Analyzing Novel Grant-Based and Grant-Free Access Schemes for Small Data Transmission
11 Analyzing Novel Grant-Based and Grant-FreeAccess Schemes for Small Data Transmission
Hui Zhou,
Student Member, IEEE,
Yansha Deng,
Member, IEEE,
Luca Feltrin,Andreas H ¨oglund.
Abstract
The Fifth Generation (5G) New Radio (NR) does not support data transmission during the randomaccess (RA) procedures, which results in unnecessary control signalling overhead and power consump-tion, especially for small data transmission. Motivated by this, we propose two new RA schemes basedon the existing grant-based (4-step) and grant-free (2-step B) RA schemes, which are NR Early DataTransmission (NR EDT) and 2-step A RA schemes, with the aim to enable data transmission during RAprocedures in Radio Resource Control (RRC) Inactive state. To compare our proposed schemes with thebenchmark schemes, we provide a spatio-temporal analytical framework to evaluate the RA schemes,which jointly models the preamble detection, Physical Uplink Shared Channel (PUSCH) decoding, anddata transmission procedures. Based on this analytical model, we derive the analytical expressions forthe overall packet transmission success probability of four RA schemes in each time slot. We alsoderive the throughput and the average energy consumption for a successful packet transmission of eachscheme. Our results show that the 2-step A and 2-step B RA schemes provide the highest overallpacket transmission success probability, the 2-step A RA scheme provides the lowest average energyconsumption in low device intensity scenario, and 2-step B RA provides the lowest average energyconsumption in high device intensity scenario.
Index Terms
Grant-based, Grant-free, 4-step, 2-step, Small data, and Energy consumption.
H. Zhou and Y. Deng are with Department of Engineering, King’s College London, London, WC2R 2LS, UK (email: { hui.zhou,yansha.deng } @kcl.ac.uk)(Corresponding author: Yansha Deng).L. Feltrin and A. H¨oglund are with the Ericsson AB (email: { luca.feltrin, andreas.hoglund } @ericsson.com). a r X i v : . [ ee ss . S Y ] F e b I. I
NTRODUCTION
As an emerging technology, the Internet of Things (IoT) enables physical objects (e.g., sensors)to be connected to the Internet, which has been implemented through massive Machine TypeCommunications (mMTC), and Ultra Reliable Low Latency Communications (URLLC) servicesin the Fifth Generation (5G) New Radio (NR). The mMTC provides ubiquitous connections, andURLLC guarantees stringent constraints of reliability and latency [1]. A plethora of applications,including unmanned aerial vehicle (UAV), wearable devices, industrial wireless sensor networks(IWSN), smart meters, and etc, are being revolutionized via IoT, in which small data packets arethe typical form of traffic generated by IoT devices (e.g., hundreds of bits) [2]. In view of this,minimizing control signalling overhead becomes a critical issue during small data transmissiondue to the following two reasons: 1) the control signalling is non-negligible compared to the smalldata packets [3]; 2) non-negligible control signalling results in unnecessary energy consumptionand degrades the battery performance of IoT devices, which is considered to be the main problemfor IoT devices with limited battery capacity [4].
RRC_ConnectedStateRRC_InactiveState RRC_InactiveState
Time
RRC_InactiveStatePacket Arrival RRC_ConnectedStateRRC_InactiveState RRC_InactiveState
Time
RRC_InactiveStatePacket Arrival RRC_Inactive State RRC_InactiveState TimeRRC_InactiveStatePacket ArrivalRAData Transmission (a) Existing 4-step and 2-step B RA schemes(b) Proposed NR EDT and 2-step A RA schemes
Fig. 1. Uplink transmission of (a) existing 4-step and 2-step B RA schemes; and (b) proposed NR EDT and 2-step A RAschemes.
The IoT device is triggered to perform random access (RA) when a new packet arrives, andtransits to Radio Resource Control (RRC) Connected state for data transmission in existing 4-stepand 2-step B RA schemes as shown in Fig. 1(a). The 4-step RA scheme utilizes a scheduling-based transmission mechanism, namely grant-based (GB) access, in which the Physical UplinkShared Channel (PUSCH) resource for step 3 transmission (i.e., Msg3) is allocated to the device The existing 2-step RA scheme is referred to as 2-step B RA scheme in the paper to differentiate with the proposed 2-stepA RA scheme only after the base station (BS) receives the preamble [5]. The 2-step B RA scheme, introducedin 3GPP Release 16, was initially developed for the unlicensed spectrum to reduce the numberof Listen Before Talk (LBT) to perform, and it also reduces the latency for RA procedures [6].The 2-step B RA scheme is categorized as grant-free (GF) access, where the PUSCH resourceis pre-allocated and the equivalent content of Msg3 in 4-step RA scheme is transmitted alongwith the preamble.RRC state transitions in the existing 4-step and 2-step B RA schemes result in unnecessarycontrol signalling overhead, especially for small data packets [7], [8]. Therefore, we proposethe transmission of small data payloads during the RA procedure, which are NR Early DataTransmission (NR EDT) and 2-step A RA schemes as shown in Fig. 1(b). In 3GPP Release15, a GB EDT scheme is specified for Narrowband Internet of Things (NB-IoT) and LongTerm Evolution for Machine Type Communication (LTE-M) for the combination of user datatransmission with Msg3 during 4-step RA procedure [9], [10]. There is no EDT for NR currently,but the NR solution will likely be very similar, and hence we use “NR EDT” to represent thisRA scheme. As a variation of the 2-step B RA scheme, the GF 2-step A RA scheme has a largerpre-allocated PUSCH resource, which enables the equivalent content of Msg3 and user data tobe transmitted along with the preamble.Recent works in [9]–[13] have evaluated the EDT, and 2-step B RA schemes via system-levelsimulation. In [9], the authors enhanced the battery life and latency of the EDT RA scheme,where three traffic models with various payload sizes and periods were considered. In [10], theauthors proposed three RA enhancements based on the EDT to reduce the collision probability,which include Parallel Preamble Transmissions, Enhanced Back-off, and Dynamic ReservedPreambles. In [11], the authors proposed a new preamble structure supporting the 2-step B RAscheme, where the uplink data indication and the buffer status are combined with the preamble.In [12], the preamble detection and PUSCH resource decoding was analyzed via link levelsimulation for different control plane payload sizes, where different Demodulation ReferenceSignal (DMRS) sequences were applied to handle potential PUSCH resource unit (PRU) collision.In [13], considering that the GF scheme is limited to small cell size due to unsynchronizeduplink, the coverage extension of 2-step B RA scheme with different PUSCH size transmissionswas exploited via system level simulation. However, the general RA model and mathematicalframework for the 4-step, NR EDT, 2-step A, and 2-step B RA schemes have never been fullyestablished, and their comparative insights have not been investigated yet.
To characterize and analyze the performance of RA schemes, stochastic geometry has beenregarded as a powerful tool to capture the uncertainty of devices’ locations in wireless networks[14], which has been utilized to analyse the 4-step RA scheme [15]–[18], and the 2-step B RAscheme [19], [20]. In [15], the authors analyzed the Signal to Noise plus Interference Ratio(SINR) outage of the 4-step RA scheme with three different preamble transmission schemes,where the mutual interference was considered. In [16], the authors analyzed the queue evolutionof the 4-step RA scheme by developing a spatio-temporal mathematical framework, in whichpreamble transmission success probability was derived. The work in [17] extended the preambletransmission probability analysis to the preamble collision of the 4-step RA scheme, where onlythe device succeeds in collision will receive the granted resource for data transmission. Thework in [18] modelled the 4-step RA scheme in the NB-IoT network under time-correlatedinterference by considering the repeated preamble transmission and collision. The work in [19]analyzed both 4-step and 2-step B RA schemes based on stochastic geometry and queueingtheory, where the device with the largest SINR succeeds in the collision. The work in [20]defined the latent access failure probability of the 2-step B RA scheme in URLLC service, andproposed a tractable approach to analyze the 2-step B RA scheme under three different hybridautomatic repeat request (HARQ) mechanisms, including Reactive, K-repetition, and Proactiveschemes. However, to the best of our knowledge, existing works have either focused on studyingpreamble SINR outage [15], [16] without considering collision, or assumed the collision happensduring preamble transmission for simplicity [17]–[20] and data transmission was ignored, whosemodel can not capture the accurate throughput and energy consumption during RA procedures.Motivated by the above, we aim to address the following fundamental questions: 1) how tofairly model the 4-step, NR EDT, 2-step A, and 2-step B RA schemes with data transmission; 2)how to capture the average energy consumption of each scheme; 3) which scheme performs betterin a specific device density scenario. To do so, we develop a novel spatio-temporal mathematicalframework to analyse the average energy consumption and overall packet transmission successprobability under each RA scheme. The main contributions of this paper can be summarized inthe following points: • We present a tractable spatio-temporal mathematical framework to analyze 4-step, NR EDT,2-step A, and 2-step B RA schemes based on stochastic geometry and probability theory, inwhich the devices are modelled as independent Poisson point process (PPP) in the spatialdomain, and the new arrival packets of each device are modelled by independent Poisson arrival process in the time domain. • We jointly model preamble detection, PUSCH decoding, and data transmission procedures,which are general and can be extended to analyze different RA schemes. We derive the exactexpressions for the preamble detection probability and the PUSCH decoding probabilitiestaking into account SINR outage and collision, and data transmission success probability. Wealso derive the overall packet transmission success probability, average energy consumption,and throughput in each time slot for each scheme. • We develop a realistic simulation framework to capture the preamble detection, PUSCHdecoding, data transmission, where overall packet transmission success probability, averageenergy consumption for packet transmission, and throughput are verified. Our results showthat both 2-step A, and 2-step B RA schemes provide the highest overall packet transmissionsuccess probability. The 2-step A RA scheme achieves the lowest energy consumption inlow device intensity scenario, and the 2-step B RA scheme achieves the lowest energyconsumption in high device intensity scenario.The rest of the paper is organized as follows. Section II presents the system model. Sections IIIderives the preamble detection, PUSCH decoding, and data transmission probabilities. Section IVderives the overall packet transmission success probability and energy consumption of a typicaldevice in each time slot. Section V presents the analytical results for performance metrics. SectionVI provides numerical results. Finally, Section VII concludes the paper.II. S
YSTEM M ODEL
We consider uplink transmission for the cellular network consisting of a single BS and multipleIoT devices , which are spatially distributed in R following independent homogeneous PPP Φ D with intensity λ D , and are assumed to be static all time once they are deployed. A. Network and Traffic Model
We consider a flat Rayleigh fading channel, where the channel power gain h ( x, y ) betweentwo generic locations x, y ∈ R is assumed to be exponentially distributed random variableswith unit mean. All the channel gains are independent of each other, independent of the spatial The Physical Random Access Channel (PRACH) root sequence planning is applied to mitigate the false alarm ratio ofpreamble detection among neighbouring BSs, thus neighbouring BSs have different preamble sets [21]. Therefore, we focus onstudying the mathematical framework for Random Access Channel (RACH) in a single cell. locations, and identically distributed (i.i.d.). For the brevity of exposition, the spatial indices ( x, y ) are dropped. We consider a standard power-law path-loss model with attenuation r − α ,where r is the propagation distance from the device to BS, and α is the path-loss exponent.An ideal full path-loss inversion power control is assumed at all devices to solve the “near-far”problem, where each device compensates for its path-loss to keep the average received signalpower at the BS equal to the same threshold ρ . We also assume that none of the devices sufferfrom truncation outage, which means the maximum transmit power of the device is large enoughto compensate uplink path-loss [16].We model the new arrived packets N m new in the m th time slot at each device using independentPoisson arrival process Λ m new with the intensity µ m new . The packets of each device line in a queueto be transmitted, and are determined by the newly arrived and undelivered packets. First ComeFirst Serve (FCFS) scheduling scheme is applied by placing the newly arrived packets at theend of the queue. Without loss of generality, we assume the buffer size of each device is largeenough, and an infinite amount of RACH attempts is assumed, where no packet is dropped untilthe packet is successfully received by the BS. B. Contention-Based Random Access Schemes
We present the detailed procedures of the existing GB 4-step and GF 2-step B RA schemes,and the proposed GB NR EDT and GF 2-step A RA schemes in this section, respectively.
1) Existing 4-step and proposed NR EDT random access:
The 4-step RA scheme is shownin Fig. 2(a). In step 1, each device randomly selects a preamble generated by Zadoff-chu (ZC)sequence cyclic shift, and transmits as Msg1 on the RA subframe, which implicitly specifies theRA-radio network temporary identifier (RA-RNTI). In step 2, the BS responds to the device withMsg2 (i.e., random access response (RAR)) containing a temporary cell RNTI (TC-RNTI), timingadvance(TA), and PUSCH resource granted for Msg3 transmission under the condition that BSsuccessfully detects the preamble. If not, the device reattempts in the next RACH opportunity.In step 3, the device transmits Msg3 (i.e., RRC connection resume request) including a deviceidentity. If multiple devices select the same preamble and RA subframe in Msg1, they receive thesame Msg2, and transmit their own Msg3 on the same PUSCH resource resulting in a collision.If the BS successfully decodes one specific Msg3 among colliding devices, in step 4, the BSsends Msg4 (i.e., RRC connection resume) with an echo of the identity transmitted in Msg3 bythe device. Those devices with matched identity succeed in the RA procedure and enter into the
RRC Connected state for data transmission with HARQ, and all failed devices have to reattemptin the next RACH opportunity. After successful data transmission, the device receives the RRCrelease with suspend from the BS, and goes back to the RRC Inactive state. We only model dataHARQ to make the comparison results more intuitive, and HARQ for both Msg3 and Msg4 isan easy extension. device BS
Msg1: Preamble Msg2: Random Rccess Response
Msg3: RRC ConnResumeRequest
Msg4: RRC ReleaseWithSuspendACK+Data device BS
Msg1: Preamble Msg2: Random Rccess Response
Msg3: RRC ConnResumeRequest
Msg4: RRC ReleaseWithSuspendACK+Data device BSData+MsgAMsgB (Preamble,
RRC ConnResumeRequest)device BSData+MsgAMsgB (Preamble,
RRC ConnResumeRequest)(RAR,RRC ReleaseWithSuspend)ACKdevice BSData+MsgAMsgB (Preamble,
RRC ConnResumeRequest)(RAR,RRC ReleaseWithSuspend)ACKdevice BS
Msg1: Preamble Msg2: Random Rccess ResponseMsg3: RRC ConnResumeRequest
Msg4: RRC ConnResumeRRC ConnResumeComplete
Data DCI ...
Data
RRC DCIACKData DCI
RRC ReleaseWithSuspend
ACKdevice BS
Msg1: Preamble Msg2: Random Rccess ResponseMsg3: RRC ConnResumeRequest
Msg4: RRC ConnResumeRRC ConnResumeComplete
Data DCI ...
Data
RRC DCIACKData DCI
RRC ReleaseWithSuspend
ACK+Data device BSMsgA MsgB(Preamble,RRC ConnResumeRequest)(RAR,RRC ConnResume)ACKRRC ConnResumeCompleteData DCI ...
DataRRC DCIData DCIRRC ReleaseWithSuspendACKdevice BSMsgA MsgB(Preamble,RRC ConnResumeRequest)(RAR,RRC ConnResume)ACKRRC ConnResumeCompleteData DCI ...
DataRRC DCIData DCIRRC ReleaseWithSuspendACK+Datadevice BSMsgA MsgB(Preamble,RRC ConnResumeRequest)(RAR,RRC ConnResume)ACKRRC ConnResumeCompleteData DCI ...
DataRRC DCIData DCIRRC ReleaseWithSuspendACK+Data (a) 4-step(c) NR EDT (b)2-step B(d) 2-step A D a t a HA R Q Fig. 2. Procedures of each scheme.
The NR EDT is illustrated in Fig. 2(c), which enables devices to transmit data with Msg3without entering into RRC Connected state [9], [10]. Since the BS would have no knowledgewhether the device has a small packet to transmit or not. Even if devices have deterministic traffic and the traffic pattern are predictable, the device identity is not known to the BS untilMsg3. Therefore, the device is required to indicate its wish to use NR EDT to the BS in Msg1by randomly selecting one of the special PRACH preambles, which have been dedicated toNR EDT by the BS in system information. Once the preamble is detected successfully, the BSgrants a larger PUSCH resource for both Msg3 and data transmission. Here, we assume thatthe packet size is smaller than the maximum transport block size (TBS), hence the data can betransmitted together with Msg3 in one slot. The device, whose Msg3 and data are successfullydecoded among colliding devices, receives Msg4 (i.e., RRC release with suspend). Since thedata is transmitted together with Msg3, no data HARQ needs to be considered in NR EDT.
2) Existing 2-step B and proposed 2-step A Random Access:
The 2-step B and 2-step A RAschemes are illustrated in Fig. 2(b)(d), where data is either transmitted after MsgB in 2-step B RAscheme in RRC Connected state, or together with MsgA in 2-step A RA scheme in RRC Inactivestate, respectively. The MsgA consists of two parts, that is, preamble and PUSCH (correspondingto Msg3 in 4-step RA scheme), which are transmitted separately over time. Unlike 4-step andNR EDT RA schemes, where the PUSCH resources are granted via Msg2, each preamble ismapped to a PUSCH in advance in 2-step A/B RA schemes. If multiple preambles are mappedto a PUSCH in the same time-frequency resource, the PUSCH transmissions of the preamblesoverlap in time and frequency, which increases the probability of PUSCH decoding failure.Alternatively, a single preamble can be mapped to a unique PUSCH time-frequency resource,which reduces the probability of PUSCH decoding failure due to collision, but significantlyincreases the physical-layer overhead in the uplink. Here, we only consider the unique mappingrelationship between preamble and PUSCH as the baseline. It is noted that if the preamble isdetected but none of PUSCH transmission is decoded successfully among the colliding devices in2-step A/B RA schemes, the BS sends a fallback MsgB with an UL grant for Msg3 transmission,and all the colliding devices fallback to the 4-step RA scheme.
C. Random Access Model
To capture the characteristics of uplink transmission with different RA schemes, we jointlymodel the preamble detection, PUSCH decoding, and data transmission, which are based onPower Delay Profile (PDP), SINR, and Block Error Rate (BLER), respectively.
1) Power Delay Profile:
PDP is utilized to model the preamble detection (i.e., Msg1 or MsgA)at the BS, which is the periodic correlation of the received preamble as a function of time. As we mentioned earlier, the preamble is generated from cyclic shift of the ZC sequence defined as z r [ k ] (cid:44) exp [ − jπrk ( k + 1) /N ZC ] , (1)where k is the sequence index, N ZC denotes the sequence length, and r is the root numberbroadcasted to devices in the system information, which is different among the neighbouringBSs .The ZC sequences have an ideal cyclic auto-correlation property, which means the magnitudeof the cyclic correlation with a circularly shifted version of itself becomes a scaled delta functionas | c rr [ τ ] | = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) √ N ZC N ZC − (cid:88) k =0 z r [ k ] z ∗ r [ k + τ ] (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) = (cid:112) N ZC δ [ τ ] , (2)where c rr [ τ ] is the discrete cyclic auto-correlation function of z r [ k ] at lag τ and [ · ] ∗ denotes thecomplex conjugate. From this property, we can observe how much the received sequences areshifted, compared to the reference ZC sequence.These sequences also have a cyclic cross-correlation property. The magnitude of the cycliccross-correlation between any two ZC sequences with different root numbers r and k is constantas | c rk [ τ ] | = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) √ N ZC N ZC − (cid:88) k =0 z r [ k ] z ∗ k [ k + τ ] (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) = 1 , (3)where k is the preamble sequence index.In principle, multiple preambles can be generated from a ZC sequence by cyclically shiftingthe sequence by a factor of cyclic shift value N CS . Thus, the i th preamble can be represented as z ir [ k ] = z r [( k + i N CS ) mod N ZC ] . (4)To detect the preamble, the BS extracts the received preamble within specific time/frequencyresources through time-domain sampling and frequency-tone extraction. The received preamblefrom a typical device can be written as [5], [22]–[26] y ir [ k ] = (cid:112) ρh z ir [ k + τ ] + σ n , (5)where τ is the sequence shift caused by the propagation delay from a typical device to the BS, ρ is the power control threshold, h is the channel power gain between the BS and a typicaldevice, and σ n denotes the average amplitude of additive noise. The BS computes PDP of a typical device via time-domain correlation between the receivedpreamble (5) and the local reference preamble sequence (4). Therefore, we formulate the PDPof preamble detection in the m th time slot as PDP m [ τ ] = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) N ZC − (cid:88) k =0 y ir [ k ] z ir [ k + τ ] ∗ (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) N ZC − (cid:88) k =0 (cid:16)(cid:112) ρh z ir [ k + τ ] + σ n (cid:17) z ir [ k + τ ] ∗ (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) , (6)where [ · ] ∗ represents the complex conjugate.
2) Signal to Noise plus Interference Ratio:
SINR is utilized to model the PUSCH decoding(i.e., Msg3 or MsgA) when the preamble is successfully detected at the BS. As we mentionedearlier, each device transmits a randomly chosen preamble to the BS, and thus devices choosingsame preamble in the same RA subframe cause the intra-cell interference in PUSCH transmission.We formulate
SINR of the PUSCH transmission in m th time slot as [15], [16] SINR m = ρh / (cid:0) I m intra + σ n (cid:1) , (7)where I m intra = (cid:88) j ∈Z in { N m New j + N m Cum j > } ρh j . (8)In (7), h is the channel power gain from a typical device to the BS, and I intra is the aggregatedintra-cell interference in the m th time slot. In (8), Z in is the set of intra-cell interfering devices, N m New j is the number of new arrived packets in the m th time slot of j th interfering UE, N m Cum j is the number of accumulated packets in the m th time slot of j th interfering device. { . } is theindicator function that takes the value 1 if the statement { . } is true, and zero otherwise. Whetherthe device generates interference is determined by the fact that if the condition { N m New j + N m Cum j > } has been satisfied. This means that the device is able to generate interference only when itsbuffer is non-empty.To solve (8), we define the buffer non-empty probability T m of each device in the m th timeslot as T m = P [ N m New + N m Cum > , which can be treated using the thinning process.
3) Block Error Rate:
For data transmission after the successful RA procedure (i.e., existing4-step and 2-step B RA schemes), we assume the BLER of each data transmission is B (e.g., B = 0 . ) [27]. If the data is transmitted during the RA procedure (i.e., proposed NR EDT and2-step A RA schemes), we do not consider data transmission separately for fairness. III. RACH P
ERFORMANCE A NALYSIS
In this section, we analyze preamble detection, PUSCH decoding, and data transmissionsuccess probabilities. As we mentioned earlier, the distribution of the devices follows PPP inthe cell. For a typical device in the cell, we can obtain the number of interfering devices in the m th time slot as P [ N = n ] = e − λ Dp T m ( λ Dp T m ) n /n ! , (9)where n is the number of interfering devices, and λ Dp is the intensity of devices that choosethe same preamble. We assume that the BS has an available preamble pool with the number ofnon-dedicated preambles ξ , known by the devices. Each preamble has an equal probability /ξ to be chosen by the device, hence the average number of the devices using the same preamble λ Dp is λ Dp = λ D /ξ, (10)where λ D is the device intensity in the cell.The T m in (9) is the buffer non-empty probability in m th time slot. Similar as [16], theaccumulated packets number of the device in any time slot should be approximately Poissondistributed. As such, we approximate the number of accumulated packets N m Cum in the m th timeslot as Poisson distribution Λ m cum with intensity µ m Cum . The intensity of accumulated packets µ m Cum ( m > in the m th time slot is derived as µ m Cum = µ m − + µ m − − P m − T m − , (11)where P m − is the overall packet transmission success probability in ( m − th time slot, and T m − is the buffer non-empty in the ( m − th time slot. Therefore, the buffer non-emptyprobability T m in (9) of each device in the m th time slot is derived as T m = 1 − e − µ m New − µ m Cum . (12) A. Preamble Detection in Msg1 and MsgA
The preamble detection is performed at step 1 of each RA scheme by calculating the PDP,where the peak values of devices choosing the same preamble locate in different positions dueto different propagation delay to the BS. However, the BS can not detect the collision during preamble detection in step 1 of RA schemes, because the multiple peak values may be alsocaused by the multipath effect. When the cell size is more than twice the distance correspondingto the maximum delay spread, the BS may be able to differentiate two devices selecting the samepreamble, since they appear distinctly apart in the PDP [28]–[30]. We aim to provide a generalanalytical framework in this paper, therefore, we assume the cell size is smaller than twice ofthe distance corresponding to the maximum delay spread, which means the collision can not bedetected during preamble detection in step 1 of the RA schemes. The preamble detection successprobability of a typical device in m th time slot conditioning on n interfering devices is derivedin the following Lemma 1 . For the brevity of exposition, we define the event with n interferingdevices as A = { N = n } . Lemma 1.
The preamble detection success probability of a typical device in the m th time slotconditioning on n interfering devices is derived as P m pre |A = 1 − (cid:34) − e − (cid:18) √ λ th N ZC − σ n (cid:19) /ρ (cid:35) n +1 , (13) where N ZC is the length of the preamble sequence, σ n is the average noise amplitude, ρ is theaverage received power at the BS, and λ th is the threshold for preamble detection.Proof. See Appendix A.We then derive the overall preamble detection success probability of a typical device in thefollowing
Theorem 1 . Theorem 1.
The overall preamble detection success probability of a typical device in m th timeslot is derived as P m pre = ∞ (cid:88) n =0 P [ N = n ] P m pre |A = ∞ (cid:88) n =0 e − λ Dp T m ( λ Dp T m ) n n ! × − (cid:34) − e − (cid:18) √ λ th N ZC − σ n (cid:19) /ρ (cid:35) n +1 . (14) Proof.
Following the proof of
Lemma 1 . B. PUSCH Decoding in Msg3 and MsgA
The PUSCH decoding is performed either in step 3 of 4-step and NR EDT RA schemes, orstep 1 of the 2-step A/B RA schemes. In order to analyse the collision happens in Msg3 or MsgA, we derive the PUSCH decoding success probability of a typical device in m th time slotconditioning on n interfering devices and preamble detection success.For the brevity of exposition, we define the preamble detection success of a typical devicewith n interfering devices as event B = (cid:40) n +1 (cid:81) j =1 { PDP mj <λ th } = 0 , A (cid:41) . Utilizing the characteristics of wireless communications, a specific signal can still be decodedin the advanced receiver when multiple signals are received at different powers, which is calledcapturing capability. This phenomenon occurs when the strongest signal power received froma typical device is sufficiently large. In other words, the capture effect occurs when the SINR of the strongest signal is larger than a specific threshold. The PUSCH decoding probability ofa typical device in m th time slot conditioning on n interfering devices and preamble detectionsuccess is derived in the following Lemma 2 . Lemma 2.
The PUSCH decoding success probability conditioning on n interfering devices andpreamble detection success is derived as P m pus |B = n +1 (cid:88) k =1 (cid:0) n +1 k (cid:1) ( − k +1 exp (cid:26) − kγ th σ ρ (cid:27) / (( n + 1) (1 + γ th ) n ) , (15) where σ is the average noise power, ρ is the average received power at the BS, and γ th is theSINR threshold for PUSCH decoding.Proof. See Appendix B.We then derive the overall PUSCH decoding success probability of a typical device in m thtime slot in the following Theorem 2 . Theorem 2.
The overall PUSCH decoding success probability of a typical device in m th timeslot is derived as P m pus = ∞ (cid:88) n =0 P [ N = n ] P m pre |A P m pus |B = ∞ (cid:88) n =0 e − λ Dp T m ( λ Dp T m ) n n ! × − (cid:34) − e − (cid:18) √ λ th N ZC − σ n (cid:19) /ρ (cid:35) n +1 × (cid:80) n +1 k =1 (cid:0) n +1 k (cid:1) ( − k +1 exp (cid:26) − kγ th σ ρ (cid:27) ( n + 1) (1 + γ th ) n . (16) Proof.
Following the proofs of
Lemma 1 and
Lemma 2 . In [31], [32], the signal-to-interference-ratio (SIR) is used, however, we use SINR as [33] C. Data transmission after RACH
For 4-step and 2-step B RA schemes, the data is transmitted after successful preamble detectionand PUSCH decoding, we can separately consider data transmission and RA procedure. For NREDT and 2-step A RA schemes, the data is transmitted during RA procedures, hence, we need tojointly study the RA analysis with data transmission analysis. For the brevity of exposition, wedefine the preamble detection success, and PUSCH decoding success with n interfering devicesas event C = { SINR o > γ th , SINR o > SINR j , B} .To model the data transmission, we assume the BLER of each data transmission is B , then,the data transmission success probability of a typical device in m th time slot conditioning onevent C is derived as P m data |C = 1 − (1 − B ) K , (17)where K is the maximum data HARQ transmission times.IV. O VERALL P ACKET T RANSMISSION S UCCESS P ROBABILITY AND E NERGY C ONSUMPTION
In this section, we analyse the overall packet transmission success probability and the energyconsumption of a typical device in m th time slot with 4-step, NR EDT, 2-step A, and 2-stepB RA schemes. Specifically, we derive the energy consumption of each message under eithersuccess or failure, and then calculate the energy consumption based on the probability theory.For ease of description, we first present definitions for general variables. As illustrated inFig. 3 and Table I, T p is the preamble transmission time [34], T s is the slot time length, T d isthe Physical Downlink Control Channel (PDCCH) decoding time, which contains the downlinkcontrol information(DCI), N RAR is the number of slots that RAR window occupies, N CRT isthe number of slots that contention resolution timer (CRT) occupies. T K2 , T (cid:52) and T PUCCH arescheduling parameters defined in the standards [35], [36]. P s and P r are the power consumptionwhen the device is in the sleep and receiving states separately, which are constants for alldevices. As for the transmit power P t , although the radiated power of each device depends onits distance to the BS due to the full-path power control, the power consumed by the amplifiersand the radio frequency (RF) hardware is actually much higher, almost regardless of the radiatedpower. Therefore, the transmit power P t is also regarded as a constant. TABLE IN
OTATION T ABLE
Notations Physical means T p The preamble transmission time T s The slot time length T d The PDCCH decoding time N RAR
The number of slots that RAR window occupies N CRT
The number of slots that CRT occupies T K2 The PUSCH scheduling parameter T (cid:52) The specific PUSCH scheduling parameter for Msg3 T PUCCH
The PUCCH scheduling parameter P s The sleep power of a typical device P r The receiving power of a typical device P t The transmit power of a typical device
A. 4-step Random Access
The data is transmitted after successful 4-step RA procedure, and the overall packet transmis-sion success only occurs when preamble detection, PUSCH decoding, and data transmission areall successful. Hence, the overall packet transmission success probability of 4-step RA schemein m th time slot is derived as P m = ∞ (cid:88) n =0 P [ N = n ] P m pre |A P m pus |B P data |C , (18)where P m pre |A is the preamble detection success probability given in Lemma 1 , P pus |B is thePUSCH decoding success probability given in Lemma 2 , and P data |C is data transmission successprobability given in (17).The energy consumption of 4-step RA scheme depends on the success or failure of preambledetection and PUSCH decoding. Therefore, we derive the energy consumption of each mes-sage with successful RA procedure, preamble detection failure, and PUSCH decoding failure,respectively.
1) Successful 4-step RA procedure:
The successful 4-step RA procedure timing relationshipis illustrated in Fig. 3, which occurs when both preamble detection and PUSCH decoding aresuccessful. P t P s P r t T p T d T s T K2 +T ∆ T PUCCH T PUCCH N RAR /2*T s T K2 Data transmission in 4-stepHARQ M s g2 DC I R A R M s g4 DC I M s g4 D a t a DC I RRC DC I R e l ea s e BS M s g2 DC I R A R M s g4 DC I M s g4 D a t a DC I RRC DC I R e l ea s e BS M s g1 M s g3 ( + D a t a ) A C K RRC D a t a A C K UE M s g1 M s g3 ( + D a t a ) A C K RRC D a t a A C K UE T s N CRT /2*T s Fig. 3. Timing relationship of successful 4-step and NR EDT RA procedure.
The device transmits Msg1 (i.e., preamble) in one slot T s . Since the preamble transmissiontime only lasts for T p , the device is in sleep state in the rest of time T s − T p . Therefore, theenergy consumption of step 1 in 4-step RA scheme can be written as E p = P t T p + P s (T s − T p ) , (19)where P t , T p , P s , and T s are given in Table I.After transmitting the Msg1, the device starts to monitor PDCCH containing DCI continuously.The device monitors the PDCCH in each slot for T d , and then stays in sleep state for the rest ofthe time T s − T d . We assume the Msg2 is scheduled following PDCCH in the same slot, and theMsg2 from the BS arrives at the half duration of the RAR window in the successful case (i.e., N RAR ∗ T s ). After receiving the Msg2, the device needs to wait for T K2 + T (cid:52) before transmittingthe Msg3 as Fig. 3. Therefore, the energy consumption of step 2 in 4-step RA scheme whenpreamble detection succeeds can be written as E Msg2s = (N
RAR / −
1) (P r T d + P s (T s − T d )) + P r T s + P s (T K2 + T (cid:52) ) , (20)where P s , P r , N RAR , T d , T s , T K2 , and T (cid:52) are given in Table I.Then, the energy consumption of transmitting Msg3 at step 3 in 4-step RA scheme can bewritten as E Msg3 = P t T s . (21)After transmitting the Msg3, the device starts the CRT and monitors the PDCCH for Msg4DCI. We assume the Msg4 from the BS arrives at the half duration of the CRT in the successfulcase (i.e., N CRT ∗ T s ). The device that succeeds in the contention receives the Msg4, and then transmits the ACK after T PUCCH as Fig. 3. Therefore, the energy consumption of step 4 in the4-step RA scheme when PUSCH decoding succeeds can be written as E Msg4s = (N
CRT / −
1) (P r T d + P s (T s − T d )) + P r T s + T PUCCH P s + P t T s , (22)where P s , P r , N CRT , T d , T s , and T PUCCH are given in Table I.The HARQ is applied to data transmission after successful 4-step RA procedure (marked withdash line in Fig. 3) to guarantee the reliability. The device first receives the data DCI, whichlasts for T d . Then, the device transmits data after T K2 , and starts to monitor the RRC DCI.We assume the RRC DCI arrives after 3 slots, which indicates the data transmission failure orsuccess. If the data transmission succeeds, the device transmits ACK after T PUCCH . Therefore,the energy consumption when the data HARQ completes in k th transmissions can be written as E k data = k (cid:2) P r T d + P s (T s − T d ) + T K2 P s + P t T s + 3 (P r T d + P s (T s − T d )) + P r T s (cid:3) +T PUCCH P s + P t T s . (23)The average data transmission energy consumption after successful 4-step RA procedure isderived as E HARQdata = K − (cid:88) k =1 B (1 − B ) k − E k data + (1 − B ) K − E Kdata (cid:124) (cid:123)(cid:122) (cid:125) I , (24)where K is the maximum data retransmission times, B (1 − B ) k − is the probability that datatransmission succeeds in the ( k − th HARQ, and term I represents the average energy con-sumption of last transmission, which depends on the probability of previous (K − failuretransmission.
2) Preamble detection failure:
The energy consumption of step 1 is the same as that of thesuccessful 4-step RA procedure. If preamble detection fails at the step 1 of 4-step RA scheme,the device will not receive the Msg2, which means the device monitors PDCCH until the endof RAR window and waits for the next RACH opportunity. Hence, the energy consumption ofstep 2 in 4-step RA scheme when preamble detection fails can be written as E Msg2f = N
RAR (P r T d + P s (T s − T d )) . (25)
3) PUSCH decoding failure:
The energy consumption of step 1, 2, and 3 are the same asthat of the successful 4-step RA procedure. If PUSCH decoding fails at the step 3 of the 4-stepRA scheme, the device will not receive Msg4, which means the device monitors PDCCH until the end of CRT and waits for the next RACH opportunity. Hence, the energy consumption ofstep 4 in 4-step RA scheme when PUSCH decoding fails can be written as E Msg4f = N
CRT (P r T d + P s (T s − T d )) . (26)Finally, the average energy consumption of a typical device in m th time slot of 4-step RAscheme is derived as E m = T m (cid:26)(cid:0) − P m pre (cid:1) ( E p + E Msg2f ) (cid:124) (cid:123)(cid:122) (cid:125) I + (cid:0) P m pre − P m pus (cid:1) ( E p + E Msg2s + E Msg3 + E Msg4f ) (cid:124) (cid:123)(cid:122) (cid:125) II + P m pus (cid:16) E p + E Msg2s + E Msg3 + E Msg4s + E HARQdata (cid:17)(cid:124) (cid:123)(cid:122) (cid:125)
III (cid:27) , (27)where term I, II, and III are the average energy consumption of 4-step RA scheme under preambledetection failure, PUSCH decoding failure, and successful 4-step RA procedure, T m is the non-empty probability of a typical device in m th time slot, P m pre is the overall preamble detectionprobability in Theorem 1 , P m pus is the overall PUSCH decoding probability in Theorem 2 . B. NR EDT
As shown in Fig. 3, NR EDT grants a larger PUSCH resource for Msg3 transmission alongwith the data (marked with dash line in Fig. 3), and the overall packet transmission successoccurs when both preamble detection and PUSCH decoding are successful. Hence, the overallpacket transmission success probability of NR EDT in m th time slot is derived as P m EDT = ∞ (cid:88) n =0 P [ N = n ] P m pre |A P m pus |B , (28)where P m pre |A is the preamble detection success probability given in Lemma 1 , and P pus |B is thePUSCH decoding success probability given in Lemma 2 .Similar as 4-step RA scheme, the energy consumption of NR EDT also depends on thesuccess or failure of preamble detection and PUSCH decoding. The difference is that the datais transmitted along with Msg3 without HARQ, whose energy consumption is E data = P t T s . Hence, the average energy consumption of a typical device in m th time slot in NR EDT RAscheme is derived as E m EDT = T m (cid:26)(cid:0) − P m pre (cid:1) ( E p + E Msg2f ) (cid:124) (cid:123)(cid:122) (cid:125) I + (cid:0) P m pre − P m pus (cid:1) ( E p + E Msg2s + E Msg3 + E data + E Msg4f ) (cid:124) (cid:123)(cid:122) (cid:125) II + P m pus ( E p + E Msg2s + E Msg3 + E data + E Msg4s ) (cid:124) (cid:123)(cid:122) (cid:125) III (cid:27) , (29)where term I, II, and III are the average energy consumption of NR EDT under preamble detectionfailure, PUSCH decoding failure, and successful RA procedure. Since data is transmitted alongwith Msg3, both term II and term III include data energy consumption E data . In (29), T m is thenon-empty probability of a typical device in m th time slot, P m pre is the overall preamble detectionprobability in Theorem 1 , and P m pus is the overall PUSCH decoding probability in Theorem 2 . C. 2-step B Random Access
Remind that if the BS detects the preamble but fails to decode the PUSCH in MsgA, thefallback mechanism in 2-step B RA scheme allows the devices to transmit Msg3 following the4-step RA scheme. Therefore, we define the fallback probability, and PUSCH decoding successprobability after the fallback as P m fb = ∞ (cid:88) n =0 P [ N = n ] P m pre |A (cid:0) − ( n + 1) P m pus |B (cid:1) , (30)and P m fb pus = ∞ (cid:88) n =0 P [ N = n ] P m pre |A (cid:0) − ( n + 1) P m pus |B (cid:1) P m pus |B , (31)respectively.In (30) and (31), P m pre |A is the preamble detection success probability given in Lemma 1 , and P pus |B is the PUSCH decoding success probability given in Lemma 2 .Since the packet can be successfully transmitted either after 2-step B RA procedure with suc-cessful preamble detection and PUSCH decoding, or after 4-step RA procedure with successfulfallback PUSCH decoding, the overall packet transmission success probability is derived as P m = ∞ (cid:88) n =0 P [ N = n ] P m pre |A P m pus |B P m data |C (cid:124) (cid:123)(cid:122) (cid:125) I + ∞ (cid:88) n =0 P [ N = n ] P m pre |A (cid:0) − ( n + 1) P m pus |B (cid:1) P m pus |B P data |C (cid:124) (cid:123)(cid:122) (cid:125) II , (32) where term I and term II represent the packet transmission success probability with successful2-step B and fallback 4-step RA procedure, respectively. In (32), P m pre |A is the preamble detectionsuccess probability given in Lemma 1 , P pus |B is the PUSCH decoding success probability givenin Lemma 2 , and P data |C is data transmission success probability given in (17).The energy consumption of 2-step B RA scheme depends on the success or failure of preambledetection and PUSCH decoding in MsgA, and PUSCH decoding after fallback. Therefore, wederive the energy consumption of each message in 2-step B RA scheme with successful 2-stepB RA procedure, preamble detection failure, PUSCH decoding failure, respectively. t T d T PUCCH T PUCCH T K2 Data transmission in 2-step BHARQ M s g B DC I s R A R D a t a DC I RRC DC I R e l ea s e BS P R A CH P U S CH ( + D a t a ) A C K RRCD a t a A C K UE T s N RAR /2*T s P t P s P r T p T s P t P s P r T p T s Fig. 4. Timing relationship of successful 2-step B and 2-step A RA procedure. a) successful 2-step B RA procedure:
The timing relationship of successful 2-step B RAprocedure is illustrated in Fig. 4. The preamble transmission lasts for T p during T s , and andPUSCH transmission lasts for T s . Hence, we derive the energy consumption of step 1 in 2-stepB RA scheme as E MsgA = P t T p + P s (T s − T p ) + P t T s , (33)where P t , T p , P s , and T s are given in Table I.After transmitting the MsgA, the device starts to monitor PDCCH containing DCI continuouslyfor T d in each slot. We assume the MsgB from the BS arrives at the half duration of the RARwindow in the successful case (i.e., N RAR ∗ T s ). The device that succeeds in the contentionreceives the MsgB, and then transmits the ACK after T PUCCH as Fig. 4. Therefore, the energyconsumption of step 2 in 2-step B RA scheme with a successful MsgB is derived as E MsgBs = (N
RAR / −
1) (P r T d + P s (T s − T d )) + P r T s + T PUCCH P s + P t T s , (34)where P s , P r , N RAR , T d , T s , and T PUCCH are given in Table I. b) Preamble detection failure: The energy consumption of step 1 is the same as that of thesuccessful 2-step B RA procedure. If preamble detection fails at the step 1 of the 2-step B RAscheme, the device will not receive MsgB, which means the device monitors PDCCH until theend of RAR window and waits for the next RACH opportunity. Hence, the energy consumptionof step 2 in 2-step A RA scheme when preamble detection fails can be written as E MsgBf = N
RAR (P r T dci + P s (T s − T d )) , (35)where P s , P r , N RAR , T d , and T s are given in Table I. c) PUSCH decoding failure: The energy consumption of step 1 is the same as that of thesuccessful 2-step B RA procedure. If the BS successfully detects the preamble in MsgA butfails to decode the PUSCH at the step 1 of the 2-step B RA scheme, the device will receive afallback MsgB with grant for Msg3 transmission following 4-step RA procedure as Fig. 3. Weassume the MsgB from the BS arrives at the half duration of the RAR window, and the devicetransmits Msg3 after T K2 + T (cid:52) . Hence, we derive the energy consumption of step 2 in 2-stepB RA scheme when fallback mechanism is satisfied as E MsgBfb = (N
RAR / −
1) (P r T d + P s (T s − T d )) + P r T s + P s (T K2 + T (cid:52) ) , (36)where P s , P r , N RAR , T d , T s , T K2 , and T (cid:52) are given in Table I.Since the data can be transmitted after successful 2-step B or successful 4-step RA procedurewith HARQ, the average energy consumption of a typical device in m th time slot in 2-step BRA scheme is derived as E m = T m (cid:26) P m pus (cid:16) E MsgA + E MsgBs + E HARQdata (cid:17)(cid:124) (cid:123)(cid:122) (cid:125) I + (cid:0) − P m pus − P m fb (cid:1) ( E MsgA + E MsgBf ) (cid:124) (cid:123)(cid:122) (cid:125) II + P m fb pus (cid:16) E MsgA + E MsgBfb + E Msg3 + E Msg4s + E HARQdata (cid:17)(cid:124) (cid:123)(cid:122) (cid:125)
III + (cid:0) P m fb − P m fb pus (cid:1) ( E MsgA + E MsgBfb + E Msg3 + E Msg4f ) (cid:124) (cid:123)(cid:122) (cid:125) IV (cid:27) , (37)where term I, II, III, IV correspond to the successful 2-step B RA procedure, preamble detectionfailure, successful 4-step RA procedure after fallback, and PUSCH decoding failure in 4-step RAprocedure after fallback, respectively. In (37), P m pus is the overall PUSCH decoding probabilityin Theorem 2 , P m fb and P m fb pus are given in (30) and (31), respectively. D. 2-step A random access
Since the packet can be successfully transmitted either during 2-step A RA procedure withsuccessful preamble detection and PUSCH decoding, or after 4-step RA procedure with suc-cessful fallback PUSCH decoding, the overall packet transmission success probability of 2-stepA RA scheme is derived as P m = ∞ (cid:88) n =0 P [ N = n ] P m pre |A P m pus |B (cid:124) (cid:123)(cid:122) (cid:125) I + ∞ (cid:88) n =0 P [ N = n ] P m pre |A (cid:0) − ( n + 1) P m pus |B (cid:1) P m pus |B P data |C (cid:124) (cid:123)(cid:122) (cid:125) II , (38)where term I and term II represent the successful packet transmission in 2-step A RA and 4-step RA procedure after fallback, respectively. In (38), P m pre |A is the preamble detection successprobability given in Lemma 1 , P pus |B is the PUSCH decoding success probability given in Lemma 2 , and P data |C is data transmission success probability given in (17).Similar as the 2-step B RA scheme, the energy consumption of 2-step A RA scheme alsodepends on the success or failure of preamble detection and PUSCH decoding. The differenceis that the data is transmitted along with MsgA without HARQ, whose energy consumption is E data = P t T s . Hence, the average energy consumption of a typical device in m th time slot in2-step A RA scheme is derived as E m = T m (cid:26) P m pus ( E MsgA + E data + E MsgBs ) (cid:124) (cid:123)(cid:122) (cid:125) I + (cid:0) − P m pus − P m fb (cid:1) ( E MsgA + E data + E MsgBf ) (cid:124) (cid:123)(cid:122) (cid:125) II + P m fb pus ( E MsgA + E data + E MsgBfb + E Msg3 + E Msg4s + E HARQdata ) (cid:124) (cid:123)(cid:122) (cid:125) III + (cid:0) P m fb − P m fb pus (cid:1) (cid:0) E MsgA + E data + E MsgBfb + E Msg3 + E Msg4f (cid:1)(cid:124) (cid:123)(cid:122) (cid:125) IV (cid:27) , (39)where term I, II, III, IV correspond to the successful 2-step A RA procedure, preamble detectionfailure, successful 4-step RA procedure after fallback, and PUSCH decoding failure in 4-step RAprocedure after fallback, respectively. In (39), P m pus is the overall PUSCH decoding probabilityin Theorem 2 , P m fb and P m fb pus are given in (30) and (31), respectively. V. P
ERFORMANCE M ETRICS
In this section, we derive the average energy consumption of each scheme for a successfulpacket transmission and the throughput of each scheme.
A. Average Energy Consumption
We have derived the energy consumption of each scheme in m th time slot in Section IV,however, the average energy consumption for a successful packet transmission in each schemeis a more important metric. Therefore, We derive the average energy consumption of a successfulpacket transmission as E [ E m ] = m (cid:88) t =1 E m / m (cid:88) t =1 T m P m , (40)where E m is the energy consumption in m th time slot of each scheme, which has been derivedfor each scheme in (27), (29), (39), (37). (cid:80) mt =1 T m P m represents the total number of successfulpacket transmission of each scheme, which can be calculated based on (12), (18), (18), (38),and (32). B. Throughput
We also analyze the system throughput performance by assuming that all packets in the systemhave the same packet size S . Therefore, the throughput in the m th time slot is defined as R m = T m P m S/ T s , (41)where T s represents the slot time length in Table I, and T m P m S represents the total size of allsuccessfully transmitted packet in m th time slot of each scheme, which can be calculated basedon (12), (18), (18), (38), and (32).VI. S IMULATION AND D ISCUSSION
In this section, we validate our analysis above via independent system level simulations basedon Monte Carlo method and the queue evolution over consecutive time slots. As mentioned inSection II, the devices are deployed via independent PPPs in a 0.1 km circle cell. We assume thatthe frequency band only impacts the slot duration. Each device employs the channel inversionpower control, and the buffer at each device is simulated to capture the new packets arrivaland accumulation process evolved along the time. The preamble detection, PUSCH decoding, and data transmission processes are jointly simulated to verify the packet transmission successprobability, average energy consumption for a packet transmission, and throughput derived insection IV and V. The advanced receiver in our model, which has been validated by Ericssonvia system-level simulation, is also compared with the basic receiver in [17]. In all figures ofthis section, we use “Ana.” and “Sim.” to abbreviate “Analytical” and “Simulation”, respectively.Unless otherwise stated, we set the same new packets arrival rate for each time slot as µ m New = 0 . packets/time-slot, ρ = − dBm, σ = − . dBm, γ th = − dB, α = 4 , T p = (133 + 9 . us , T slot = 0 . ms, T dci = 107 . us , N RAR = 40 , N CRT = 48 . T K2 = 0 . ms, T (cid:52) = 1 . ms, T PUCCH = 964 . us, P s =15 uW, P r = 80 mW, P t = 500 mW, N ZC = 839 , λ th = − . dB, K = 4 . Fig. 5. Packet transmission success probability in each time slot.We set the device intensity λ Dp = thtime slot with different device intensity Fig. 5 plots the overall packet transmission success probability with four RA schemes versustime slot with λ Dp = 5 . The analytical curves of 4-step, NR EDT, 2-step A, and 2-step B RAschemes are plotted using (18), (28), (38) and (32). The close match between the analytical curvesand simulation points validates the accuracy of our developed spatio-temporal mathematicalframework. In Fig. 5, we see that the overall packet transmission success probability of eachscheme enters into the stable region in the advanced receiver. However, the overall packettransmission success probability of each scheme keeps decreasing as time evolves in the basicreceiver. This is because the BS can not decode the PUSCH if multiple colliding devices’ SINRis higher than the threshold in the basic receiver. Therefore, the new arrival packets can not betransmitted to the BS in time, and leads to the traffic congestion. We also observe that the overall packet transmission success probabilities of 2-step A/B RAschemes are almost the same, and the overall packet transmission success probabilities of 4-stepand NR EDT RA schemes are almost the same. This can be explained by the reason that the datatransmission after RACH achieves high success probability in 4-step and 2-step B RA schemesdue to HARQ. We also notice that the success probabilities of 2-step A/B RA schemes are higherthan the 4-step and NR EDT schemes because of the fallback mechanism in the 2-step A/B RAschemes, which enables the packet to be successfully transmitted after fallback to 4-step RAscheme. This advantage is more obvious in the basic receiver due to higher fallback probability.Fig. 6 plots the overall packet transmission success probability with four RA schemes versusdevice intensity in th time slot. In Fig. 6, we observe that the overall packet transmissionsuccess probability of all schemes decreases with the increasing device intensity, due to theincreasing aggregate interference from more devices transmitting signals simultaneously. Wealso observe that the decreasing rate is almost linear in the advanced receiver, and more sharplyin the basic receiver due to more serious traffic congestion. Fig. 7. Average energy consumption for packet transmissionin each time slot. We set the device intensity λ Dp = th time slot with different device intensity Fig. 7 plots the average energy consumption for a successful packet transmission with four RAschemes versus time slot. The analytical curves of 4-step, NR EDT, 2-step A and 2-step B RAschemes are plotted using (27), (29), (39), (37) and (40). In Fig. 7, we observe that the averageenergy consumption for a successful packet transmission reaches a stable state in the advancedreceiver, however, the average energy consumption keeps increasing with time-evolving in thebasic receiver due to low overall packet transmission probability. Fig. 8 plots the average energy consumption for a successful packet transmission with four RAschemes versus device intensity. In Fig. 8, we see that the average energy consumption follows4-step > NR EDT > > > > > Fig. 9. Average throughput in each time slot. We set the deviceintensity λ Dp = th time slot with different deviceintensity Fig. 9 and Fig. 10 plot the throughput using (41) with four RA schemes versus the time slotand the device intensity, respectively. In Fig. 9, we can observe that the throughput reaches thehighest value in the advanced receiver, which is determined by the new packets arrival rate duringeach RACH period. It also shows that the throughput of 4-step and NR EDT RA schemes inbasic receiver rises and then decreases due to serious traffic congestion. In Fig. 10, we observethat all schemes can deal with low intensity scenario effectively, and the average throughput inthe basic receiver decreases more sharply. In the advanced receiver, the average throughput isalmost the same for all schemes. In the basic receiver, the average throughput follows 2-step A = > NR EDT = VII. C
ONCLUSION
In this paper, we developed a spatio-temporal mathematical model to analyze the potentialRA schemes for small data transmission. We first analyzed the preamble detection probability,PUSCH decoding probability, and data transmission performed of a typical device. We thenderived the overall packet transmission success probability of a typical device with 4-step, NREDT, 2-step A, and 2-step B schemes by modelling the queue evolution over consecutive timeslots. We also provided the average energy consumption for a successful packet transmission,and throughput analysis for each scheme. Our numerical results have shown that the 2-stepA/B RA schemes achieve the same packet transmission success probability. The 4-step and NREDT RA schemes reach the same packet transmission success probability. The average energyconsumption for packet transmission of the 2-step A RA scheme is lowest in low device densityscenario, and the 2-step B RA scheme reaches the lowest average energy consumption for packettransmission in high device density scenario.A
PPENDIX
AA P
ROOF OF L EMMA m th time slot is defined as P m pre |A = 1 − n +1 (cid:89) j =1 P [PDP mj [ τ ] < λ th |A ] , (42)where n +1 (cid:81) j =1 P [PDP mj [ τ ] < λ th | N = n ] is the probability that the PDP peak values of n +1 collidingdevices are below the threshold λ th , hence, none of the colliding devices succeeds in preambledetection. As indicated in (42), the preamble transmission is successful only when at least onePDP peak value of n + 1 colliding devices is above the threshold λ th .We can calculate the Cumulative Distribution Function (CDF) of PDP peak value of a typicaldevice based on (6) as P (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) N ZC − (cid:88) k =0 (cid:16)(cid:112) ρh z ir [ k + τ ] + σ n (cid:17) z ir [ k + τ ] ∗ (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) < λ th |A = P (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) N ZC (cid:112) ρh + N ZC − (cid:88) k =0 ∼ σ n (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) < λ th |A = P (cid:34) h < (cid:18) √ λ th N ZC − σ n (cid:19) /ρ |A (cid:35) = 1 − e − (cid:18) √ λ th N ZC − σ n (cid:19) /ρ . (43)Substituting (43) into (42), we can obtain the preamble detection success probability as (13). A PPENDIX
BA P
ROOF OF L EMMA P m pus |B = P [SINR o > γ th , SINR o > SINR j |B ]= P [SINR o > γ th | SINR o > SINR j , B ] (cid:124) (cid:123)(cid:122) (cid:125) I P [SINR o > SINR j |B ] (cid:124) (cid:123)(cid:122) (cid:125) II , (44)where term I is the PUSCH transmission success probability that the received SINR of typicaldevice is above the threshold conditioning on its SINR is higher than all interfering devices,term II is the probability that the received PUSCH SINR of a typical device is the strongestamong n + 1 colliding devices.The Complementary Cumulative Distribution Function (CCDF) of the maximum channel gainbetween n + 1 independent Rayleigh fading channel gains is derived as F h max | N = n ( h ) = 1 − (1 − exp ( − h )) n +1 , (45)Substituting (45) and (7) into (44) and noting that P [SINR o > SINR j |B ] = 1 / ( n + 1) , we obtain P m pus |B = E I intra (cid:40) − (cid:18) − exp (cid:26) γ th ρ (cid:0) σ + I intra (cid:1)(cid:27)(cid:19) n +1 (cid:41) /n + 1 . (46)Because of the independency of the PPP in different regions and after applying the binomialexpansion for the numerator of (46), we obtain P m pus |B = n +1 (cid:88) k =1 (cid:0) n +1 k (cid:1) ( − k +1 exp (cid:26) − kγ th σ ρ (cid:27) L I intra (cid:18) γ th ρ (cid:12)(cid:12)(cid:12) B (cid:19) /n + 1 , (47)where L I intra ( · ) denotes the Laplace Transform of the aggregate intra-cell interference I intra . TheLaplace Transform of the aggregate intra-cell interference I intra is given in [16] as L I intra (cid:18) γ th ρ (cid:12)(cid:12)(cid:12) B (cid:19) = 1 / (1 + γ th ) n . (48)Substituting the Laplace Transform of the aggregated intra-cell interference (48) into (47), wecan obtain (15) R EFERENCES [1]
Study on scenarios and requirements for next generation access technologies , document TR 38.913 V15.0.0, 3GPP, Sophia,Antipolis, France, 2018.[2] H. M. Wang, Q. Yang, Z. Ding, and H. V. Poor, “Secure Short-Packet Communications for Mission-Critical IoTApplications,”
IEEE Trans. Wirel. Commun. , vol. 18, no. 5, pp. 2565–2578, May 2019.[3] G. Durisi, T. Koch, and P. Popovski, “Toward Massive, Ultrareliable, and Low-Latency Wireless Communication withShort Packets,”
Proc. IEEE , vol. 104, no. 9, pp. 1711–1726, Sep. 2016.[4] S. Han, X. Xu, Z. Liu, P. Xiao, K. Moessner, X. Tao, and P. Zhang, “Energy-Efficient Short Packet Communications forUplink NOMA-Based Massive MTC Networks,”
IEEE Trans. Veh. Technol. , vol. 68, no. 12, pp. 12 066–12 078, Dec. 2019.[5] H. S. Jang, S. M. Kim, H. S. Park, and D. K. Sung, “An Early Preamble Collision Detection Scheme Based on TaggedPreambles for Cellular M2M Random Access,”
IEEE Trans. Veh. Technol. , vol. 66, no. 7, pp. 5974–5984, Jul. 2017.[6]
Use Cases and Scenarios for 2-Step RACH , document R1-1910905, TSG-RAN WG1 98, 3GPP, Ericsson, Chongqing,China, Oct. 2019.[7] S. Hailu, M. Saily, and O. Tirkkonen, “RRC State handling for 5G,”
IEEE Commun. Mag. , vol. 57, no. 1, pp. 106–113,Jan. 2019.[8]
Radio Resource Control (RRC) Protocol specification , document TS 38.331 V16.1.0, 3GPP, Sophia, Antipolis, France, Jul.2018.[9] A. Hoglund, D. P. Van, T. Tirronen, O. Liberg, Y. Sui, and E. A. Yavuz, “3GPP Release 15 Early Data Transmission,”
IEEE Commun. Stand. Mag. , vol. 2, no. 2, pp. 90–96, Jun. 2018.[10] J. Thota and A. Aijaz, “On Performance Evaluation of Random Access Enhancements for 5G uRLLC,” in
IEEE Wirel.Commun. Netw. Conf. WCNC , vol. 2019-April. IEEE, Apr. 2019, pp. 1–7.[11] S. Kim, S. Kim, J. Kim, K. Lee, S. Choi, and B. Shim, “Low Latency Random Access for Small Cell Toward FutureCellular Networks,”
IEEE Access , vol. 7, pp. 178 563–178 576, Dec. 2019.[12] , document R1-1910690, TSG-RAN WG1 98bis, 3GPP, Nokia, Nokia Shanghai Bell,Chongqing, China, Oct. 2019.[13]
Results on MsgA Coverage vs. Packet Size with HARQ , document R1-1910908, TSG-RAN WG1 98bis, 3GPP, Ericsson,Chongqing, China, Oct. 2019.[14] M. Haenggi,
Stochastic geometry for wireless networks . Cambridge: Cambridge University Press, 2009.[15] M. Gharbieh, H. Elsawy, A. Bader, and M. S. Alouini, “Spatiotemporal Stochastic Modeling of IoT Enabled CellularNetworks: Scalability and Stability Analysis,”
IEEE Trans. Commun. , vol. 65, no. 8, pp. 3585–3600, Aug. 2017.[16] N. Jiang, Y. Deng, X. Kang, and A. Nallanathan, “Random access analysis for massive IoT networks under a new spatio-temporal model: A stochastic geometry approach,”
IEEE Trans. Commun. , vol. 66, no. 11, pp. 5788–5803, Nov. 2018.[17] N. Jiang, Y. Deng, A. Nallanathan, X. Kang, and T. Q. Quek, “Analyzing random access collisions in massive IoTnetworks,”
IEEE Trans. Wirel. Commun. , vol. 17, no. 10, pp. 6853–6870, Aug. 2018.[18] N. Jiang, Y. Deng, M. Condoluci, W. Guo, A. Nallanathan, and M. Dohler, “RACH Preamble Repetition in NB-IoTNetwork,”
IEEE Commun. Lett. , vol. 22, no. 6, pp. 1244–1247, Jun. 2018.[19] M. Gharbieh, H. ElSawy, H. C. Yang, A. Bader, and M. S. Alouini, “Spatiotemporal Model for Uplink IoT Traffic:Scheduling and Random Access Paradox,”
IEEE Trans. Wirel. Commun. , vol. 17, no. 12, pp. 8357–8372, Dec. 2018.[20] Y. Liu, Y. Deng, M. Elkashlan, A. Nallanathan, and G. K. Karagiannidis, “Analyzing Grant-Free Access for URLLCService,” pp. 1–30, 2020. [Online]. Available: http://arxiv.org/abs/2002.07842 [21] S. Ahmadi,
5G NR: Architecture, technology, implementation, and operation of 3GPP new radio standards . ElsevierLTD, Oxford, 2019.[22] X. Lin, A. Adhikary, and Y. P. Eric Wang, “Random Access Preamble Design and Detection for 3GPP Narrowband IoTSystems,”
IEEE Wirel. Commun. Lett. , vol. 5, no. 6, pp. 640–643, Dec. 2016.[23] H. Q. Ta, Z. Wang, S. W. Kim, J. J. Nielsen, and P. Popovski, “Preamble Detection in NB-IoT Random Access withLimited-Capacity Backhaul,” in
IEEE Int. Conf. Commun.
IEEE, May 2019, pp. 1–6.[24] Z. Wang and V. W. Wong, “Optimal Access Class Barring for Stationary Machine Type Communication Devices WithTiming Advance Information,”
IEEE Trans. Wirel. Commun. , vol. 14, no. 10, pp. 5374–5387, Oct. 2015.[25] M. Shirvanimoghaddam, M. Dohler, and S. J. Johnson, “Massive Multiple Access Based on Superposition Raptor Codesfor Cellular M2M Communications,”
IEEE Trans. Wirel. Commun. , vol. 16, no. 1, pp. 307–319, Jan. 2017.[26] Y. Liang, X. Li, J. Zhang, and Z. Ding, “Non-Orthogonal Random Access for 5G Networks,”
IEEE Trans. Wirel. Commun. ,vol. 16, no. 7, pp. 4817–4831, Jul. 2017.[27] C. Yu, L. Yu, Y. Wu, Y. He, and Q. Lu, “Uplink scheduling and link adaptation for narrowband internet of things systems,”
IEEE Access , vol. 5, pp. 1724–1734, Feb. 2017.[28] C. Anton-Haro and M. Dohler,
Machine-to-machine (M2M) communications: architecture, performance and applications .Elsevier, 2014.[29] S. Sesia, I. Toufik, and M. Baker,
LTE - The UMTS Long Term Evolution: From Theory to Practice: Second Edition . JohnWiley & Sons, 2011.[30] E. Dahlman, S. Parkvall, and J. Skold, . Amsterdam: Academic Press,2013.[31] J. Kim and J. Lee, “Exploiting the capture effect to enhance RACH performance in cellular-based M2M communications,”
Sensors (Switzerland) , vol. 17, no. 10, p. 2169, Sep. 2017.[32] Z. Zhang and Y. J. Liu, “Comments on “The Effect of Capture on Performance of Multichannel Slotted ALOHA System”,”
IEEE Trans. Commun. , vol. 41, no. 10, pp. 1433–1435, Jun. 1993.[33] A. Zanella and M. Zorzi, “Theoretical analysis of the capture probability in wireless systems with multiple packet receptioncapabilities,”
IEEE Trans. Commun. , vol. 60, no. 4, pp. 1058–1071, Apr. 2012.[34] E. Dahlman, S. Parkvall, and J. Sk¨old,
5G NR: The Next generation wireless Access technology . London: AcademicPress, 2018.[35]
Physical layer procedures for control , document TS 38.213 V16.2.0, 3GPP, Sophia, Antipolis, France, 2020.[36]