I Introduction
The international telecommunication union has identified ultrareliable lowlatency communication (URLLC), machinetype communication (mMTC) and enhanced mobile broadband (eMBB) as the three main services in the fifth generation (5G) mobile communication that aims to provide good connectivity for many various communication applications [1, 2, 3]. Among these three services, URLLC remains the most challenging technology due to the need of completely new system design in order to achieve the extremely high system reliability and low latency in 5G cellular systems. Existing mobile communication systems, such as longterm evolution (LTE) systems and its predecessors, were prominently designed to achieve the goal of high throughput in mobile communications, yet they can also achieve highly reliable communications in the physical layer at the expense of complicated closedloop protocol stack to inevitably result in large networking latency of tens to hundreds of milliseconds (ms). This indicates that there exists a tradeoff between high reliability and low latency in system network architecture and subsequent communication protocols of mobile communication networks. Such a reliabilitylatency tradeoff problem intrinsically impedes the existing cellular systems to extend their services in missioncritical communication contexts with ultra high reliability and low latency constraints, such as wireless control and automation in industrial environments, vehicletovehicle communications for safety and efficiency improvements, the tactile internet which allows controlling both real and virtual objects with realtime haptic feedback [4, 5].
The message transmission time for missioncritical applications needs to be on the order of tens of microseconds because the human reaction time is on the order of tens of milliseconds [6] or less toward 1 msec for fully autonomous application scenarios. The endtoend latency of the LTE systems is usually in the range of ms, which cannot be further reduced in that the backbone network of the LTE systems typically uses the best effort delivery mechanism that is not optimized for latencysensitive services. To reduce the endtoend latency in the LTE systems, it is necessary to fundamentally change the system architecture relying on the closedloop communications and backbone links. The latency of the backbone link can be significantly reduced by appropriate communication architecture and implementation of network protocols to construct the dedicated connection for URLLC services [7]. To reduce the latency in the physical layer, transmission overhead needs to be suppressed by streamlining the grantfree transmission mechanism of the physical layer access and allocating resources properly [8]. Nonetheless, reducing the latency in the communication and backbone links is still insufficient to effectively perform (ultra) lowlatency transmission in the current LTE systems because most of the transmission latency is incurred by the control signaling (e.g., grant and pilot signaling usually takes ms per scheduling). Accordingly, the most important and essential means that enables URLLC in 5G heterogeneous cellular networks (HetNets) toward the target latency of one millisecond is to completely redesign the transmission protocols in the physical layer of the HetNets [5, 9].
Ia Motivation and Prior Related Work
To effectively reduce latency in 5G HetNets, the essential approach is to adopt feedbackfree openloop communications
so that no retransmission is needed and receivers can save time in performing additional processing and protocol. Indeed, this approach seems to be the best we can do on the receiver side since retransmission latency is completely avoided. Openloop communications has a distinct advantage to significantly reduce control signaling overhead relative to closedloop communications for power control and channel estimation in the traditional and current cellular systems. As such, in this paper we focus on how to fulfill URLLC through proactive openloop communications in a HetNet owing to the fact that extremely reliable openloop communications is the key to low latency.
All the existing URLLC works in the literature are hardly dedicated to studying the openloop communications or without retransmission [10, 11, 12, 13, 14, 15]. Some of the recent works focus on how to perform URLLC in wireless systems by employing retransmissions, short packet designs and their corresponding estimation algorithms for pointtopoint transmission [10, 11, 12, 13]. Reference [10], for example, studied the energylatency tradeoff problem in URLLC systems with hybrid automatic repeat request (HARQ), whereas reference [11] proposed an efficient receiver design that is able to exploit useful information in the data transmission period so as to improve the reliability of short packet transmission. There are some of the recent works that investigated resource allocation problems in wireless networks under the URLLC constraint. In [14], the authors studied how to minimize the required system bandwidth as well as optimize the resource allocation schemes to maximize URLLC loads, whereas the problem of optimizing resource allocation in the short blocklength regime for URLLC was investigated in [15]. Furthermore, there are few recent works that looked into the URLLC design from the perspective of physicallayer system interfaces and wireless channel characteristics. The recent work in [16], for example, adopted coding to seamlessly distribute coded payload and redundancy data across multiple available communication interfaces to offer URLLC without intervention in the baseband/PHY layer design. The problem of how URLLC is affected by wireless channel dynamics and robustness was thoroughly addressed in [17].
IB Contributions
Although these aforementioned works and many others in the literature provide a good study on how to achieve URLLC and use it as a constraint to optimize the singlecell performance by using the closedloop communications and retransmissions, they cannot reveal a good networkwise perspective on how interferences from other cells and user/cell association schemes impact the URLLC performance of cellular systems. To accurately and thoroughly exploit the URLLC performances in a cellular network, in this paper we consider a largescale multitier heterogeneous network (HetNet) model in which all (mobile) users and all access points (APs) adopt openloop communications and URLLC messages received by each AP are sent to its nearby anchor node performing edge computing in order to reduce the communication latency. Our main contributions are summarized as follows.

To enhance the communication reliability between users and APs by taking advantage of coordinated multipoint (CoMP) transmission/reception, we propose the proactive multicell association (PMCA) scheme that allows each user to associate with multiple APs in the uplink and downlink. The distribution of the number of the users associating with an AP in each tier is accurately derived, which is first found to the bet of our knowledge. Also, it importantly indicates that the void AP phenomenon that was discovered in singlecell association still exists in the PMCA scheme and needs to be considered in the analysis of ultrareliable communications.

According to the PMCA scheme, a user can associate with APs and it thus forms its own virtual cell consisting itself and the APs. The uplink noncollision reliability of a user in the cell of an AP is found for the proactive openloop communications and we therefore characterize the uplink communication reliability of a virtual cell for the noncollaborative and collaborative AP cases in a lowcomplexity form.

From the analyses of the communication reliability in the uplink and downlink, we are able to show that the communication reliability is significantly influenced by the densities of the users and the APs and the number of the APs in a virtual cell. The PMCA scheme indeed improves the communication reliability of a user and achieves communication reliability by appropriately deploying APs for a given user density.

The uplink and downlink endtoend delays between users and their anchor node are modeled and analyzed. We not only clarify the fundamental interplay among the delays, the number of the APs in a virtual cell and the user and AP densities, but also show that achieving the target latency of one millisecond is certainly possible provided the APs are deployed with a sufficient density for a given user density and the radio resources of each AP are properly scheduled and allocated.
IC Paper Organization
The rest of this paper is organized as follows. In Section II, we first specify the system architecture of a HetNet for URLLC and then introduce the openloop communications and propose the PMCA scheme. Section III models and analyzes the uplink and downlink communication reliabilities for the PMCA scheme and some numerical results are provided to validate the correctness and accuracy of the analytical results. In Section IV, the endtoend latency problem for the openloop communications and PMCA scheme is investigated and some numerical results are also presented to evaluate the latency performance of the openloop communications and PMCA scheme. Finally, Section V summarizes our findings in this paper and points out some future research issues in URLLC using the PMCA scheme.
Ii System Model and Assumptions
In this paper, we consider an interferencelimited planar HetNet in which there are two tiers of APs and the APs in the same tier are of the same type and performance. In particular, the APs in the th tier form an independent homogeneous Poisson point process (PPP) of density and they can be expressed as set given by
(1) 
where denotes AP in the th tier and its location. Without loss of generality, we assume the first tier consists of the macrocell APs and the second tier consists of the small cell APs. A macrocell AP has a much larger transmit power than a small cell AP, whereas the density of the macro AP is much smaller than that of the small cell APs. To effectively achieve URLLC in the HetNet, all APs are connected to their nearby anchor nodes that manage several APs and are colocated with the edge/fog computing facilities, and a cloud radio access architecture comprised of a core network and a cloud is also employed in the HetNet. Macrocell APs and anchor nodes are connected to the core network which helps send complex computing tasks to the cloud for further data processing and management. An illustrative example of the system model depicted here is shown in Fig. 1 (a). In addition, all (URLLC) users in the HetNet also form an independent homogeneous PPP of density and they are denoted by set as
(2) 
where stands for user and its location. Openloop communications is used in the HetNet, i.e., there is no feedback between a AP and a user. All APs and users are assumed to be equipped with a single antenna. Such an assumption is made because transmitters are unable to acquire their channel state information feedbacks from their corresponding receivers so that the multiantenna transmission gain cannot be exploited. In the following, we elaborate the main idea of how to employ openloop communications to achieve URLLC in the HetNet.
Iia Openloop Communications and Proactive Multicell Association
As mentioned in Section I, closedloop communications fundamentally incurs more latency than openloop communications owing to feedback. This point manifests that openloop communications turns out to be the best solution to reducing latency from the receiver perspective because feedbackrelated communication latency is completely avoided. However, the reliability performance of wireless communications could be seriously weakened due to lack of feedback transmission in that it cannot be improved by using the hybrid automatic repeat request (ARQ), a combination of highrate forward errorcorrecting coding and ARQ error control, which is commonly used by closedloop communications. This phenomenon reveals that there seemingly exists a tradeoff between latency and reliability in wireless communications. However, this tradeoff can be absolutely alleviated or tackled by ultrareliable openloop communications since closedloop feedback hardly further benefits the reliability of a wireless channel with extremely high reliability.
To create an ultrareliable openloop communications context for the users in the HetNet, the users are suggested to proactively associate with multiple APs at the same time so that their communication reliability can be improved by spatial channel diversity and even boosted whenever the CoMP transmission technique is performed between the associated multiple APs. This proactive multicell association approach leads to the concept of the virtual cell of users, that is, each user seems to form its own virtual cell that encloses all the APs associated with it [18] and an illustrative example of the virtual cell is shown in Fig. 1(a). All the radio resources in a virtual cell can be scheduled and allocated by utilizing the cloud computing technology. Thus, letting users form their virtual cell (i.e., associate with multiple APs) has an advantage in largely reducing control signaling for frequent handovers between small cell APs, which certainly means the handover latency can be reduced. However, a user should not associate with too many APs at the same time because the signaling overhead due to multiAP synchronization could deteriorate the latency performance of its virtual cell. To clarify the fundamental interplay among reliability, latency and multicell association, we formally propose the PMCA scheme in the following and then study its related statistical properties.
IiB Proactive Multicell Association (PMCA) and Its Related Statistics
Assume that each user in the network is able to associate with APs by using the following PMCA scheme. Let be defined as
(3) 
where , , is the pathloss exponent, positive constant is the tier cell association bias, and denotes the Euclidean distance between nodes and . For a typical user located at the origin, is thus the th biased nearest AP of the typical user by averaging out the channel fading gain effect on the user side. More specifically, is the th nearest AP of the typical user if for all , whereas becomes the th strongest AP of the typical user if where is the transmit power of the tier APs. The APs associated with the typical user can be expressed as a set given by
(4) 
which is called the virtual cell of the typical user.
According to our results in [19][20], the distribution of the number of the users associating with an AP is found for the singlecell association scheme. The method of deriving it cannot be directly applied to the case of the PMCA scheme because the cells of the APs are no longer disjoint in the multicell association case. Nonetheless, the idea behind the method is still fairly helpful for us to derive the distribution of the number of the users within the cell of an AP for the PMCA scheme, as shown in the following lemma.
Lemma 1.
Suppose each user in the network adopts the PMCA scheme in (3) to associate with APs in the network. Let denote the number of the users associating with a tier AP and its distribution (i.e., ) can be accurately found as
(5) 
where for is the Gamma function., is constant and .
Proof:
See Appendix A. ∎
To validate the correctness and accuracy of in (5), we adopt the network parameters for a twotier HetNet shown in Fig. 2 to numerically simulate for . As can be seen in Fig. 2, the simulated results of accurately coincide with its corresponding analytical results of found in (5). Hence, (5) is correct and very accurate. Since the result in Lemma 1 is very accurate, there are some important implications that can be drawn. First, we can learn that the average number of the users associating with a tier AP is and this means the average cell size of a tier AP is [20, 21]. In other words, the average cell size of an AP increases times as users associate with APs. Second, for users only associate with a single AP so that the cells of the APs do not overlap and the entire network area consists of weighted Voronoitessellated cells. For
, the cells of the APs may overlap in part and the cell sizes of the APs and the numbers of the users associating with the APs are no longer completely independent. Third, the probability that a tier
AP is not associated with any users, referred to as the tier void probability, can be found as(6) 
For a dense cellular network with a moderate user density, this void probability may not be small that the void APs could be a considerable amount in the network. For example, we use the network parameters for simulation in Fig. 2 to find the void probabilities and for and the void probability of small cell APs is actually not small at all (there are 20 of the small cell APs that are void.). Thus, such a void cell phenomenon for the PMCA scheme, as illustrated in Fig. 1 (b), must be considered in the interference model [19, 22] when the user density is not very large if compared with the density of the small cell APs.
IiC The Truncated Shot Signal Process in a Virtual Cell
As the PMCA scheme and the virtual cell of a user introduced in Section IIB, we define the thtruncated shot signal process of the virtual cell of the typical user as follows^{1}^{1}1When goes to infinity, is traditionally referred to as (complete) Poisson shot noise process [23, 24] since it contains weighted signal powers in a Poisson field of transmitters. Since only contains the signals emitted from the first weighted nearest transmitters in the network, it is called the thtruncated shot signal process.:
(7) 
where is already defined in (3), is the cell association bias of AP
, and it is a nonnegative random variable (RV) associated with
. We call the thtruncated shot signal process because it does not capture the cumulative effect at the typical user of the random shocks from the different random locations (i.e., ), and can be viewed as the impulse function of AP that gives the weighted attenuation of the transmit power of in space. Let denote the Laplace transform of a nonnegative RV for and some statistical results regarding are presented in the following theorem.Theorem 1.
Assume all the ’s of the thtruncated shot signal process in (7) are i.i.d. exponential RVs with unit mean. If we define and , then the Laplace transform of can be explicitly found as
(8) 
where , is the probability that a user associates with a tier AP, for is defined as
(9) 
and . For the Laplace transform of , it can be explicitly found as
(10) 
In addition, the upper bound on can be found as
(11) 
where is a Gamma RV with shape parameter and rate parameter .
Proof:
See Appendix C. ∎
The above results of Laplace transform in Theorem 1 indicate that in general the closedform results of and are unable to be obtained except in some special cases. For instance, letting and can be shown as
(12) 
Nonetheless, we can still resort to some numerical techniques to evaluate the Laplace transforms of and and the distributions of and by numerically evaluating the inverse Laplace transform of and . In addition, we are still able to understand the distribution behaviors of from the closedform lower bound on . Theorem 1 plays an important role in the following analyses of the communication reliability that will be defined in the following subsection.
Iii Communication Reliability Analysis for Proactive Multicell Association
In this section, we would like to exploit the fundamental performances and limits of the communication reliability of users in the uplink and downlink when the PMCA scheme is employed in the HetNet. We assume that the orthogonal frequency division multiple access (OFDMA) is adopted in the HetNet and the communication reliability analyses are proceeded in accordance with how the radio resource blocks (RB) in the cell of each AP are requested by a user in the uplink and allocated by an AP in the downlink. We will first specify how users access the RBs of an AP and then propose and analyze the uplink communication reliability. Afterwards, we will continue to study the communication reliability in the downlink case.
Iiia Analysis of Uplink Communication Reliability
According to the PMCA scheme and the virtual cell of a user specified in Section IIB, our interest here is to study how likely a user is able to successfully access available RBs of an AP and then send its message to the APs in its virtual cell through the openloop uplink communications. To establish the uplink access from a user to the APs, we propose the following PMCAbased radio resource allocation scheme for uplink openloop communications:

To make a user have good uplink connections, the user forms its virtual cell by associating with its first nearest APs. Thus, all the cell association biases in (3) are unity, i.e., for all .

Each radio RB serves as the basic unit while scheduling radio resources. Multiple radio RBs in a single time slot are mapped to a single (virtual) radio resource unit (RRU) for transmitting a message. Users are allowed to transmit one message in each time slot.

Due to lacking of channel state information of each AP in the virtual cell, a user proactively allocates the radio resource in a distributed manner, that is, it has to proactively (e.g., randomly) select RRUs for the APs in its virtual cell.
Since each user has to randomly select the uplink RRUs in its virtual cell without considering how other users select their RRUs, multiple users in the cell of an AP could share the same RRUs, which leads to transmission collisions as indicated in Fig. 1 (a). Such intracell collisions among users associating with the same AP may directly lead to users’ failures in the uplink transmissions. The probability that there is no uplink collision in the virtual cell, referred to as the uplink noncollision reliability, is found in the following lemma.
Lemma 2.
Suppose a user adopts the PMCA scheme in (3) to form its virtual cell with APs. If the probability that the user selects any one of the RRUs for each AP in its virtual cell is , then the uplink noncollision reliability of each AP in its virtual cell is found as
(13) 
where is the probability that an AP in the virtual cell is from . Hence, the uplink noncollision reliability of the user in its virtual cell is
(14) 
Proof:
See Appendix B. ∎
Lemma 2 reveals that the uplink noncollision reliability of each AP is mainly influenced by and , e.g., it decreases whenever decreases by increasing and/or decreases; thereby, lesser APs in the virtual cell and/or more radio resources may significantly improve the uplink noncollision reliability^{2}^{2}2In general, does not have a significant impact on in that usually as well as and these two condition leads to in most of practical cases. Note that the uplink noncollision reliability of a user may not always increase as increases since for and increasing in this situation may not increase because decreases in this case. In addition to the uplink collision problem happening to APs, whether a user is able to successfully send its messages to at least one AP in its virtual cell also depends upon all the communication link statuses in the virtual cell. Let denote the uplink signaltointerference ratio (SIR) from a typical user located at the origin to the th AP in the virtual cell, and it can be expressed as
(15) 
where denotes the uplink fading channel gain from the typical user to AP , is the transmit power used by the typical user for AP , is the transmit power of user , is the uplink fading channel gain from , and represents the set of the actively transmitting users using the same RRU as the typical user. All uplink fading channel gains are assumed to be i.i.d. exponential RVs with unit mean, i.e., for all and for all .
According to (15), we can consider two cases of noncollaborative and collaborative APs to define the uplink communication reliability in a virtual cell. The case of noncollaborative APs corresponds to the situation in which all APs in the virtual cell are not perfectly coordinated so that they cannot perfectly complete CoMP transmission and reception, whereas when all APs in the virtual cell are perfectly coordinated so that they are able to collaboratively do CoMP transmission and reception corresponds to the case of collaborative APs. For the case of noncollaborative APs, the uplink communication reliability is defined as the probability that a message sent by a user in a virtual cell is successfully received by at least one noncollision AP in the virtual cell, and it can be expressed as
(16) 
where is the indicator function that is unity if event is true and zero otherwise, is the SIR threshold for successful decoding, and is the subset of the APs without collision in set . For the case of collaborative APs, the uplink communication reliability is defined as
(17) 
where . Namely, in (17) is the probability that the noncollision APs in the virtual cell jointly and successfully decode the uplink message^{3}^{3}3For the sake of analytical tractability, we consider that noncoherent signal combing happens among all the noncollision APs in the virtual cell even though such a combining leads to a suboptimal SIR performance..
Theorem 2.
Suppose each user employs the PMCA scheme in (3) to form its virtual cell with APs. If all the APs in the virtual are unable to collaborate, the uplink communication reliability defined in (16) is accurately found as
(18) 
where that is given in (6) with for and is given in (13). For the case of , can be approximately found as
(19) 
When all the APs in the virtual cell are able to collaborate to jointly decode the uplink message, in (17) can be upper bounded by
(20) 
Proof:
See Appendix D. ∎
From the results in Theorem 2, the uplink reliability in (18) monotonically increases as increases even though increasing makes reduce and it thereupon reduces the number of the void cells and induces more interference. However, suffers from the diminishing returns problem as increases so that associating with too many APs may not be an efficient means to significantly improve for a user. In particular, (18) can be used to obtain the following result
(21) 
which indicates as and we thus know for large , i.e., the diminishing returns problem occurs. According to (18)(20), another two efficient approaches to boosting are reducing the probability of scheduling each RRU in each cell and densely deploying APs in the HetNet, that is, we need small and large in that small suppresses the magnitude of the interference and large gives rise to a small number of the users associating with an AP. For instance, if , , then for , and for . Note that in (19) characterizes the fundamental limit of the uplink communication reliability if all APs cannot collaborate in the uplink and it can be used to evaluate whether the PMCA and resource allocation schemes can achieve some target value of . If and , for example, we require in order to achieve . In other words, the target reliability is not able to be achieved by the PMCA scheme if . Furthermore, in (17) is certainly larger than that in (16). However, the lower bound on in (20) may not be larger than the result in (19). These aforementioned observations will be numerically validated in Section IIIC.
IiiB Analysis of Downlink Communication Reliability
In this subsection, we would like to study the downlink communication reliability of users in their virtual cells. To establish the benchmark performance, we assume that the frequency reuse factor in this cellular network is unity (i.e., all APs can share the entire available frequency band) so that we can evaluate the downlink communication reliability in the worst case scenario of interference. We also assume that each downlink RRU in the cell of each AP is only allocated to one user in the cell and users adopt the PMCA scheme to associate with the first strongest APs (i.e., in (3)). In the virtual cell of the typical user, the SIR of the link from the th strongest AP to the typical user is defined as
(22) 
where denotes the downlink fading channel gain from to the typical user, is also the downlink fading channel gain from to the typical user, and is a Bernoulli RV that is unity if is not void and zero otherwise. All ’s and ’s are assumed to be i.i.d. exponential RVs with unit mean. Note that and it can be found by using (6). The term in (22) is the interference from all nonvoid APs that are not in the virtual cell, whereas the term in (22) is the intravirtualcell interference that is from other APs in the virtual cell if the APs in the virtual cell are not coordinated to avoid using the same RRU used by the th AP. This represents the worst case of the downlink SIR of the th AP in the virtual cell. In this case, the downlink communication reliability of a virtual cell with APs is defined as
(23) 
which is the probability that there is at least one AP in the virtual cell that can successfully transmit to the user in the virtual cell. When all the APs in the virtual cell can collaborate to eliminate the intravirtualcell interference in the virtual cell, the downlink communication reliability can be simply written as
(24) 
Theorem 3.
Suppose all APs in a virtual cell are not coordinated so that there exists the intravirtualcell interference in the virtual cell. The downlink communication reliability in the case of noncollaborative APs defined in (23) is explicitly upper bounded by
(25) 
where and . When goes to infinity, can be approximately found in closed form given by
(26) 
For the case of collaborative APs, the upper bound on in (24) can be found as
(27) 
Proof:
See Appendix E. ∎
From the results in Theorem 3, we realize that increasing indeed improves even though it reduces the tier void probability , yet it also suffers from the diminishing returns problem, like the uplink communication reliability. The tier void probability also significantly impacts when the number of the APs in a virtual cell is not large so that densely deploying APs may largely improve since it helps increase . Moreover, can be interpreted as the probability that all APs statically allocate their RRUs with equal probability and it has to be small in order to achieve ultrareliable communications. The result in (26) that does not depend on the densities of the APs and users is the fundamental limit of the downlink communication reliability when all noncollaborative APs use different RRUs to transmit a message to the same user. It reveals whether ultrareliable communications can be attained by the PMCA and resource allocation schemes. For example, if and , we need to achieve , i.e., each RRU cannot be scheduled with a probability more than in this case. Otherwise, the PMCA scheme cannot successfully achieve the downlink communication reliability of no matter how many APs are associated in a virtual cell. Furthermore, in (27) for the case of collaborative APs is certainly higher than that in (25) and it can also provide some insights into how to schedule resources and deploy APs in the HetNet so as to achieve the predesignated target value of . In the following subsection, some numerical results and discussions will be provided to evaluate the performances of the downlink communication reliability for the PMCA scheme.
IiiC Numerical Results and Discussions
Parameter AP Type (Tier )  Macrocell AP (1)  Small cell AP (2) 
Transmit Power (W)  20  5 
User Density (users/m)  
AP Density (APs/m)  
RRU Selection Probability  0.05  
SIR Threshold  1  
Pathloss Exponent  4  
Tier Association Bias (Uplink, Downlink) 
To validate the analytical results obtained in the previous subsections and evaluate the communication reliability performances of openloop communications and PMCA, some numerical results are provided in this subsection and they are obtained based on the network parameters in Table I. Our objective here is to see whether the openloop communications and the PMCA scheme can achieve the uplink and downlink communication reliabilities up to the target value of that is one of the reliability requirement for URLLC services in a 5G system. We first show the simulation results of the uplink reliability for the noncollaborative scenario in Fig. 3 and the analytical results corresponding to this scenario are found by (18).
In Fig. 3(a), we are able to see that the simulated uplink communication reliability for is higher than when is roughly smaller than 0.2 and its corresponding analytical result is just slightly higher than it. This validates not only that PMCA and openloop communications are indeed able to achieve the reliability target as long as the APs are sufficiently and densely deployed in the HetNet, but also that the analytical result in (18) is fairly close to its simulated counterpart so that the received uplink SIRs at different APs that are dependent in theory can be assumed to be independent while deriving (18). Note that decreases as increases. This phenomenon is because more and more interferences are generated as is getting larger and larger so that more and more APs are associated with users and getting active. Fig. 3(b) illustrates how increases as increases. As shown in the figure, significantly improves as increases from 1 to 3 and it seems not to improve much after , which demonstrates the diminishing returns problem of mentioned above. In light of this, users may significantly improve their uplink communication reliability by only associating with 3 or 4 APs, which certainly can be implemented in practice since associating too many APs may incur excess control signaling overhead and latency. The simulation results of the uplink communication reliability for the case of collaborative APs are shown in Fig. 4 and their corresponding analytical upper bound is calculated by using (20). First, we can observe that the simulated results of the uplink reliability in Fig. 4(a) are all above the target reliability of even as increases up to a high value, which is much better than the simulated results in the case of noncollaborative APs. Thus, the uplink communication reliability in the case of collaborative APs is much less sensitive to , which is a good thing from the perspective of AP deployment since we do not need to deploy many APs to reduce so as to increase , especially when the user population in the network is very large. Like the case of noncooperative APs, we can also see that the analytical upper bound on is also very much tight, which validates the correctness and tightness of (20). Fig. 4(b) illustrates how increases with in the case of collaborative APs and it is obvious that reaches up to the target value after , which is better than the result in Fig. 3(b) as expected. Thus, this expounds that the PMCA scheme should be implemented together with the CoMP scheme in order to easily to serve the URLLC traffic.
The simulated results of the downlink communication reliability for the cases of noncollaborative and collaborative APs are shown in Figs. 5 and 6, respectively. In general, these results also have the same ascending/descending curve trends as their corresponding results in Figs. 3 and 5, but there are still some subtle discrepancies between them. For example, we can observe that in general the downlink communication reliability is better than its uplink counterpart so that they all reach the target value of . This is because users do not get much interference from their first strongest APs owing to PMCA in the downlink whereas APs would get strong interference from their nearby users in the uplink. Furthermore, in the downlink APs do not “blindly” allocate their RRUs so that they do not suffer from the reliability problem of accessing available channels. This reveals that the the bottle neck of successfully achieving URLLC requirements by using openloop communications and PMCA is the uplink issue and we need to pay more attention to the uplink system designs.
Iv Modeling and Analysis of Communication Latency
Thanks to facilitating openloop communications, the latency caused by control signaling is completely eliminated as earlier explanation. The communication latency between an anchor node and a user is mostly contributed by the transmission delay between the anchor node and its associated APs and the communication delay between the APs and the user associated with them ^{4}^{4}4Note that our focus in this section is to study the communication delays induced by openloop communications and the PMCA scheme and thus some delays not directly related to openloop communications and the PMCA scheme, such as signal processing delays on the transmitter and receiver sides are ignored.. The major difference between uplink and downlink is that uplink RRU collisions incur additional channel access delay. In the following, we will first develop the modeling and analysis approach to the uplink communication delay for openloop communications and PCMA and we then apply the similar approach to characterize the downlink communication delay.
Iva Uplink Communication Delay
The uplink communication delay mainly consists of the channel access delay , uplink transmission delay and uplink backhaul delay , and it can be expressed as
(28) 
Since there are APs in a virtual cell and a user has to randomly select an RRU for each of the APs, RRU collisions could happen in the cells of the APs. When a user starts to contend RRUs in its virtual cell, the channel access delay can be defined as the lapse of time needed by the user to successfully contend at least one RRU from the APs. Thus, can be modeled as a geometric RV with parameter where is the noncollision probability found in (14), and its mean is . represents the average number of times for a user to successfully contend a channel and then send a message, i.e., its unit is channel access attempts/message, and it can be transformed to seconds/message if each channel attempt is equal to how many seconds needed for transmitting a message. The uplink transmission delay is the lapse of time needed by the user to successfully transmit a message to at least one of the APs and it can be modeled as an ergodic process. Hence, the mean of the uplink transmission delay is found as
(29) 
where the unit of is transmitting times/message and it can be transformed to seconds if the time duration (seconds) of transmitting a message is determined.
The uplink backhaul delay is defined as the minimum transmission time needed for the APs in a virtual cell to transmit a message to their anchor node so that it can be written as
(30) 
where denotes the uplink backhaul delay from the th AP to the anchor node. We further assume that the backhaul link statuses between the th AP and the anchor node independently vary with time, which gives rise to a reasonable assumption that is well characterized by an exponential RV with parameter so that the message arrival process can be modeled as an independent Poisson process. In light of this, the distribution of in the noncollaborative AP case is
since all ’s are independent and that denotes the number of the noncollision APs in the virtual cell is a binomial RV with parameters and . We thus have the mean of found as follows:
(31) 
If , we can get . For the case of coordinated APs, because only one message is sent from the virtual cell to the anchor node. The mean of is and the unit of can be set as times/RRU. The mean of the uplink communication delay is readily obtained by
(32) 
which can be employed to evaluate the uplink latency performance.
IvB Downlink Communication Delay
In the downlink, since each AP is able to allocate its resource to its received message, the downlink communication delay mostly consists of the downlink backhaul delay and transmission delay , i.e., it can be simply written as
(33) 
The downlink backhual delay is defined as the maximum time elapsed from the start time of sending a message from the anchor node to the end time when all APs in the virtual cell receive the message. Suppose the message arrival process at each AP can be modeled as an independent Poisson process and the downlink backhual delay can be expressed as
(34) 
where is the downlink backhaul delay from the anchor node to the th AP in the virtual cell. In light of this, the distribution of is found as
The downlink transmission delay is the time duration in which the APs in the virtual cell successfully transmit a message to the user and its mean can be characterized by the downlink communication reliability, i.e., and its bound can be found by using Theorem 3. Accordingly, the mean of the downlink communication delay is given by
(35) 
Hence, increases as increases in the case of collaborative APs, but it decreases as increases in the case of noncollaborative APs.
IvC Numerical Results
In this subsection, we would like to numerically demonstrate how and vary with the densities of the APs and users and the number of the APs in a virtual cell. Assume the total available bandwidth is 100 MHz and there are 20 subbands (channels) so that each subband has 5 MHz and . By assuming an URLLC message of 512 bits and , users/APs thus need at most ms to transmit one message because the transmitting rate is at least Mbps. The means of the uplink and downlink communication delays found in the previous subsection need to transform their unit to ms by multiplying 0.1024 ms. Fig. 7 shows the simulation results of the sum of and based on the network parameters in Table I and messages/ms. In Fig. 7, we see that the sum of and does not vary much with and the delay performance in the case of collaborative APs is worse than that in the case of noncollaborative APs. Fig. 7(b) also shows how the delay performances in both cases change along . As expected, when gets larger, in the cases of collaborative and noncollaborative APs becomes larger and smaller, respectively. For the case of collaborative APs, the mean of the total delays increases as the number of the APs in the virtual cell increases, which is mainly because the downlink backhaul delay dominates the total delays. Although increasing the number of the APs in a virtual cell indeed improves the communication reliability, it degrades the delay performance. Hence, we should be aware of the tradeoff problem between the communication reliability and latency when users associate with multiple APs.
V Concluding Remarks
This paper provides an alternative effective approach to achieving URLLC in a HetNet by using openloop communications and multicell association. Such a solution stems from the idea that extremely reliable communications is hardly benefited by receiver’s feedback that causes additional latency, which breaks the longstanding concept of a tradeoff between communication reliability and latency from the prevailing closedloop communications in the current cellular system and its predecessors. From the perspective of latency, ultrareliable openloop communications is the key to ultimately fulfilling the goal of ultralow latency in the network. To analytically demonstrate this point, the users in the HetNet are assumed to proactively associate with multiple APs in their virtual cell so as to significantly improve their link reliability. The communication reliability problems in the uplink and downlink are accurately modeled and analyzed by considering the void cell phenomenon for the multicell association case. Their analytical and simulated results indicate that the target reliability of can be accomplished by the PMCA scheme. The latency problems in the uplink and downlink are studied as well and their analytical and simulated results ensure that ultralow latency of 1 ms can be achieved by the PMCA scheme if the APs are sufficiently deployed and the number of the APs in a virtual cell is properly chosen. In addition, there are a few interesting approaches able to further improve the communication reliability of the PMCA scheme when the latency constraint of one ms is satisfied. For example, we may devise new multiuser detection techniques that can be performed over multiple APs to extract the message at the receiver without channel state information. We may also design new error correction coding schemes for openloop communications that can be distributively performed over multiple APs to further enhance the communication reliability at receivers.
[Proofs of Lemmas and Theorems]
a Proof of Lemma 1
According to Theorem 1 in [20], we can obtain the following result:
where and is an exponential random variable with parameter . Let be a homogeneous PPP of density and is the th nearest point in to the origin. Also, we define and it is a homogeneous PPP of density based on the result of Theorem 1 in [22]. This means that can be viewed as a sole homogeneous PPP equivalent to the superposition of all independent homogeneous PPPs in the network (i.e., ) when all tier APs in are scaled by . Thus, (3) can be equivalently expressed as
where stands for the equivalence in distribution. This result also indicates that the typical user can be imaged to equivalently associate with the first nearest APs in .
Since the typical user can associate with its first weighed nearest APs in the network, the distance between the typical user and its th weighed nearest AP is and where is the sum of i.i.d. exponential random variables (RVs) which have the same distribution as and thus is a Gamma RV with shape and rate . Let denote the cell area of AP in which all users associate with when the PMCA scheme is adopted and each user associates with its first nearest APs in . From [22] and [25], we learn that the Lebesgue measure of , d
Comments
There are no comments yet.