A Resource Optimization for Two-Step Random Access in 5G New Radio

This paper presents a resource optimization method for the 2-step random access (RA) procedure in the 5th generation new radio (5G NR). In 2-step RA, the MsgA includes a sequence as a preamble on the physical random access channel (PRACH) and uplink payload on the physical uplink shared channel (PUSCH). The mapping between PRACH slots and PUSCH slots is specified by system configuration parameters. The network reserves the corresponding PUSCH resource fixedly, regardless of the random access occasion (RO) occupancy rate and the uplink data traffic request. It deprives the uplink scheduling resource efficiency in cases of some RO unoccupied. To achieve higher utilization efficiency, this paper studies the reusing of the PUSCH slots and occasions fixed to RACH in MsgA. By detecting the preambles in RO before the corresponding PUSCH slots, the network acquires the occupancy of the RO. Then the PUSCH occasion (PO) in reserved PUSCH can be released, which conforms to the RO detection result. The release of the previously reserved PUSCH occasions can be rescheduled and reused by the user equipment (UE) for uplink data transmission. Hence more wireless resources can be scheduled in contrast to the existing allocation of uplink share channel in 2-step type random access. It suggests that using the method improves the efficiency of resource utilization.


Introduction
The procedure of random access (RA) on the physical random access channel (PRACH) is used for achieving uplink (UL) grants and synchronization of user equipment (UE).The RA in the 5th generation new radio (5G NR) should satisfy lower latency and enhanced mobile scenarios.2-step RACH is designed to support reduced latency [1][2].For 4-step RACH, the first message named Msg1 in time order carries only the preamble.The user identity information should be transmitted in Msg3 after receiving Msg2 from the base station.While in the 2-step RACH type, the message called MsgA comprises both preamble sequence and information in the physical uplink shared channel (PUSCH) [3][4][5][6].
The study in [7] provides a design of the channel structure of RA, including MsgA preamble and uplink data parts and receiver processing framework.It suggests that using low payload enhances high resource efficiency of utilization and allows more users to multiplex within PUSCH.In the study of [8], a RA scheme is designed to alleviate the RACH overload problem in the massive machine type communication (mMTC) system.To effectively increase preamble resources and reduce the preamble collision probability, it proposes a timing advance resource expansion method.A procedure of resource allocation wait scheme is designed to reduce the RA failure caused by the lack of PUSCH resources.For the implementation of massive ultra-reliable and low-latency communications, [9] indicates that non-orthogonal multiple access with grant-free non-orthogonal is promising, in case of the challenges of massive multiple access and time-sensitive traffics.A differentiated power level access implemented by a dynamically distributed framework is proposed.Compared to the small data transmission random access schemes with the basic schemes, it provides a spatiotemporal analytical framework to assess the schemes [10].It jointly considers both the detection of the preamble, the PUSCH demodulation and the data transmission.
In this paper, we described an optimization method to enhance resource utilization efficiency without any changing of the frame structure.In the case of existing free random access resources, the assigned preambles in some random access occasions (RO) are not correctly detected, and the corresponding reserved PUSCH occasion (PO) in PUSCH can be released.They will be rescheduled and reused for a follow-up uplink data transmission, rather than kept leisurely.
The rest of this paper is organized as follows.In section II, the model of the 2-step RA procedure is presented.In section III, an optimization method for 2-step RA is described, and the performance of enhanced resource utilization is analyzed.Numerical evaluations are given in Section IV.Finally, Section V concludes the study.

Random access procedures
Two types of RA procedures are supported in 5G NR: 4-step RA type as type 1 and 2-step RA type as type 2, which are shown in Figure 1.For the 2-step RA type, it supports both contention-based (CB) and contention-free (CF) random access.The Msg1 of the 4-step RA type is the first information from UE to the network, which consists of a preamble on PRACH.After Msg1, the UE will receive a response from the base station (gNB) within an advanced configured time window.For contention-based RA, after reception of Msg2, the UE sends its user identity information which is called Msg3 in the uplink resource.Different from the 4-step RA, the first information as MsgA of the 2-step RA type includes a preamble and a payload, which are on PRACH and PUSCH respectively.After the transmission of MsgA, the UE waits for response information within the configured window.For contention-based RA, if contention resolution has been successfully resolved after receiving the response, it ends the random access procedure.If the 2-step RA random access is not finished upon some times of transmissions and retransmissions, the UE will switch to the 4-step type contention-based RA.The PUSCH used in MsgA is deployed by time and frequency resources.PUSCH is associated with the demodulation reference signal (DMRS).An example of PO mapping is illustrated in Figure 2. One PRACH slot has got 4 RO consecutively in frequency and time domain.Within a single RO, the number of contention-based preamble sets as 8. Accordingly, two POs occupy the frequency resources and each associates with 4 DMRS sequences.The base station configures multiple PUSCH slot resources in the time domain.As shown in Figure 2, once the configuration has been defined, the mapping between the PRACH preamble in ROs and the PUSCH resources in POs of MsgA is fixed during the procedure of Figure 2.An example of the mapping between RO and PO of MsgA in 2-step RACH.

Optimization method analysis
In this paper, an optimization method of reusing some PUSCH in the PO of MsgA is proposed.The optimization is operated by the base station in the following way, which is invisible to the UE.Firstly, on the PRACH slots, the base station searches the RO resource and all the corresponding preambles.By obtaining all the preamble detection results, the unused preamble and RO are recorded.Afterward, the unused PO can be correspondingly listed.The PUSCH resources in the list do not need to carry the uplink payload of MsgA in the 2-step RACH procedure and can be released.Hence, during the time offset between PRACH slots and MsgA PUSCH slots, the network will re-schedule the available PO in the downlink symbols.
The distribution of RO occupation conforms to the Poisson process.Assuming the total number of available RO of 2-step RACH is K , the occurrence probability of event X indicating k RO is used, which is represented by the following distribution: where  is the parameter of the Poisson process and 0   .The parameter describes the average number that the PRACH RO is occupied occurrence per unit of time.
All preambles on RO that are not occupied can be released, which depends on the probability distribution of RO.In case of at least one RO being not occupied, the probability of releasing the PO on PUSCH of MsgA can be expressed as: ( On each RO, the UE randomly selects one preamble sequence from the maximum number of the available preambles associated with the RO.The transmission of the preamble can be corrected and detected by the base station with probability that is related to signal-to-noise ratio (SNR).The detection probabilities among multiple preambles on one RO are independent and equally distributed.
By defining the probability of event U existing undetected preamble as   U P under the condition that k ROs are occupied, the probability that where p is the corrected detection probability of a single preamble in the receiver.According to the law of total probability, the probability of releasing the PO on PUSCH of MsgA in the case of k ROs used can be represented as: Therefore, the probability of PO resource being released is expressed as: ( The ratio of released PO resources to the total PO number is related to the preamble sequence search results.There are D preambles supported by each RO.If no preamble is detected on the RO, in other words, the RO is not occupied, all PO resources corresponding to the current RO are released.The number of PO associated with DMRS can be released is represented as: While for scenarios where RO is used, the situation is different.On the i k th RO from the k occupied RO, the number of preambles that can be detected is   where C 2 1 x x indicates a combination formula.In the above method, if the corresponding preamble is not checked out, then the PO on the PUSCH slot of MsgA is released.Therefore, the number of PO associated with DMRS will be released, which can be expressed as: . It demonstrates that among the D k  available POs associated with DMRS, N POs associated with DMRS can be released for uplink transmission rather than MsgA data.Based on Equation (6) and Equation ( 8), it can be obtained that the ratio of released PO associated with DMRS for uplink scheduling in the total MsgA PO resource is which is concerned with the RO occupancy rate and preamble detection results.

Numerical evaluations
In this section, performance evaluations for the probability and ratio of releasing PO in MsgA PUSCH are presented.A PRACH slot has got     In the case of fixed k , the relationship between the release ratio of PO and the detection probability of the preamble is provided in Figures 7 and 8.With the increase of preamble sequence detection probability from 0.1 to 0.999, the proportion of PO release decreases.As shown in the performance curves, more preambles detected in used RO means less PO will be released and rescheduled by the network for uplink transmission after the 2-step PRACH procedure.

Conclusion
An optimization method to enhance the resource utilization efficiency for 2-step RA without changing any structure of the frame is provided in this paper.It studies and analyses the reusing PO of the PUSCH slots which is fixedly reserved to MsgA in 2-step random access.According to the detection result of the preambles on RO, the PO that can be released is determined.The releasing PO resources will be rescheduled and reused.The performance of the optimization has been analyzed and simulated.All results of simulation assessments are in accordance with the theoretical analysis.In conclusion, the method enhances the efficiency of resource utilization of the uplink share channel in 2-step random access.

Figure 1 .
Figure 1.CB random access of 4-step type and 2-step type.For 2-step random access, UE transmits a payload on PUSCH after transmitting a preamble on PRACH.The access of UE chooses the time and frequency resources as PUSCH occasions in the UL bandwidth part (BWP).The mapping between PRACH preambles and PUSCH occasion is configured on each PUSCH.The preamble on PRACH and data parts on PUSCH in 2-step RA MsgA are time division multiplexed.The PUSCH used in MsgA is deployed by time and frequency resources.PUSCH is associated with the demodulation reference signal (DMRS).An example of PO mapping is illustrated in Figure2.One PRACH slot has got 4 RO consecutively in frequency and time domain.Within a single RO, the number of contention-based preamble sets as 8. Accordingly, two POs occupy the frequency resources and each associates with 4 DMRS sequences.The base station configures multiple PUSCH slot resources in the time domain.As shown in Figure2, once the configuration has been defined, the mapping between the PRACH preamble in ROs and the PUSCH resources in POs of MsgA is fixed during the procedure of all available preambles on one RO is related to the number of preambles D : RO used.Since it follows the Poisson distribution of the usage of RO, the mathematical expectation of the number of RO occupied is  .For a single RO, the number of contention-based the total number of POs associated with DMRS is 32 or 64 depending on the values of K and D .It depicts the performance of PO releasing probability in Figure3for 4  K .The comparison of PO releasing probabilities in case of different parameters  of the Poisson process are shown, respectively.More PO associated with DMRS is released as the increase of .Assuming that the probability of preamble successful detection is p , the probability of PO releasing decreases as the increase of p .Similar results are also applicable for 8  K , as shown in Figure 4.

Figure 4 .
Figure 3. Probability of releasing PO, K = 4.Figure 4. Probability of releasing PO, K = 8.The ratios of releasing PO associated with DMRS are represented in Figures5 and 6.The multiple curves in Figures5 and 6indicate the differences among different probabilities of preamble detection.Under the situation that k RO has been occupied by

Figure 7 .
Figure 7. PO releasing ratio with the probability of preamble detection, K = 4.

Figure 8 .
Figure 8. PO releasing ratio with the probability of preamble detection, K = 8.