Wanwei Tang＊, Shaoli Kang, Bin Ren, Xinwei Yue

1 School of Electronic and Information Engineering, Beihang University, Beijing 100191, China

2 Intelligence and Information Engineering College, Tangshan University, Tangshan 063000, China

3 State Key Laboratory of Wireless Mobile Communications, China Academy of Telecommunications Technology, Beijing 100191, China

I. INTRODUCTION

With the explosive growth of data traffic and advent of a variety of smart terminals communications, massive machine type communication (mMTC) becomes one of important application scenarios for the fifth generation mobile communication (5G) [1-3]. In order to reduce the high signaling overhead for the transmission of small packet in mMTC, grantfree (GF) transmission has drawn considerable attention in new radio (NR). The agreement that NR should target to support uplink (UL)GF for mMTC has been passed in the third generation partnership project (3GPP) radio access network 1 (RAN1) #85 and RAN1#86 meeting. Authors in [4] proposed a GF transmission scheme by combining MA with physical layer optimization. A compressed sensing based ACK feedback scheme for GF transmission was proposed in [5]. GF can be implied in orthogonal frequency division multiple access(OFDMA) or non-orthogonal multiple access(NMA) [6, 7]. However, GF-OFDMA cannot efficiently support massive connectivity, especially for the UL transmission, since it is limited by orthogonal resource allocation. In order to support the extremely high connection density, GF-NMA has been investigated in some literatures. Authors in [8] proposed an UL GF sparse code multiple access (GF-SCMA)scheme, which allows different mMTC UEs contending for some pre-con figured resources.In [9], a dynamic compressive sensing-based multi-user detection is proposed to realize both user activity and data detection for UL GFNMA. As a potential implementation scheme for GF-NMA, GF pattern division multiple access (GF-PDMA) is warmly discussed in the standard. For the GF-NMA based on symbol level spreading, such as GF-SCMA or GF-PDMA, they provides another dimension for resource sharing symbols (or patterns). A traditional resource pool (time & frequency)could be extended to include patterns. Specifically, each resource group in the pool is associated with a pattern matrix. AUE selects a time-frequency resource as well as a pattern from the pattern matrix for transmission. Obviously，enlarging the resource pool could reduce collision probability. Compared with GF-SCMA, GF-PDMA use the patterns with different diversity which means that it can provide greater resource pool than SCMA. For example a typical matrix with dimension 4× 6while for GF-PDMA, the pattern matrix can be a subset comprised of any 6 columns from the matrix Some initial system level simulation results of GF-PDMA are presented in [10, 11].

In this paper, a UL GF scheme based on PDMA (GF-PDMA)has been proposed.Resource definition and allocation for UL GF-PDMA scheme are investigated.

Although some primary researches on GF-PDMA have been done in the aforementioned literatures, there are still some issues need to be investigated, such as details and designs of the resource definition, allocation,and selection as well as the potential collision management [12]. Motivated by this, we take a typical NMA scheme, PDMA [13, 14],as a subject investigated and propose an UL GF-PDMA scheme in this paper. The primary contributions of this paper are summarized as follows:

1) We first analyze the transmission latency of grant based PDMA (GB-PDMA) and GF-PDMA. The analysis results show that GF scheme can reduce at least 1.07 ms compared with GB scheme under the assumption that a scheduling request (SR) period is 1 transmission time interval (TTI) and 1 TTI is equal to 2 orthogonal frequency division multiplexing(OFDM) symbols.

2) We propose the more detailed definition of GF-PDMA resource and analyze the scalability to confront pattern collision for GF-PDMA. The link-level simulation (LLS)results are presented to demonstrate that lower pattern collision frequency (e.g., less than 3 times) has few influences on the system performance.

3) We discuss the transmission scheme for GF-PDMA in detail. The system-level simulation (SLS) is conducted and the simulation results demonstrate that GF-PDMA carries higher system overload (nearly 2.15 times than GF-OFDMA).

The remainder of this paper is organized as follows: Section II provides the system model for UL GF-PDMA. Latency properties of GB-PDMA and GF-PDMA are analyzed in Section III. Resource definition, allocation and transmission mechanism for UL GF-PDMA are introduced in Section IV. Numerical results of LLS and SLS are presented in Section V.Finally, Section VI concludes this paper.

II. SYSTEM MODEL

PDMA is proposed based on former research about successive interference cancellation amenable multiple access (SAMA) [15, 16].An UL PDMA system model is depicted as ifgure1.

At the transmitter, the data ofKusers will experience a series of operations such as channel encoding, PDMA modulation & encoding and OFDM modulation. Then the data of users will be mapped on the resources defined on power, time & frequency or spatial domain with PDMA pattern matrix. The design methods of PDMA pattern matrix are described in[17]. For GF-PDMA, users pick pattern randomly from the given PDMA pattern matrix.

At the receiver, the received information from users to the base station (BS) can be expressed as

whereyis aN×1 vector composed by received signals,is aK×1 modulation symbol vector transmitted byKusers; andxkis the modulation symbol of thekthuser,nindicates the additive noise at BS and molded bydenotes PDMA equivalent channel response matrix with dimensionoverload rate, which means thatNresource elements (REs) are occupied byKusers.

For reducing computational burden and accelerating simulation, we take a typical PDMA pattern matrixas an example. Then the PDMA equivalent channel response matrix is given by

wherehijis the channel response between theithuser and thejthRE.

Figure 2 shows the pattern matrix and related resource mapping. Where, the diversities of pattern 1, pattern 2 and pattern 3 are 2, 1 and 1, respectively. GF-PDMA makes the users do not need to wait the signaling from BS and transmit the data based on a mode of arriveand-go. So the users pick the PDMA pattern from the pattern matrix randomly. Without lose of generality, we assume that user 1 picks pattern 1, and the data from user 1 are mapped onto both two REs, user 2 pick pattern 2 and the data from user 2 are mapped onto RE 1 and user 3 pick pattern 3 and the data from user 3 are mapped onto RE 2.

Fig. 1. UL PDMA system model.

Fig. 2. Three users multiplexing on two REs.

Fig. 3. The factor graph of BP-IDD receiver based on PDMA pattern matrix

The multi-user detection algorithm based on belief propagation algorithm and iterative detection- decoding (BP-IDD) at the receiver can be simply explained as figure 3 [18]. infigure 3, thekthuser’s codes,decoded by Turbo decoder are converted into users’ data symbols, then these symbols are involved in the BP iteration operation between user nodeand channel nodealso means the received signal on thejthRE).

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Table I. Computation complexity of receiver.

The BP-IDD detection algorithm is shown in Algorithm 1. Wheredenote the transmission information from user node to channel node and from channel node to user node respectivelythe priori log likelihood ratio (LLR) ofck,mgiven by the Turbo decoder in the previous iteration;whereMdenotes the size of modulation constellation;Tin,Toutanddfrepresent IDD inner iteration number,outer iteration number, and maximum row weight of PDMA pattern matrix;N(k)jis the set comprising of all elements ofN(k)jexcludingj.

Table I shows computation complexity of the BP -IDD receiver and BP receiver. It should also be noted that the computation of Turbo decoder is not accounted.

From table 1, we can see that the BP-IDD isTouttimes more complexity than BP on addition operation. However, BP-IDD can further improve the performance of BP, since that the reliability of the symbols is further improved after Turbo decoding.

III. ANALYSIS ON TRANSMISSION LATENCY FOR GB-PDMA AND GFPDMA

In the GB-PDMA scheme, a user sends a scheduling request (SR) to the serving BS periodically, however, the style of packet arriving is aperiodic and massive in mMTC scenario. Higher signaling overhead exists in GB-PDMA scheme, which significantly reduces the system capacity. GF-PDMA transmission allows the users to transmit their packets at any time. In GF-PDMA, transmission from users does not need the explicit scheduling grant from BS and multiple users can share the same time and frequency resources.

Figure 4 describes the main difference between GB-PDMA and GF-PDMA scheme.For UL GB-PDMA transmission, before transmitting the data packet, a user sends a SR and receives a scheduling grant. Sending SR needs to wait for a SR-valid resource and a corresponding scheduling grant transmitted to the user in response. After the grant is decoded successfully, the data transmission starts.At the receiver, the BS decodes and detects whether the data is correct or not. If not, BS generates and sends negative acknowledge-ment (NACK) to the user. After the NACK is decoded successfully, the data retransmission starts. So the total delay for one GB-PDMA transmission concludes 7 parts shown infigure 4 (a), i.e., average waiting time for physical UL control channel (PUCCH), a user send SR on PUCCH, BS decodes SR and generates the scheduling grant, transmission of scheduling grant, user processing delay, transmission of UL data and data decoding in BS. The latency expression can be given by

For GF-PDMA scheme, the total delay for one transmission only concludes 3 parts shown in figure 4 (b), i.e., average waiting time for UL access, transmission of UL data and buffer status report on PUSCH and data decoding in BS. The corresponding latency expression can be given by

If SR period is 1 transmission time interval(TTI) and 1 TTI is equal to 2 OFDM symbols.(3) and (4) can be further expressed as

From (5) and (6), we can see that the GF-PDMA can reduce about 1.07 ms latency compared with GB-PDMA.

IV. TRANSMISSION SCHEME DESIGN FOR UL GF-PDMA

4.1 Resource definition and allocation for GF-PDMA

For the UL PDMA with GF access, several users may share the same pattern on the same REs, and due to the random access nature,those users may transmit at the same time. BPIDD receiver described in Section II is used to detect the data streams and distinguish multiple users with their channel state as long as these users use different pilot sequences or different demodulation reference signal (DMRS).Pattern reuse can help to increase the effective system overload and the number of connection to realize the massive connectivity.

Fig. 4. Comparison of latency between GB-PDMA and GF-PDMA transmission.

Fig. 5. Definition of a GF transmission unit.

In order to support UL GF-PDMA, radio resources are defined for the proposed multiple access scheme. As shown in figure 5, a basic resource unit （BTU） is comprised of time & frequency, PDMA pattern and pilot sequence. There are 3 unique patterns defined over 2 time & frequency resources and 4 pilot sequences associated with each pattern.The allocation of pilot resources and PDMA pattern matrix resources are introduced as follows：those BTUs with serial number (0,1, 2), (3, 4, 5), (6, 7, 8) or (9, 10, 11) have the identical pilot resource yet different PDMA patterns whereas the BTUs with serial number (0, 3, 6, 9) have different pilot sequences yet identical PDMA patterng1=[1 1]T, the BTUs with serial number (1, 4, 7, 10) have different pilot sequences yet identical PDMA patterng2=[1 0]Tand so forth.

In order to evaluate the performance of confronting collision，we add the PDMA patterns collision times continuously. Takingas an example, we investigate the average performance of 3, 4, 5 or 6 users under the assumption of 0, 1, 2 and 3 times collisions.

If multiple users pick pattern 1 simultaneously, (1) can be expressed as:

4.2 Transmission mechanism based on GF-PDMA

In the mMTC scenario, most of the communications are sporadic [19], i.e., few of them being active at a relatively long time duration.The transmitted packets are usually with low data rate and small sizes. At the user side, a user can randomly choose a pattern from a predefined matrix, when multiple users choose the same pattern, they will be allocated different pilot sequences to distinguish between each other (as shown in figure 5). At the BS side, the dynamic UL grant is no longer necessary for GF-PDMA since UL grants occupy downlink (DL) control channel resources,elimination of grant signaling for traffic with UL GF-PDMA means that DL signaling overhead can be reduced.

The proposed GF-PDMA features a six-step transmission procedure, which is described as follows:

Step 1:The BS and the users predefine the key GF parameters such as system bandwidth,time & frequency partition ration, data transmission format, BTU and the mapping rule between BTU and users.

Step 2:The users send random access request and access BS using the current LTE access scheme.

Step 3:The BS builds a one to one mapping relationship according to the mapping parameters (e.g., path loss, position, UL receiving power and UL signal noise ratio(SNR)), then inform the relationship to users and acquire all the candidates carried on every PDMA BTU.

The mapping rules from users to BS are described as follows:

Rule 1: When the users access the base station, the BS allocates the corresponding PDMA BTU to the users. When the users send data, they can use the allocated resource.

According to the number of the users in the deployment scenario and the ability of the BS processor, the BS selects suitable PDMA pattern matrix, and allocates the patterns with high and low diversity to the users far and near from the BS respectively. Each user will pick a pattern randomly from the pattern matrix. Specifically, PDMA patterns are divided into different groups according to the different diversity, and the patterns with the same diversity are divided into the same groups. Then the data in different groups, established time &frequency and pilot resources are mapped onto the PDMA BTUs. Thereinto，the main consideration for grouping with diversity is that the distribution and the UL channel conditions of the users are different, therefore, those users with similar channel conditions are allocated into the groups with same diversity.

Rule 2:When the users access the BS, the BS does not allocate explicit resources to the users. According to the specific characteristics of the user (such as physical ID), the users are mapped onto the corresponding PDMA BTU according to certain rules (e.g., conduct modular operation between the user physical ID and the number of PDMA BTU).

Rule 3:Using ergodic searching method,count the number of users on each BTU, and the BTUs with the least number of users have the priority to carry the coming data.

Step 4:The users acquire the mapping relationship that the BS sends and transmit data and pilot on the allocated PDMA BTU at the same time when there are data need to send.

Step 5:The BS monitors all the signals of the candidates on every PDMA BTU and determines the users whether to send data or not. Then the BS will conduct pilot channel estimation and data detection for those users sending data.

Step 6:The BS determines whether there are multi-user pilot collisions (pilot collision is defined as more than two users select the same pilot on the same PDMA BTU), i.e., whether the time interval receiving the data from a user is longer the certain fixed threshold value, if yes, the pilot collision exists otherwise non-exist. When the pilot collision happens,there are two methods to address the problem.

Method 1:the BS conducts one schedule transmission for the user on the reserved granted time & frequency resource and informs the user map on a new PDMA BTU by downlink signaling.

Method 2:the BS informs the users that there are multiple pilot collisions, then the users generate a random back off time and each user sends its data after the corresponding back off time.

V. NUMERICAL RESULTS

In this section, we present some results and analysis of LLS and SLS. For LLS, we evaluate the scalability of GF-PDMA by increasing the pattern collision, and for SLS, we evaluate the system packet dropping rate (PDR) by varying the system traf fi c loading (packet arrival rate(PAR)) to verify the GF-PDMA’s capability to support massive connections for mMTC.

5.1 LLS simulation results

The assumptions for LLS simulation are shown as table 2.

As listed in table 2, the patterns of PDMA are designed as Section II. The dimension of PDMA pattern is 2 with 0 or 1 non-zero elements in each pattern. There are up to 6 users in a group with pattern matrix. PDMA layers are detected with the BP-IDD detector and 6 physical resource blocks (PRB) are used in the simulation. For the OFDMA, the minimum mean square error (MMSE) algorithm[20] is used for detection.

Table II. UL GF-PDMA link-level simulation assumptions.

Fig. 6. LLS simulation results for multiple users pick pattern 2.

The LLS results in terms of block error rate(BLER) performance are shown in figure 6 and figure 7.

infigure 6, we evaluate the average performances of multiple users picking pattern 2.The results show that performance loss is very small when collision is less than three times.However, three times collision brings nearly 0.8 dB performance degradation @ BLER=0.01 compared with no collision but still is better than OFDMA.

Fig. 7. LLS simulation results for multiple users pick pattern 1.

Table III. UL GF-PDMA system-level simulation assumptions.

infigure 7, we assume that user 1, user 4,user 5 and user 6 pick pattern 1, then we can see that the average performances of users are not been greatly affected when the number of collisions is less than 3. And there is about 0.1 dB performance degradation when 3 times collision happens @ BLER=0.01) compared with no collision. And the average BLER performance of PDMA still outperforms that of OFDM even there are 3 times collision happening.

Comparing figure 6 and figure 7, we can observe that multiple users picking pattern 1 is slightly better than they picking pattern 2,since that pattern 1,g1=[1 1]T, has higher diversity than pattern 2,g2=[1 0]T. The LLS simulation results show that with the pattern design and BP-IDD receiver, PDMA is robust to pattern collision, thus enables GF transmission.

5.2 SLS simulation results

The mMTC traffic is small packet with sparse packet arrival, which is assumed that the packet size is equivalent to the transport block size in the simulation. System packet arrival rate should meet the requirement of packet dropping rate ＜= 1%. The packet dropping criteria is given as follows: drop a packet if the packet reaches the maximum number of transmissions N and cannot be decoded correctly where N is maximum number of HARQ transmissions in the simulation, or if its transfer is not completed within a maximum transfer time, e.g.[10ms].

The users in the simulation are assumed to adopt the GF transmission scheme, and collisions happen when they occupy the same RE groups and pattern. For OFDMA, the signal of collided users is treated as interference.For PDMA, the base station tries to detect those collided users by BP-IDD algorithm.For OFDMA, minimum mean square error(MMSE) algorithm is used to detect the data from multiple users. The methodology for the simulation is described in [21] and the detailed simulation parameters for SLS are listed in table 3.

In the simulation, by varying the system traffic loading in the simulations, we evaluate the system PDR. A user packet will be dropped, if, for example in this evaluation,the packet transmissions failed after the retransmissions exceed a certain time limit. We provide preliminary SLS simulation results below. Figure 8 illustrates the performance of GF-PDMA and GF-OFDMA, where it shows the system PDR vs. packet arrival rate.

For OFDMA and PDMA, a 20 bytes packet is transmitted in one TTI. In the simulation,the maximal number of HARQ transmissions is 8 and random back-off is used.

Figure 8 demonstrates the system PDR as a function of packet arrival rate for GF-PDMA and GF-OFDMA. It is observed that GF-PDMA has shown the significant performance enhancement over the GF-OFDMA baseline.It is shown that the GF-OFDMA PDR performance degrades much faster with the traffic load increasing than GF-PDMA. Specifically,@ PDR 1% point of interest in terms of packet arrival rate, GF-PDMA demonstrates nearly 111% gain over the GF-OFDMA baseline(i.e., GF-PDMA is 2.11 times the capability of GF-OFDMA).

In figure 9, GF-PDMA demonstrates a large advantage over GF-OFDMA in terms of supported number of users to achieve the same system PDR. The GF-PDMA gains over GF-OFDMA are 1.9, 1.96 and 2.11 in terms of number of users the system support for given system PDRs of 0.4%, 0.8% and 1%, respectively. The significant gain of GF-PDMA can be explained by the fact that multiple users can multiplex on same resources and the collisions can also be handled well by BP-IDD algorithm.

The SLS results infigure8 and figure9 also show that GF-PDMA is able to achieve significant gains over GF-OFDMA under different packet arrival rate (or traffic loading) scenarios.

Fig. 8. System level simulation results of GF-PDMA compared with GF-OFDMA.

Fig. 9. Capacity supported based on different PDR.

VI. CONCLUSIONS

In this paper, an UL GF scheme based on PDMA (GF-PDMA) has been proposed.Resource definition and allocation for UL GF-PDMA scheme are investigated. Transmission scheme is described and system performances are presented. LLS simulation results reveal that the collision of PDMA pattern has very limited impact on the reliability (BLER)performance with a given collision times (less than 3 times). SLS simulation results show that GF-PDMA outperforms GF-OFDMA in terms of PDR and system capacity. All the results demonstrate that the proposed scheme,GF-PDMA, can efficiently support massive connections for mMTC.

ACKNOWLEDGEMENT

This work was supported by National High Technology Research and Development Program of China (863 Program, No.2015AA01A709).

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