An Enhanced Random Access with PreambleAssisted ShortPacket Transmissions for Cellular IoT Communications
(Extended Version)
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Abstract
We propose an enhanced random access (RA) with preambleassisted shortpacket transmissions to support cellular Internetofthings (IoT) communications. A key feature of the proposed scheme is that the base station (e.g., eNodeB in LTE networks) utilizes the RA preambles as uplink reference signals to estimate uplink channel state information of IoT devices, which subsequently provides additional opportunities to transmit shortpackets during the RA procedure without extra signaling (e.g., connection and scheduling requests). Through simulations, we evaluate the performance of the proposed scheme in terms of a channel estimation mean squared error, a bit error rate, a preamble collision probability, and a success probability of shortpacket transmissions. The results show that the proposed scheme can support reliable and lowlatency featured shortpacket transmissions during the RA procedure by efficiently incorporating both multiple antenna and detection techniques.
I Introduction
With emerging information technologies, the idea of Internetofthings (IoT) has proliferated to support our convenient life [1]. In a wide range of IoT applications such as smart metering and ehealth, most IoT devices are expected to generate smallsized packets rather than longsized ones, which is a major difference from the design goal of the cellular networks (e.g., LTE/LTEA). Accordingly, there have been a number of studies to tailor the commercial cellular networks to support the traffic generated by the IoT devices [2].
A connectionoriented scheduling mechanism in cellular systems makes a challenge in supporting shortpacket transmissions. For every data transmission, each device should request uplink resources after establishing a connection through a random access (RA) procedure. Thus, the signaling overhead (i.e., a ratio of the number of bits to the amount of signalings) significantly increases as the packet size decreases [3].
A number of studies have investigated to efficiently support shortpacket transmissions in cellular networks [4, 5, 6, 7]. Grantfree protocols have been studied in recent [4] where each IoT device transmits shortpackets through the prereserved radio resources instead of ondemand connection and scheduling requests. This approach may effectively reduce the signaling overhead during the shortpacket transmissions. However, it requires significant modifications in the current cellular networks. To overcome this limitation, data transmission during the RA procedure was investigated. Wiriaatmadja and Choi [5] and Jang et al. [6] proposed a hybrid RA scheme and a messageembedded RA scheme, respectively. However, the performance of the previous work is still limited due to the collision problem during the contentionbased RA procedure.
Recently, Kim et al. [7] proposed a novel RA preamble detector which utilizes multiple ZadoffChu (ZC) sequences. This showed the feasibility of an almost collisionfree environment by increasing the number of RA preambles without any performance degradation in the RA procedure.
In this letter, we propose an enhanced RA scheme to support shortpacket transmissions. The proposed scheme additionally utilizes RA preambles to estimate the uplink channel state information of IoT devices, and enables the IoT devices to transmit shortpackets along with the RA procedure without any extra signalings. Simulation results show that only a few more root sequences are sufficient to newly provide an additional functionality of reliable and lowlatency featured shortpacket transmissions during the RA procedure.
Ii System Model
We consider a single LTE/LTEA cell network, where the eNodeB is equipped with antennas. Each IoT device with a single antenna attempts its RA at the next available RA slot, periodically configured in time domain, when a new packet is ready for transmissions. Here, we consider a single RA slot, where devices simultaneously attempt RAs.
Iii An Enhanced Random Access for PreambleAssisted ShortPacket Transmissions
ZC sequence has been used to generate not only RA preamble but also demodulation reference signal (DMRS) in LTE [10]. Thus, the RA preamble might be feasible to replace the role of the uplink reference signal. However, RA preambles cannot be directly used to estimate the uplink channel state information (CSI) due to preamble collisions during the RA procedure, which consequently results in wrong channel estimations. If this functionality is available with the RA procedure, preambleassisted shortpacket transmissions are feasible and able to effectively reduce signaling overhead during the transmissions. In this section, we propose an enhanced RA procedure to support shortpacket transmissions, and its main features are summarized as follows:

The proposed scheme utilizes multiple root sequences to sufficiently increase the number of available RA preambles, which effectively mitigates preamble collisions.

The proposed scheme enables the eNodeB to estimate the uplink CSI of IoT devices using the RA preambles and decode shortpackets using the estimated CSI.
Iiia Procedure
In detail, the proposed scheme consists of four steps as follows:

Preamble and shortpacket transmissions: Each device generates an RA preamble based on randomly selected root and preamble indices, , and , respectively. The generated RA preamble is expressed as for , where , , and denote the ZC sequence with a root index of , the size of cyclic shift, and the length of the ZC sequence, respectively [10]. After preamble transmissions through the PRACH, each device transmits a shortpacket through the PUSCHSPT. Note that any mapping rule between the selected preamble and the location of resources within the PUSCHSPT is not required since each device utilizes the entire resources within the PUSCHSPT.

Channel estimation through RA preambles: The eNodeB estimates the uplink CSI through the received RA preambles. This step should be performed for each of received signals from the entire antennas, i.e., for all , but we describe it from the perspective of to clearly explain the key feature. Let denote the timedomain received signal through the PRACH at the antenna ,
(1) where denotes the signal strength, denotes the channel coefficient from the IoT device to the antenna of the eNodeB, denotes the transmitted RA preamble from the IoT device , denotes the additive Gaussian noise at the antenna of the eNodeB with zero mean and variance of , and denotes a convolution operation.
Fig. 2 shows the channel estimation procedure. The correlation between ZC sequences with the same root index shows an ideal autocorrelation property (i.e., ) and it is useful to explicitly grasp multipath channels that each of RA preambles experiences. To acquire channel estimates, the eNodeB calculates correlations between and the entire root sequences (i.e., ). The correlation at lag between and is denoted by for in (2) shown at the top of the next page, where and denote a set of IoT devices choosing root index and a conjugate operation, respectively. Accordingly, multiple channels between each IoT device and the eNodeB are captured from the correlation result. Thus, the eNodeB should separate those of channel impulse responses (CIRs) to clearly differentiate the channel estimates [11].
(2) Especially, when the eNodeB configures multiple ZC sequences, the orthogonality among the RA preambles does not hold any more due to the crosscorrelation property between ZC sequences with different root indices (i.e., ). Thus, it is difficult to acquire the correct CSI from the received RA preambles due to the interference among RA preambles generated from different root sequences as shown in (2).
To resolve this problem, the received signal should be processed in advance. We thus employ an enhanced PRACH detector proposed in [7], which effectively separates into multiple signals with different root sequences (i.e., ).
^{6} Consequently, the eNodeB acquires the channel estimates using for all instead of for all . Note that the complexity of the channel estimation procedure depends on that of the PRACH detector [7], which is linearly increased according to the number of used ZC sequences. But the complexity is not high enough to be handled at the eNodeB.Fig. 3 shows an example of channel estimations when three IoT devices are considered. Orthogonal preambles can provide accurate channel estimates but the preamble collision may occur due to the limited number of available RA preambles, which results in completely wrong channel estimates. Nonorthogonal preambles effectively mitigate the collision problem while slightly degrading the accuracy of channel estimation.
Fig. 3: Comparison of channel estimates when 
Data decoding: Using the channel estimates (i.e., ) acquired in step (2), the eNodeB decodes shortpackets received through the PUSCHSPT based on the ZF decoder. When RA preambles are received without any collisions and mis/erroneous detections, the full rank ZF matrix (i.e., the number of independent RA preambles) to successfully decode shortpackets is available. Otherwise, the ZF matrix does not satisfy the full rank condition, which results in decoding failure.

Acknowledgment: The eNodeB transmits the acknowledgment to successfully decoded shortpackets.
Iv Numerical Results
We perform link level simulations using LTE/LTEA related parameters specified in Table I.
Parameters  Values 
Number of antennas at the eNodeB ()  8, 16 
Number of IoT devices ()  1 8 
Number of root sequences ()  1, 5 
SNR ()  5 25 dB 
, ,  839, 13, 64 
We also consider the following metrics to evaluate the proposed scheme.

Mean squared error (MSE): MSE quantifies the accuracy of channel estimation. When the channel estimates differ from the original channel realizations, the data can be wrongly decoded. The MSE given by is calculated as
(3) Note that a closedform derivation of the channel estimate is difficult in general due to the error propagation effects during the signal reconstruction, which also implies that the accuracy of decreases as increases.

Bit error rate (BER): BER quantifies the reliability of the transmissions, denoted by , where and represent the transmitted and received bit, respectively. Since the accuracy of is the most critical factor to affect , also decreases as increases.

Collision probability: Preamble collision occurs when two or more devices select the same root and preamble indices. When the number of RA attempting IoT devices at a certain RA slot is given by , the collision probability denoted by can be expressed as
(4) which decreases as increases.

Success probability: Shortpackets are successfully transmitted when each IoT device does not experience any preamble collisions and transmission errors.
^{7} Thus, a success probability of shortpacket transmissions is defined as(5) Note that mainly depends on when a reliable communication link is guaranteed (i.e., ). Increasing slightly degrades due to the inaccuracy of channel estimations caused by the signal reconstruction errors but it can significantly decrease in (4). Thus, increasing can effectively improve .
Fig. 4 shows the MSE between the channel realizations and estimates for varying the number of multiplexed preambles and SNR when the proposed scheme is applied. The MSE highly depends on the number of multiplexed preambles. When orthogonal preambles are considered, the MSE shows a constant value. On the contrary, when nonorthogonal preambles are considered, the MSE slightly increases due to the error propagation effect during the signal reconstruction. Despite a slight loss in accuracy of channel estimations, the result reveals the feasibility of the proposed scheme to be used in practice. Note that the channel estimation is independently performed for the received signals from each of antennas, and, thus, the number of antennas does not affect the MSE performance.
Fig. 5 shows both a collision probability and the BER for varying the number of IoT devices, , when and the SNR is set to dB. Note that a full rank ZF matrix is unavailable when preamble collisions occur. Thus, we measure bit errors when no preamble collision occurs to exclusively investigate reliability of sending shortpackets. As increases, increases since the number of RA preambles is limited. The accuracy of channel estimations degrades as increases, which consequently increases . Increasing helps to mitigate but degrades due to the noiserise among nonorthogonal RA preambles. Thus, there is a tradeoff relationship between and with respect to .
Fig. 6 shows a success probability for varying when the SNR is set to 23 dB. We verify that highly depends on rather than . Our proposed scheme can utilize multiple root sequences while avoiding a significant degradation in BER. Thus, using a few more root sequences is sufficient to significantly increase , which enables to achieve lowlatency (e.g., ms) at the same time.
V Conclusions
In this letter, we proposed the enhanced RA with preambleassisted shortpacket transmissions in cellular IoT networks. The key feature of the proposed scheme is to acquire uplink CSI of IoT devices using the RA preambles, which can support shortpacket transmissions along with the RA procedure without extra signalings. Simulation results show that mitigating the collision probability is of importance to improve the success probability of shortpacket transmissions. Thus, only a few more root sequences are sufficient to newly provide an additional functionality of reliable and lowlatency featured shortpacket transmissions along with the RA procedure.
Footnotes
 thanks: This is an extended version of the journal paper accepted to be published in IEEE Communications Letter with the same title. This is the authors version of the work. It is posted here for your personal use. Not for redistribution.
 thanks: T. Kim and I. Bang are with the Agency for Defense Development, Daejeon, 34186, Republic of Korea (email: {taehoonkim,ikbang}@add.re.kr).
 thanks: Corresponding author and research done while working at National University of Singapore. This work was supported by the National Research Foundation of Korea (NRF2018R1A6A3A03012996).
 As the number of ZC sequences increases, the number of available preambles increases, which is effective to alleviate preamble collisions. However, the occurrence of erroneous detection increases due to the noiserise among ZC sequences with different root indices.
 Considering a Poisson arrival model, [8], where , , , and denote the number of IoT devices within a cell, a packet arrival rate, a period of RA slot, and a collision probability, respectively. As increases, collision events cause an increasing of the load per RA slot due to backlogging [9] in the upcoming slots. Especially, when , the throughput of PRACH starts to be deteriorated.
 Even though we consider a single cell scenario, the same principle can be applied to the multicell scenario. Preliminary knowledge to the detector is a set of root sequences utilized at the home cell and the neighboring cells. This preprocessing effectively alleviates the interference caused by other root sequences but may still contain signal reconstruction errors.
 We do not take mis and erroneous detections into consideration, since their occurrences can be made negligible by adjusting the detection threshold.
 1 ms (preamble transmission) + 1 ms (shortpacket transmission) + 3 ms (processing time at the eNodeB) + 1 ms (acknowledgement) = 6 ms.
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