n\boldmath{w}(I)j|2+I(I)k,n. (4)

For the first transmission phase, in total there are symbols available for the BS to perform information multicasting. Note that although the seminal work [28] shows that in an AWGN channel, encoding over finite blocklength can result in a penalty on the channel capacity, it is recently shown in [29] that in a fading channel, the outage is dominated by channel fading, rather than the finite blocklength coding. As a result, in this paper we ignore the effect of finite blocklength coding, and the minimum SINR target required to convey bits messages to any user in group using symbols is then expressed as

 ¯γ(I)n=2Kn∑k=1Dk,nτ1B−1,   ∀n. (5)

Then, we define an indicator function for each user as follows:

 ϕ(I)k,n=⎧⎨⎩1,if γ(I)k,n≥¯γ(I)n,0,if γ(I)k,n<¯γ(I)n. (6)
Definition 1

The th user in group is defined as a leader of group if it can decode the messages in the first transmission phase, i.e., . Moreover, the set of leaders in group is defined as , .

3.2 Phase II

In the second phase over the remaining second, the leaders in each group help relay the messages to the unsuccessful users in the same group via the local D2D networks. Since the leaders in group has decoded the message , they merely need to relay the message with bits information to the other users.

Due to the lack of CSI of the D2D networks, in this paper we assume that power control is not conducted among users and each leader simply transmits at its full power for relaying the messages. Suppose that all the users possess a common transmit power constraint . The transmit signal of the th user in group in the second phase is thus expressed as

 x(II)k,n=ϕ(I)k,n√Psn,   k=1,⋯,Kn, n=1,⋯,N. (7)

As a result, in Phase II, the received signal for each unsuccessful user in Phase I is expressed as

 y(II)k,n=∑(i,j)≠(k,n)hk,n,i,jx(II)i,j+z(II)k,n=∑i≠khk,n,i,nϕ(I)i,n√Psn+∑j≠nKj∑i=1hk,n,i,jϕ(I)i,j√Psj+z(II)k,n, if ϕ(I)k,n=0, (8)

where denotes the superposition of the AWGN and the inter-cell interference at the th user in group in Phase II, with a power .

The corresponding SINR to decode based on is thus

 γ(II)k,n=∣∣ ∣∣∑i≠khk,n,i,nϕ(I)i,n√P∣∣ ∣∣2∑j≠n∣∣ ∣∣Kj∑i=1hk,n,i,jϕ(I)i,j√P∣∣ ∣∣2+I(II)k,n,   if ϕ(I)k,n=0. (9)

Similar to (5), the minimum SINR requirement to relay bits information using symbols in Phase II can be expressed as

 ¯γ(II)n=2∑k∉ΘnDk,nτ2B−1,   ∀n. (10)

Then, we define an indicator function for each user as follows:

 ϕ(II)k,n={1,if γ(II)k,n<¯γ(II)n and γ(II)k,n≥¯γ(II)n,0,otherwise. (11)

As a result, if an unsuccessful user in Phase I decodes the messages in Phase II, and otherwise.

At last, define and , , respectively. Thus, the cardinalities of and , i.e., and , indicate the numbers of users of group that decode their messages successfully in Phase I (leaders) and Phase II, respectively. Moreover, denotes the total number of successful users within the cell after second.

Definition 2

Given a time slot of duration second, if some beamforming vectors ’s satisfying the transmit power constraints (2) can be found at the BS such that all the users can receive their messages under the proposed two-phase transmission protocol, i.e., , then ultra-reliable communication is established over the second. Otherwise, we say outage occurs within this second.

3.3 Problem Formulation

To achieve ultra-reliable communication over any particular duration , we need to design the beamforming vectors at the BS to maximize the total number of the successful users, i.e.,

 maximize{\boldmath{w}(I)n} N∑n=1|Φ(I)n|+N∑n=1|Φ(II)n| (12a) subject to N∑n=1∥\boldmath{w}(I)n∥2≤PBS. (12b)

If the optimal value to the above problem is , then ultra-reliable communication is achieved according to Definition 2.

4 Leader Selection based Beamforming Design

Since in practice it is hard to acquire the CSI of the D2D networks, i.e., ’s, the challenge to solve problem (12) lies in the lack of the user SINRs in Phase II at the BS side given any beamforming solution ’s in Phase I. In this section, we propose an efficient leader selection based beamforming design for solving problem (12) without any knowledge of ’s.

4.1 Problem Reformulation

The proposed two-phase transmission protocol in Section 3 arises from the observation that if one group has at least one leader in the first phase, then with a very high probability, all the other users in the same group will decode the messages successfully over the D2D network in the second phase due to their proximity to the leaders. Motivated by this, even without any knowledge of ’s in Phase II, reliable communications can be achieved if the beamforming solution ’s meets two requirements in Phase I: on one hand, each group should have at least one leader since otherwise no user in this group can decode the messages after Phase II; on the other hand, the total number of leaders should be maximized such that fewer information bits and thus lower SINR targets are required in Phase II, as shown in (10). Therefore, we are interested in the following problem in the case without the knowledge of ’s in problem (12):

 maximize{\boldmath{w}(I)n} N∑n=1|Φ(I)n| (13a) subject to |Φ(I)n|≥1,   ∀n, (13b) N∑n=1∥\boldmath{w}(I)n∥2≤PBS. (13c)

In problem (13), ’s as given in (6) are complicated and discontinuous functions over the beamforming vectors, which make it challenging to apply optimization technique to solve problem (13). To tackle the issue arising from non-continuous ’s, let us define , . It can then be shown that problem (13) is equivalent to the following problem:

 minimize{\boldmath{w}(I)n,\boldmath{t}(I)n} N∑n=1|\boldmath{t}(I)n|0 (14a) subject to γ(I)k,n+t(I)k,n≥¯γ(I)n, ∀k, ∀n, (14b) |\boldmath{t}(I)n|0≤Kn−1, ∀n, (14c) t(I)k,n≥0, ∀k, ∀n, (14d) N∑n=1∥\boldmath{w}(I)n∥2≤PBS, (14e)

where ’s are given in (4). The equivalence between problem (13) and problem (14) lies in the fact that the auxiliary variables ’s characterize the gap between the SINR targets and achievable SINRs in Phase I, thus the number of zero ’s denotes the number of leaders in Phase I, and constraint (14c) guarantees at least one leader in each group. Such an equivalent transformation based on the auxiliary variables ’s results in a continuous problem (14). Moreover, since we desire more zero elements in ’s, the sparse optimization technique can now be used to solve the problem.

The difficulty to solve (14) lies in the multiple cardinality constraints (14c). To ensure at least one leader in each group in Phase I without dealing with the complicated cardinality constraints (14c), in this paper, we propose the following novel leader selection based beamforming problem:

 minimize{\boldmath{w}(I)n,\boldmath{t}(I)n} N∑n=1|\boldmath{t}(I)n|1+N∑n=1βnKn ⎷Kn∏k=1t(I)k,n (15a) subject to (???), (???), (???), (15b)

where is the corresponding penalty weight for group , .

Note that in the objective function of problem (15), we use the convex functions ’s to approximate non-convex functions ’s in problem (14) based on standard sparse optimization technique. In addition, we define a new penalty for each group as 1 in the objective function of problem (14). It is easily observed that for each group , its penalty is zero if at least one element of is zero. As a result, the new penalty can lead to the desired sparsity pattern, i.e., at least one zero in , . In the rest of this section, we aim to solve the above leader selection based beamforming design problem.

4.2 Beamforming Design to Problem (15)

The new penalty in problem (15) enables us to bypass the complicated cardinality constraints of ’s in problem (14). However, problem (15) is a non-convex problem and it is thus difficult to find its globally optimal solution. On one hand, the penalty in the objective function is non-convex. On the other hand, the SINR constraints given in are also non-convex. In the following, we propose an algorithm based on the successive convex approximation technique that always yields a locally optimal solution to problem (15).

First, we provide a convex upper bound to the objective function of problem (15).

Proposition 1

The function is concave over ’s. As a result, its first-order approximation at any given point , :

 f({t(I)k,n,^t(I)k,n})=N∑n=1βnKn ⎷Kn∏k=1^t(I)k,n+N∑n=1βnKnKn ⎷Kn∏k=1^t(I)k,n⎡⎢⎣1^t(I)1,n,⋯,1^t(I)Kn,n⎤⎥⎦(\boldmath{t}(I)n−^\boldmath{t}(I)n), (16)

serves as its upper bound.

{IEEEproof}

Please refer to Appendix .1.

Next, we deal with the non-convex SINR constraints (14b). Well-known methods to deal with the multicasting SINR constraints include semidefinite relaxation (SDR) [30] and successive convex approximation [31]. Recently, it is shown in [32] that the successive convex approximation based algorithm in general achieves better performance in multicasting than the SDR-based algorithm when the number of antennas at the BS and the number of devices are large. As a result, in this paper, we adopt the successive convex approximation technique to deal with the non-convex SINR constraints (14b). First, the SINR constraints (14b) can be re-formulated as

 |\boldmath{h}Tk,n\boldmath{w}(I)n|2¯γ(I)n+I(I)k,nt(I)k,n≥∑j≠n|\boldmath{h}Tk,n% \boldmath{w}(I)j|2+I(I)k,n,   ∀k, ∀n. (17)

The main issue is that is a convex function, rather than a concave function, over . We use the first-order approximation to provide concave upper bounds to ’s as in [31]. Specifically, define

 ak,n=R(\boldmath{h}Tk,n% \boldmath{w}(I)n),   ∀k, ∀n, (18) bk,n=I(\boldmath{h}Tk,n% \boldmath{w}(I)n),   ∀k, ∀n. (19)

Then we have , . Given any point ’s satisfying the transmit power constraint (2), we can define ’s and ’s as (18) and (19). Then, the first-order approximation to at this particular point is given by

 Unknown environment '% (20)

To summarize, by introducing the auxiliary variables ’s and ’s, given any point ’s, we can use the following convex constraints to approximate the non-convex constraints (17):

 gk,n(ak,n,bk,n,^ak,n,^bk,n)¯γ(I)n+I(I)k,nt(I)k,n≥∑j≠n|\boldmath{h}Tk,n\boldmath{w}(I)j|2+I(I)k,n,   ∀k, ∀n. (21)

With the above approximations, given any fixed point ’s and ’s, we can solve the following convex problem:

 minimize{\boldmath{w}(I)n,\boldmath{t}(I)n,\boldmath{a}n,% \boldmath{b}n} N∑n=1|\boldmath{t}(I)n|1+f({t(I)k,n,^t(I)k,n}) (22a) subject to (???), (???), (???), (???), (???), (22b)

where , , , and is as given in (16). Since problem (22) is a convex problem, it can be globally solved by CVX [33]. The successive convex approximation method based algorithm to solve the leader selection based beamforming problem, i.e., problem (15), proceeds by iteratively updating ’s and ’s (thus ’s and ’s) based on the solution to problem (22). The proposed algorithm is summarized in Algorithm 1. The convergence behaviour of Algorithm 1 is guaranteed in the following proposition.

Proposition 2

Monotonic convergence of Algorithm 1 is guaranteed, i.e.,

 N∑n=1|\boldmath{t}(I,l+1)n|1+N∑n=1βnKn ⎷Kn∏k=1t(I,l+1)k,n≤N∑n=1|\boldmath{t}(I,l)n|1+N∑n=1βnKn ⎷Kn∏k=1t(I,l)k,n,

where denotes the index of iteration of Algorithm 1. Moreover, the converged solution satisfies all the constraints as well as the Karush-Kuhn-Tucker (KKT) conditions of problem (15).

{IEEEproof}

Please refer to Appendix .2.

Toward this end, the leader selection based beamforming design for solving problem (12) to maximize the total number of active users under the proposed two-phase transmission scheme in Section 3 and achieve ultra-reliable communication as defined in Definition 2 is summarized as follows. First, we solve problem (15) via Algorithm 1 and use ’s to calculate ’s based on (6). Then, we calculate ’s based on (11). At last, we can claim reliable communications if .

5 Benchmark Schemes for Ultra-Reliable Communications

In this section, we briefly introduce some other potential approaches for ultra-reliable communications as benchmark schemes. Simulation comparisons are provided in Section 6 to show the performance gain of our proposed scheme over the benchmark schemes.

5.1 Benchmark Scheme 1: Our Proposed Scheme but without Leader Selection

First, to illustrate the importance of leader selection in our proposed two-phase transmission scheme, in the following we consider one benchmark scheme in which the number of leaders is maximized in Phase I without encouraging at least one leader for each group. In this case, problem (15) reduces to

 minimize{\boldmath{w}(I)n,\boldmath{t}(I)n} N∑n=1|\boldmath{t}(I)n|0 (23a) subject to (???), (???), (???). (23b)

In other words, the penalty for encouraging at least one leader in each group is removed. Problem (23) can be solved similarly to problem (15).

As a remark, the strategy that maximizes the total number of leaders in Phase I is expected to activate more users in the cell-center groups that close to the BS, because they have strong direct channels and suffer little from the inter-cell interference. As a result, it is expected that with the beamforming solution to problem (23), there are many leaders in each of the cell-center groups, while there is no leader in the cell-edge groups. Our proposed scheme tries to activate at least one leader in each group by solving problem (15), which promotes fairness among difference groups in Phase I and thus makes the best use of the D2D network in Phase II, as later verified by numerical results in Section 6.

5.2 Benchmark Scheme 2: Occupy CoW Protocol [24]

Occupy CoW protocol is first proposed in [24] for achieving ultra-reliable communications in a similar setup to this paper. Specifically, Occupy CoW protocol is also a two-phase transmission protocol where user messages are transmitted from the BS to the users in the first phase and the successful users help relay the messages to the other users via the D2D network in the second phase. The main difference of Occupy CoW protocol to our proposed protocol lies in the fact that all the users form one group, rather than groups based on their geographic locations. As a result, in the first phase, the BS combines all users’ messages together, i.e., , and multicasts this entire message to all the users, while in the second phase, the successful users in Phase I can help all the unsuccessful users via the D2D network. Note that [24] only considers the case that the BS has one single antenna. To make a fair comparison, in the following we briefly introduce how to design the beamforming under the Occupy CoW protocol if the BS has multiple antennas.

Let denote the entire message intended for all the users. The received signal at each user in the first phase is expressed as

 y(I)k,n=\boldmath{h}Tk,n% \boldmath{w}(I)s+z(I)k,n,   ∀k,n, (24)

where denotes the multicast beamforming at the BS in Phase I. The corresponding SINR to decode is

 γ(I)k,n=|\boldmath{h}Tk,n\boldmath{w}(I)|2I(I)k,n,   ∀k,n. (25)

Similar to (5) in Section 3, to decode a message of bits using symbols, the identical minimum SINR requirement for all the users is expressed as:

 ¯γ(I)=2N∑n=1Kn∑k=1Dk,nBτ1−1. (26)

The indicator function of each user in Phase I then depends on whether its SINR satisfies this common SINR target or not, i.e.,

 ϕ(I)k,n=⎧⎨⎩1,if γ(I)k,n≥¯γ(I),0,if γ(I)k,n<¯γ(I). (27)

The users that decode the messages successfully in the first phase can then relay the messages to the other users in the second phase. Similar to Section 3.2, each leader only needs to relay the message with bits information to the other users, where denotes the set of leaders located in group . The minimum SINR requirement to send the above message using symbols is

 ¯γ(II)=2N∑n=1∑k∉ΘnDk,nBτ2−1. (28)

The key to achieve ultra-reliable communications for the Occupy CoW protocol is the assumption that full diversity gain can be achieved in the second phase even though there is no cooperation between the BS and leaders. Specifically, [24] assumes that if the th user in group does not decode the messages in Phase I, based on some space-time coding technique, its SINR achieved from the second phase transmission is

 γ(II)k,n=max(i,j)≠(k,n)γ(i,j)k,n, if ϕ(I)k,n=0, (29)

where

 γ(i,j)k,n=ϕ(I)i,jP|hk,n,i,j|2I(II)k,n,   ∀(i,j)≠(k,n), (30)

denotes the individual SINRs of the orthogonal signals from the th user in group . Depending on whether its SINR in Phase II satisfies the SINR target or not, the indicator functions of the unsuccessful users in Phase I are defined as

 ϕ(II)k,n={1,if γ(II)k,n<¯γ(II) and γ(II)k,n≥¯γ(II),0,otherwise. (31)

Under the Occupy Cow protocol, the objective of designing the beamforming vectors is to maximize the total number of successful users in Phase I such that more leaders can help relay the messages in Phase II, i.e.,

 minimize{\boldmath{w}(I),\boldmath{t}(I)n} N∑n=1|\boldmath{t}(I)n|0 (32a) subject to γ(I)k,n+t(I)k,n≥¯γ(I), ∀k,n, (32b) t(I)k,n≥0, ∀k,n, (32c) ∥\boldmath{w}(I)∥2≤PBS. (32d)

Similar to Algorithm 1, we can use sparse optimization and successive convex approximation techniques to solve problem (32), and then determine whether ultra-reliable communication is established under the Occupy CoW protocol, i.e., whether all the users receive their messages over second.

Note that in [24], all the users’ channels are assumed to have the same distribution since the locations of the users are not considered in the channel model. This paper shows that if in practice the effect of user locations on user channels is considered, we should group the users in close proximity together since the gain of D2D network in Phase II mainly comes from the adjacent users. Note that in Phase I, user grouping leads to multi-group multicast, instead of single-group multicast under the Occupy CoW protocol in [24]. If there is only one antenna at the BS, Occupy CoW is more powerful since there is no inter-group interference in Phase I if the BS does not separate users into groups in the spatial domain. If the BS is equipped with multiple antennas, however, our proposed scheme in Section 3 works better since the BS can adjust beams in Phase I and utilize the spatial multiplexing gain to activate one leader in each group as long as . Note that for Occupy CoW, the BS only designs one beam in Phase I to satisfy the SINR targets of all the users, which is hard. The increased degree of freedom, i.e., optimization of beams rather than one beam, ensures that our proposed scheme is much powerful than Occupy CoW, as later verified by numerical results in Section 6.

5.3 Benchmark Scheme 3: Modified Occupy CoW Protocol with Leader Selection

Leader selection introduced in Section 4 can be applied in Occupy CoW as well. In the first phase, although all users’ messages are combined together, we can design to activate at least one leader in each geographical group. The considered problem is thus formulated as

 minimize{\boldmath{w}(I),\boldmath{t}(I)n} N∑n=1|\boldmath{t}(I)n|0+N∑n=1βnKn ⎷Kn∏k=1t(I)k,n (33a) subject to (???), (???), (???). (33b)

This problem can be solved similarly as problem (15).

For Occupy CoW, combining all users’ messages together significantly increases the SINR targets of all the users as compared to our proposed scheme and thus leads to a reduction of the number of leaders in Phase I. In Phase II, an geographically isolated group without a leader nevertheless cannot rely on the far away leaders in other groups. As a result, even if leader selection is considered in Occupy CoW, its probability of reliable communications is much lower than our proposed scheme, as later verified by numerical results in Section 6.

5.4 Benchmark Scheme 4: One-Phase Transmission Protocol with Broadcasting

The proposed scheme in Section 3 and Occupy CoW proposed in [24] both advocate a two-phase transmission for achieving ultra-reliable communications by utilizing the D2D network in the second phase. In the rest of this section, we introduce some possible approaches with one-phase transmission where only the downlink communication from the BS to the users is considered. First, consider the case of broadcasting. In this case, the received signal of the th user in group is

 yk,n=\boldmath{h}Tk,n\boldmath{w}k,nsk,n+\boldmath{h}Tk,n∑(i,j)≠(k,n)% \boldmath{w}i,jsi,j+zk,n,   ∀k,n, (34)

where denotes the message for the th user in group , denotes the corresponding beamforming vector, and denotes the superposition of the AWGN and inter-group interference, with a power . The SINR for decoding is thus

 γk,n=|\boldmath{h}Tk,n% \boldmath{w}k,n|2∑(i,j)≠