I Introduction
Fifthgeneration mobile networks (5G) will address not only the evolutionary aspects of higher data rates but also the revolutionary aspect of use cases such as massive machine type communication (mMTC) and ultrareliable low latency communication (URLLC) which poses diverse and stringent requirements [1]. In the context of URLLC such as factory automation or vehicular communication, which require an extremely high reliability (e.g., frame error rates of or , respectively) while providing endtoend delay of 1ms [2]. Moreover, different requirements face major challenge of reducing latency while providing higher reliability services in the Radio Access Network (RAN) of 5G New Radio (NR), as well as coexistence with different service categories such as enhanced mobile broadband (eMBB). Some of the major challenges and key component issues related to ultrareliability are enhanced control channel reliability, link adaptation, interference mitigation. Also, notice that coexistence with other services such as eMBB is related with preemptive scheduling and link adaptation [3]. These metrics make physical layer design of URLLC very complicated [4].
Multiconnectivity with signaltonoise ratio (SNR) gain at receiver side using schemes like joint decoding, selection combining and maximal ratio combining (MRC) are discussed in [5]. Use of various diversity sources, packet design and access protocols as key component supporting URLLC in wireless communication system are discussed in [6]. Authors in [7] discussed the way to offer URLLC without intervention in physical layer design by using interface diversity and integrating multiple communication interfaces, where each interface is based on different technology. An energy efficient power allocation strategy for the Chase Combining Hybrid Automatic Repeat Request (CCHARQ) using finite blocklength to achieve ultrareliable communication are discussed in [8]. Authors in [9] investigate cooperative communications via relaying protocols to meet ultrareliable communication (URC) as feasible alternative to typical direct communications framework. In[10], authors focus in the problem of downlink cellular networks with Rayleigh fading and stringent reliability constraint by using topological characteristics of the scenario, and show that ultrareliable region is attained by using multiple antennas at the receiving User Equipment (UE) for finite and infinite blocklength coding.
Different from [10] our work is mainly based on achieving the ultrareliable region of operation by means of cooperation/coordination of Remote Radio Heads () for downlink transmission. Specifically, we consider silencing scheme, where some part of the interfering remains in on state and the other are in off, and the Maximum Ratio Transmission (MRT) different from MRC in [10] where we allow diversity at transmission side rather at receiving side providing significant diversity gain to cope with very stringent reliability constraints. The multiconnectivity scenario and basis of our system model assumption is mainly based on [5]. Further, ensuring high reliability using multiple node redundant transmission is also included in the study of enhancements for URLLC support in the 5G Core network in 3GPP (Release 16) [11]. The system model is CRAN enabled architecture and the main benefit of CRAN architecture is that the signal processing tasks of each smallcell base station (BS) are migrated to Base Band Unit (BBU) pool while enabling coordinated multipoint transmission, centralized resource allocation, joint user scheduling and data flow control [12]. The main contribution of this work can be listed as follows:

we attain accurate closedform approximations to the outage probabilities when the UE operates under full interference, silencing (mitigating interference by silencing some
) and MRT schemes; 
we address the rate control problem constrained on target reliability constraints for the proposed schemes;

numerical results show the superiority of the MRT scheme and the feasibility of ultrareliable operation when the number of increases;

we show that our analytical results are valid by corroborating them via Monte Carlo simulations.
Next, Section II introduces the system model and assumptions. Section III presents the diversity and reliability formulation strategy, while Section IV shows numerical analysis and rate control under reliability constraints. Finally, Section V concludes the paper.
Notation:
is a normalized exponential random variable with Cumulative Distribution Function (CDF)
, while is gamma random variablewith the Probability Density Function (PDF)
. Also, = is the incomplete gamma function, and denote the Gaussian regularized hypergeometric function[13].Ii System model
Consider a multinode downlink cellular network in which there are spatially distributed in a given area . In the topology, there is a typical link () which is assumed to be close to UE and other distributed which are equidistant with UE^{1}^{1}1Notice that in real word setups the UE could be at any location in a given time. In this work, we have relaxed this by assuming equal distances to interfering nodes for analytical tractability and getting closedform solutions such that some insights can be discussed.. The links are further connected to cloud networks where BBU is present by wireless or fixed line connections. The CRAN is enabled with computation and storage units enabling edge computing as shown in Fig.1. We assume all other are using the same channel to transmit data to their corresponding user equipment UE. Here, we refer to the typical link between UE and as typical link^{2}^{2}2Notice that we focus the analysis on the reference user only. with length while the distance between each and UE is denoted by , . We assume channel undergoes quasistatic Rayleigh fading and path loss exponent is denoted by . We focus on the analysis of the typical link’s performance when the remaining are:

not cooperating (thus, not edge computing or CRANenabled).
Furthermore, UE is equipped with single antenna and we assume that the fading realizations can be treated as independent events and gains from spatial diversity can be fully attained.
Consider that each transmits with fixed unit power and there is a dense network deployment such that system is interference limited, therefore the impact of noise can be neglected. Under these settings, SignaltoInterference Ratio at UE is given by
(1) 
with, where is the number of cooperating and is the interference from the other remaining . We denote the squaredenvelope coefficients of the typical link and other as , , respectively. Under these assumptions, we derive the closedform expression for the outage probabilities under each transmission scheme. The analytical results are corroborated via Monte Carlo simulations and discussed in IV.
Iii Diversity and Reliability
Herein, we consider the typical link experiences interference from all neighbouring due to lack of coordination or of backhaul infrastructure for enabling the CRAN. The CDF of is and can be formulated for the different schemes in consideration when CRAN performs different strategies to serve UE. Note that threshold is [10], where is the transmission rate whereas, .
Theorem 1.
The CDF of the when silencing by limiting interference at UE side is
(2) 
with representing the case of full interference.
Proof.
Please refer to Appendix A. ∎
Iiia Maximum Ratio Transmission (MRT)
MRT is the scheme where the typical as well as the cooperating RRHs are jointly coordinated in transmission to UE as Channel State Information (CSI) is already assumed to be available at CRAN.
Theorem 2.
The CDF of the in the case when UE is served through MRT is
(3) 
where models to case full interference scenario and theorem is valid for .
Proof.
Please refer to Appendix B. ∎
Iv Numerical analysis
Numerical analysis and results are presented in this section to evaluate the system performance in terms of reliability for the proposed schemes. In the analysis, we set , unless stated otherwise. The topology consists of located away from the UE of interest such that, . The represents the number of cooperating out of total number of in a given area which are cooperating with the in case of MRT, or in silent mode limiting the interference factor in (1). Herein, we have used Monte Carlo simulation of runs and some schemes not closely match the targeted reliability of (five 9’s) as it requires longer simulation samples. Further work is required so to improve the accuracy on the tail of the distribution.
We compute the CDF of distribution with respect to threshold (dB) for the proposed schemes as shown in Figure 2. As shown, MRT scheme has left tail distribution already exceeding the value of for same value of in comparison with silencing scheme. While the left tail of silencing scheme with silenced has left tail distribution going greater than in comparison with full interference, but with a reduction in interference factor. The distribution shows that as value of increases limiting the interference at UE there is significant improvement at the left tail of the SIR distribution of the analyzed schemes.
Figure 3 shows the reliability performance of coordinating out with silencing and MRT schemes. The shaded region in figure represents the ultrareliable region of operation in case of URLLC which clearly shows that even with in cooperation, MRT scheme outperforms all the other schemes. So, the diversity gain from MRT is superior than that of silencing schemes. Although, with more in silent mode mitigating interference to UE has significant improvement in reliability. In the figure models the case of full interference. All, the results are validated via Monte Carlo simulations.
We generalize the presented topology by comparing all the three schemes in Figure 4 in terms of threshold
(dB). We show that with same value of threshold and distances, MRT scheme easily achieves reliability target of five 9’s which is practically infeasible for other schemes. For example, silencing schemes attains reliability target at lower threshold while MRT has some higher threshold for same target reliability. MRT scheme requires prior channel estimation and optimum resource allocation which can be costly at implementation. However, such schemes are being tested in practice
[5], but not under interference limited constraints considered herein.Iva Rate control under reliability constraints
In this section, we evaluate rate control strategies with reliability constraints for the given system model in case of silencing and the MRT scheme.
Lemma 1.
Assuming silencing scheme, then guaranteeing the reliability constraint given by , requires adopting a transmit rate given by
(4) 
In case , (4) models the full interference scenario.
Proof.
However, in case for MRT scheme where should be used to calculate the rate from (2), it is difficult to simplify the equation and invert the term and as there is not any standard integral with these hypergeometric functions. In order to evaluate rate analysis we proceed solving numerically
(5) 
We evaluate the transmission rate for the given target reliability constraints () for silencing and MRT schemes in Figure 5. In the rate analysis, silencing scheme is evaluated from (4) while MRT scheme is done through numerical analysis from (5). We show that for given target reliability constraint as number of increases there is significant improvement over the rate in both cases. MRT allows a significantly higher rate for achieving given target reliability constraint. It means that limiting the interference either from silencing or MRT schemes can enhance the rate for given reliability constraints. Obviously for , both the scheme have same rate values.
The cooperation of in the vicinity of interference limited network leads to the increase in reliability. However, there is a fundamental question that should be answered: what is the minimum number of needed to cooperate to achieve ultrareliable communication and have optimum allocation of the resources? For this analysis, we used the problem by formulating the argument based on CDF from (2) and (2) as subjected to case with constrained .
Figure 6 shows the clear outlook of the optimum number of cooperating to meet the given reliability constraints. In the analysis we used the total number of in the given area to be and we used the threshold dB. The analysis shows that with MRT scheme even with minimum cooperation of can achieve the higher reliability constrains in comparison to silencing schemes. In case of reliability of five 9’s which is considered as ultrareliable operating region only out of 10 in case of MRT can satisfy the target relaibilty but this number can be higher in case of silencing scheme. The increase in threshold can also lead to increase , which requires more resources at CRAN and .
V conclusion
In this paper, we proposed spatial diversity and multiconnectivity schemes for a downlink cellular system to achive ultrareliable communication. The performance depends on the transmit rate, distance to the UE, path loss exponent and number of in cooperation and interfering. We provide numerical results and discussion by showing outage probability and reliability analysis of the schemes when varying different system parameters. The numerical results show the performance of MRT scheme and also the feasibility of ultrareliable operations when the number of cooperating increases. In case of moderate reliability, silencing scheme is also feasible. We reached accurate closedform solution for the distribution for full interference, silencing and MRT schemes. Finally, our analytical closedform results are corroborated via Monte Carlo solutions.
Acknowledgement
This research has been financially supported by Academy of Finland 6Genesis Flagship (grant 318927), Academy of Finland (Aka) (Grants n.319008, n.307492) and by the Finnish Funding Agency for Technology and Innovation (Tekes), Bittium Wireless, Keysight Technologies Finland, Kyynel, MediaTek Wireless, Nokia Solution and Networks.
Appendix A Proof of Theorem 1
In case of silencing some RRHs, interference reduces to then we proceed as follows from (1)
(6) 
where the last step comes from using the CDF of . Next, we decondition (A) of using the fact that
follows a gamma distribution
[14] with PDF, . Thus we proceed to calculate CDF as(7) 
where (a) comes from substituting the respective CDFs, the integral in (b) is the definition of gamma function [14] and reduces since , which simplifying renders (c), concluding the proof.
Appendix B Proof of Theorem 2
Since cooperates with the in (1) becomes
(8) 
whose CDF is
(9) 
where (a) asssumes that , and , the integral in (b) comes after applying the CDFs of and deconditioning on and . From definition of hypergeometric function [13] we obtain (2). Note that (2) is our final closedform solution for , while is neglected since the UE connects to the closest .
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