# On the Capacity of 5G NR Grant-Free Scheduling with Shared Radio Resources to Support Ultra-Reliable and Low-Latency Communications

^{*}

## Abstract

**:**

## 1. Introduction

^{−6}[2]), control-to-control applications (maximum latency of 4 ms and a reliability of 1–10

^{−8}[1]) and factory automation (maximum latency between 0.25 ms and 2.5 ms and reliability requirements up to 1–10

^{−9}[3]). These applications require the exchange of information between sensors, actuators and controllers through an industrial sensor and control network. 5G has the potential to provide the connectivity required by the Industry 4.0 to digitalize factories and to support data-intensive services while ubiquitously guaranteeing low latency and reliable connections. This has actually been acknowledged through the establishment of the 5G Alliance for Connected Industries and Automation (5G-ACIA) [4].

## 2. Related Work

^{−5}while some critical Industry 4.0 applications require higher reliability levels.

## 3. Grant-Free Scheduling

^{−6}. Control-to-control applications require a maximum latency of 4 ms and a reliability of 1–10

^{−8}. Factory automation applications usually demand maximum latency values in the range 0.25–2.5 ms and reliability levels up to 1–10

^{−9}. In this case, simulations can be very computationally expensive if we want to compute the packet reception rate (1 − ${P}_{c}$) with reliability demands in the order of 1–10

^{−6}to 1–10

^{−9}. In these scenarios, errors are very rare, and we need long and computationally expensive simulations to achieve accurate results. The analytical methodology utilized in this study is then an adequate and efficient tool for scenarios with demanding URLLC communication requirements.

#### 3.1. Collisions with Other UEs

_{1}that has to transmit the K replicas of a packet in slots ${s}_{i}$, ${s}_{i+1}$, …, ${s}_{i+K-1}$. For the sake of clarity, we consider an example with K = 4, and ${s}_{i}$ corresponding to ${s}_{3}$. ${P}_{c}$ is then equal to the probability of collision of the 4 replicas transmitted in ${s}_{3},$ ${s}_{4}$, ${s}_{5}$, and ${s}_{6}$, which is represented by ${P}_{rc}\left({s}_{3},{s}_{4},{s}_{5},{s}_{6}\right)$:

_{1}) have an active transmission in ${s}_{3}$ (i.e., ${n}_{3}^{act}\ge $ 1), and that one or more of the ${n}_{3}^{act}$ UEs select the same RB as UE

_{1}for their transmission. ${n}_{3}^{act}$ is equal to n

_{0}+ n

_{1}+ n

_{2}+ n

_{3}, and the probability ${P}_{rc}\left({s}_{3}\right)$ has to consider all possible combinations of n

_{0}, n

_{1}, n

_{2}and n

_{3}that result in ${n}_{3}^{act}\ge $ 1. The probability $P({n}_{3}^{act}\ge 1)$ can then be expressed as:

_{i}in each slot, and are equal to:

_{1}and all active UEs in the slot previous to ${s}_{i}.$ The cardinality of ${R}_{i}$ is then equal to:

_{1}for their transmissions. This probability is equal to 1 − ${P}_{nrc}({n}_{3}^{act},U)$. ${P}_{rc}\left({s}_{3}\right)$ is then calculated as:

_{1}, n

_{2}, n

_{3}and n

_{4}of UEs that have new packets to transmit in ${s}_{1}$, ${s}_{2}$, ${s}_{3}$, and ${s}_{4}$, respectively. The probability that UEs have new packets to transmit in ${s}_{1}$, ${s}_{2}$, and ${s}_{3}$ is already included in (11) $({P}_{tx}({n}_{1},{R}_{1}),$ ${P}_{tx}({n}_{2},{R}_{2}),$ and ${P}_{tx}({n}_{3},{R}_{3})$ respectively). In this context, ${P}_{rc}({s}_{3})$ and ${P}_{rc}({s}_{4})$ are not independent, and they must be calculated jointly. We then compute the joint probability ${P}_{rc}({s}_{3},{s}_{4})$ that the replicas transmitted in ${s}_{3}$ and ${s}_{4}$ collide with transmissions from other UEs. Computing ${P}_{rc}({s}_{3},{s}_{4})$ only requires including in (11) the probability that there are UEs with new packets to be transmitted in ${s}_{4}$ (i.e., ${P}_{tx}({n}_{4},{R}_{4})),$ and the probability that one or more of the active ${n}_{4}^{act}$ UEs in ${s}_{4}$ select the same RB for their transmission than UE

_{1}. ${P}_{rc}({s}_{3},{s}_{4})$ can then be expressed as:

#### 3.2. Self-Collisions

_{1}that was generated before t

_{0}. Let us then suppose then that a second packet p

_{2}is generated before the K replicas of the previous packet p

_{1}have been transmitted. This is a self-collision. If a self-collision happens, p

_{2}can be stored, and its transmission will start after the UE has transmitted the K

^{th}replica of p

_{1}(i.e., at t

_{1}in Figure 2). The transmission of the K replicas of p

_{2}will finish at t

_{2}that is equal to:

_{2}may finish after the latency deadline L, due to the time p

_{2}being stored as the K replicas of p

_{1}are being transmitted. We then analyze the probability ${P}_{sc}$ that the transmission of K replicas of a packet is not completed before L due to the effect of self-collisions. This probability depends upon the number of replicas K and on the time instant at which p

_{2}was generated. Figure 2 illustrates how self-collisions affect the probability of completing the transmission of p

_{2}before L, with L equal to 1 ms. L = 1 ms implies that the maximum number of replicas K that can be transmitted per packet is 8. However, it is possible to transmit less than 8 replicas, and Figure 2 represents the case in which K is set equal to 4, 6 or 8. p

_{2}can be transmitted before the deadline L if it is generated at any time instant after t

_{2}− L, where t

_{2}is the time at which the transmission of the K replicas of p

_{2}is finished (the transmission of p

_{2}starts when the transmission of the K replicas of p

_{1}has finished at t

_{1}). If p

_{2}is generated before t

_{2}− L, it is not possible to complete the transmission of the K replicas of p

_{2}before the latency deadline L. ${P}_{sc}$ can then be computed as the probability that the time between the generation of two consecutive packets at a UE falls within the interval [0, ∆t], where ∆t represents the time difference between t

_{2}− L and the time ${t}_{{p}_{1}}$ at which p

_{1}is generated (see (26)). ${P}_{sc}$ can then be expressed as:

## 4. Validation

## 5. Performance Evaluation

^{−9}. This study also evaluates the performance of 5G NR grant-free scheduling as a function of the number of UEs, the number of reserved radio resources, and the number K of replicas.

_{sc}= 0 and P

_{rel}= 1 − P

_{c}). The figure shows the value of ${P}_{c}$ that can be achieved as a function of the number of UEs for latency requirements (L) of 0.25, 0.5, 0.75 and 1 ms. We focus on services with the most stringent latency requirements, given the challenge to satisfy high reliability levels when latency decreases [23]. For each value of L, the grant-free scheduling scheme is executed with the maximum possible number of replicas K that can be transmitted within the required latency. For example, if the maximum latency L that can be tolerated is equal to 1 ms, the maximum number of replicas K that can be transmitted within 1 ms is equal to 8 (L = 1 ms corresponds to 8⋅${T}_{slot}$ when ${T}_{slot}$ = 0.125 ms). Figure 4 also shows the performance achieved for two values of λ (0.1 and 1 packet(s)). The results depicted in Figure 4 clearly show that reducing the probability ${P}_{c}$ of not receiving a packet to values as low as 10

^{−9}, (and hence reaching reliability levels of 1–10

^{−9}when the effect of self-collisions is not considered), can only be achieved with high values of K and values of L equal to 0.75 or 1 ms. Figure 4 also shows that the probability ${P}_{c}$ increases with the number of UEs, since the risk of collision is higher. As a result, the capacity of 5G NR grant-free scheduling to support high reliability levels is significantly decreased as the number of UEs to be supported increases. Figure 4 also shows that the difficulty in supporting high reliability levels increases with λ, since the probability ${P}_{c}$ increases as a result of a higher risk of collision between UEs.

^{−5}. Figure 5 shows that grant-free scheduling with K-repetitions and shared resources can achieve a reliability equal to 1–10

^{−5}with only K = 2 if we do not consider self-collisions. Grant-free scheduling with K = 2 can also guarantee a latency as low as 0.25 ms. For low values of the packet generation rate (i.e., λ = 0.1 packets), grant-free scheduling with 2 repetitions can support up to 34 UEs with a reliability of 1–10

^{−5}and L = 0.25 ms if we do not consider self-collisions. The number of UEs that can be supported decreases with λ, since the risk of collision with other UEs increases when each UE transmits more packets per second. For example, only 4 UEs can be supported with L = 0.25 ms and a reliability of 1–10

^{−5}when λ = 1 packet. If the latency requirement is relaxed to 0.5 ms or even higher, grant-free scheduling can support more than 500 UEs with only K = 4 when λ = 0.1 packets. If λ increases, grant-free scheduling can only guarantee the required reliability for 500 UEs if the latency requirement is 1 ms, and each UE can transmit 8 replicas of the same packet. These results show that the reliability and latency levels that can be achieved with grant-free scheduling depend upon configuration parameters (e.g., K), the traffic (e.g., λ) and the number of UEs supported. An adequate configuration and optimization of grant-free scheduling based on the network conditions could help support stringent reliability and latency levels. However, it is important to note that these results are achieved without considering self-collisions. The impact of self-collisions might be non-negligible when, for example, K and/or λ increase.

^{−6}). Some Industry 4.0 applications (e.g., factory automation) require even higher reliability levels (up to 1–10

^{−9}), as discussed in [3]. It is then important analyzing whether grant-free scheduling with K-repetitions and shared resources can guarantee reliability levels of the order of 1–10

^{−9}. Figure 4 and Figure 5 show that grant-free scheduling can only guarantee very high reliability levels with high values of K, which limits the latency requirements (L) that can be satisfied. For example, a probability to correctly receive a packet equal to 1–10

^{−7}cannot be guaranteed when L < 0.5 ms, even for the lower packet generation rates. If the reliability requirement increases to ${P}_{rel}=$ 1–10

^{−9}, grant-free scheduling can only support 5 UEs with L = 0.75 ms and λ = 0.1 packets. It can support 86 UEs if the latency requirement is relaxed to 1 ms. However, if λ increases to 1 packet then grant-free scheduling can only support 10 UEs with a reliability of 1–10

^{−9}even if L is equal to 1 ms.

_{rel}= 1 − P

_{c}when the effect of self-collisions is not taken into account, i.e., P

_{sc}= 0). Figure 6 shows that the number of UEs that grant-free scheduling with K-repetitions can support for a given set of requirements strongly depends upon the number of RBs available. UEs randomly select an RB for each transmission from the U RBs available per slot. The probability that several UEs select the same RB for their transmissions increases when the number of RBs per slot decreases. Consequently, the probability ${P}_{c}$ that a packet is not correctly received due to packet collisions, increases. In addition, the number of UEs that can achieve a target reliability level also decreases when the number of RBs per slot decreases. For example, 443 UEs can be supported with L = 0.5 ms (and hence K = 4) and ${P}_{c}$ = 10

^{−5}when U is equal to 5 RBs. This number decreases to 69 UEs when U decreases to 3 RBs. This is a significant reduction of 84%. This reduction increases when the reliability demand increases. For example, 86 UEs can be supported with ${P}_{c}$ = 10

^{−9}and L = 1 ms (and hence K = 8) when U is equal to 6. However, only 6 UEs can achieve these values of ${P}_{c}$ and L if U decreases to 4 (i.e., a 93% reduction).

_{2}is generated before the K replicas of the previous packet p

_{1}have been transmitted, p

_{2}will be stored and transmitted after completing the transmission of the K replicas of p

_{1}. Due to the time that p

_{2}is stored, the transmission of its K replicas may finish after the latency deadline L. As presented in Section 3.2, it is not possible to complete the transmission of the K replicas of p

_{2}before the latency deadline L if p

_{2}is generated before t

_{2}− L (t

_{2}is the time at which the transmission of the K replicas of p

_{2}is finished as shown in Figure 2). This results in that the probability ${P}_{sc}$ (the probability that the transmission of K replicas of a packet is not completed before L due to the effect of self-collisions) is equal to the probability that the time between the generation of two consecutive packets at a UE falls within the interval [0, ∆t], where ∆t represents the time difference between t

_{2}− L and the time ${t}_{{p}_{1}}$ at which p

_{1}is generated (see (25) and (26)).

_{1}and ∆t

_{2}. For K = 4 in Figure 2, ∆t

_{1}is equal to 0 and ∆t

_{2}is equal to ${T}_{slot}$, since p

_{1}can be homogeneously generated between t

_{0}and t

_{0}− ${T}_{slot}.$ When K = 6, ∆t

_{1}is equal to 4 $\cdot {T}_{slot}$, and ∆t

_{2}is equal to (4+1) $\cdot {T}_{slot}$, since p

_{1}can be homogeneously generated between t

_{0}and t

_{0}− ${T}_{slot}.$ Similarly, ∆t

_{1}and ∆t

_{2}are equal to 8 $\cdot {T}_{slot}$ and (8+1) $\cdot {T}_{slot}$ for K = 8. Table 1 shows the value of ${P}_{sc}$ given in (26) when ∆t is equal to ∆t

_{1}or ∆t

_{2}considering L = 1 ms and K = 4, 6 and 8. ∆t = ∆t

_{1}corresponds to the scenario where self-collisions are less probable, while ∆t = ∆t

_{2}corresponds to the case in which they are more probable.

^{−4}and 9.99 × 10

^{−4}when K is equal to 4 and 8, respectively, and λ = 1 packet. It is also important to highlight that a comparison of results in Figure 4 and Table 1 shows that ${P}_{sc}$ can be actually higher than ${P}_{c}.$ This is for example the case when K = 8: ${P}_{c}$ is lower than 10

^{−7}and 10

^{−5}for λ equal to 0.1 and 1 packet(s), respectively (Figure 4), while ${P}_{sc}$ is approximately equal to 10

^{−4}and 10

^{−3}(Table 1). Grant-free scheduling can hence be limited by the effect of self-collisions, in particular when K increases. It is then important that the reliability (or probability that a packet is correctly received before the latency deadline) of grant-free scheduling with K-repetitions and shared radio resources is computed considering both the effect of collisions from other UEs and the effect of self-collisions following (1).

_{1}for computing ${P}_{sc}$. ∆t = ∆t

_{1}corresponds to the case where self-collisions are less probable. Figure 4 shows that it is necessary to transmit a high number of replicas K within L to combat collisions from other UEs and correctly receive a packet at the BS. For example, Figure 4 shows that K must be equal to 8 in order to achieve ${P}_{rel}$ = 1–10

^{−9}when ${P}_{sc}$ = 0 and λ is equal to 1 packet. However, Table 1 showed that the effect of self-collisions increases with K even to the point that self-collisions limit the reliability that can be achieved. This is actually shown in Figure 7 when we consider L = 1 ms. In principle, it could be possible to satisfy a 1 ms latency requirement if we transmit 4, 6 or 8 replicas of a packet. Figure 7 shows that if K = 4 and ∆t = ∆t

_{1}(for computing ${P}_{sc}$ in (26)), the impact of self-collisions is not relevant, and the reliability levels of 1–10

^{−5}can be satisfied for more than 500 UEs and 80 UEs when λ is equal to 0.1 and 1 packet(s), respectively; these results are in line with those observed in Figure 4 for K = 4. However, when K is equal to 6 or 8, the effect of self-collisions becomes more relevant (Table 1), and Figure 7 shows that it can actually limit the maximum reliability that can be achieved independently of the number of UEs. In fact, the maximum reliability that can be achieved is approximately equal to 1 − ${P}_{sc}$. In this case, for K = 8 and λ = 1 packet/s, the maximum reliability (when ${P}_{sc}$ is computed considering ∆t = ∆t

_{1}) that can be achieved is 1–10

^{−3}when the latency requirement L is equal to 1 ms. It should be noted that reliability levels even higher than 1 − ${P}_{c}$ = 1–10

^{−9}were achieved when the effect of self-collisions was not considered (Figure 4). The results discussed so far correspond to the scenario where ${P}_{sc}$ has been computed considering ∆t = ∆t

_{1}. This corresponds to the scenario where self-collisions are less probable. Figure 7 also shows the reliability that can be achieved with L = 1 ms and K = 4 when ∆t = ∆t

_{avg}. This ∆t

_{avg}is the average value of ∆t. ∆t

_{avg}= (∆t

_{1}+ ∆t

_{2})/2, since ∆t is homogeneously distributed between ∆t

_{1}and ∆t

_{2}. Figure 7 shows that in this case it is not possible to achieve a reliability higher than 1–6.3 × 10

^{−5}and 1–6.3 × 10

^{−4}when λ is equal to 0.1 and 1 packet(s). Figure 7 also shows that the reliability becomes again nearly independent of the number of UEs that are being supported. The degradation of reliability experienced from ∆t = ∆t

_{1}to ∆t = ∆t

_{avg}is again due to a major relevance of the effect of self-collisions when we compute the reliability.

_{total}latency that is equal to:

_{total}= 2 T

_{L1/L2}+ T

_{align}+ 2 T

_{proc}+ 3 T

_{tx}= 2.3 ms

_{L}

_{1/L2}is the L1/L2 processing latency at the BS and the UE, T

_{align}is the alignment latency (the alignment latency is the time elapsed from the moment the UE is ready to transmit to the actual time the transmission starts), T

_{proc}is the processing latency (this latency represents the latency between the reception of the SR and the transmission of the grant message), and T

_{tx}is the time required to transmit the SR and grant messages. Following [24], we consider T

_{L}

_{1/L2}= T

_{align}= T

_{tx}= 1 TTI, and T

_{proc}= 2.33 TTI. These values are a best-case scenario, since they represent reduced processing times that can be achieved with 3GPP Release 15 compared to Release 14. Equation (27) shows that the total latency (2.3 ms) introduced by the grant-based scheduling process to assign dedicated resources to UEs is higher than the latency achieved with the 5G NR grant-free scheduling implementation analyzed in this study. For example, Figure 7 shows that this implementation can guarantee latency levels below 1 ms (this latency is guaranteed with a reliability up to 1–10

^{−5}when K = 4, λ = 0.1 packets, U = 6, and ∆t = ∆t

_{avg}).

^{−5}. Satisfying this demand requires reserving 300 RBs (one per UE) in a 1 ms time windowA lower number of resources would be necessary if traffic was periodic and we could estimate when each UE would require resources for their transmission. In this case, several UEs could share the same RB if they generate their packets at different time instants. This would reduce the total number of RBs necessary to serve all users. This is not possible in the case of aperiodic traffic, since we cannot predict when a UE would need radio resources. Figure 7 shows that our implementation of 5G NR grant-free scheduling with 4-repetitions and shared resources can support 300 UEs (with their latency and reliability demands) with only 48 RBs in a time window of 1 ms. This is 84% less radio resources than if we reserve dedicated resources per UE (with aperiodic traffic) for their first transmission using semi-persistent scheduling. These results clearly show that the implemented 5G NR grant-free scheduling with shared resources can better support URLLC applications with aperiodic traffic and stringent communication requirements than other existing proposals. However, the conducted analysis (e.g., Figure 7) has also shown that new solutions will be needed to guarantee very demanding reliability and latency levels such as those foreseen for some URLLC services in 3GPP Release 16.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Illustration of the Fifth Generation New Radio (5G NR) resource grid map: Transmission of a data packet with four repetitions and a random selection of Resource Blocks (RBs) per slot.

**Figure 3.**Comparison of analytical and simulation results for different latency requirements L and number of repetitions K (U = 6, λ = 0.1 packets).

**Figure 4.**${P}_{c}$ as function of the number of User Equipments (UEs) and for different latency requirements L: (

**a**) λ = 0.1 packets; (

**b**) λ = 1 packet.

**Figure 5.**Number of UEs supported with different requirements (L and P

_{rel}= 1 − P

_{c}, when P

_{sc}= 0): (

**a**) λ = 0.1 packets; (

**b**) λ = 1 packet.

**Figure 6.**Number of UEs supported for a given L and P

_{rel}= 1 − P

_{c}with P

_{sc}= 0 as a function of the number U of available RBs per T

_{slot}(λ = 0.1 packets).

**Figure 7.**Reliability for different latency requirements L and number of repetitions K (U = 6): (

**a**) λ = 0.1 packets; (

**b**) λ = 1 packet.

K | Λ = 0.1 Packets | Λ = 1 Packet | ||
---|---|---|---|---|

∆t = ∆t_{1} | ∆t = ∆t_{2} | ∆t = ∆t_{1} | ∆t = ∆t_{2} | |

4 | 0 | 1.25 × 10^{−5} | 0 | 1.25 × 10^{−4} |

6 | 5.00 × 10^{−5} | 6.25 × 10^{−5} | 5.00 × 10^{−4} | 6.25 × 10^{−4} |

8 | 9.99 × 10^{−5} | 1.13 × 10^{−4} | 9.99 × 10^{−4} | 1.13 × 10^{−3} |

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Lucas-Estañ, M.C.; Gozalvez, J.; Sepulcre, M.
On the Capacity of 5G NR Grant-Free Scheduling with Shared Radio Resources to Support Ultra-Reliable and Low-Latency Communications. *Sensors* **2019**, *19*, 3575.
https://doi.org/10.3390/s19163575

**AMA Style**

Lucas-Estañ MC, Gozalvez J, Sepulcre M.
On the Capacity of 5G NR Grant-Free Scheduling with Shared Radio Resources to Support Ultra-Reliable and Low-Latency Communications. *Sensors*. 2019; 19(16):3575.
https://doi.org/10.3390/s19163575

**Chicago/Turabian Style**

Lucas-Estañ, M. Carmen, Javier Gozalvez, and Miguel Sepulcre.
2019. "On the Capacity of 5G NR Grant-Free Scheduling with Shared Radio Resources to Support Ultra-Reliable and Low-Latency Communications" *Sensors* 19, no. 16: 3575.
https://doi.org/10.3390/s19163575