King s Research Portal

Transcription

1 Kng s Research Portal DOI: /TWC Document Verson Peer revewed verson Lnk to publcaton record n Kng's Research Portal Ctaton for publshed verson (APA): Shrvanmoghaddam, M., L, Y., Dohler, M., Vucetc, B., & Feng, S. (2015). Probablstc Rateless Multple Access for Machne-to-Machne Communcaton. DOI: /TWC Ctng ths paper Please note that where the full-text provded on Kng's Research Portal s the Author Accepted Manuscrpt or Post-Prnt verson ths may dffer from the fnal Publshed verson. If ctng, t s advsed that you check and use the publsher's defntve verson for pagnaton, volume/ssue, and date of publcaton detals. And where the fnal publshed verson s provded on the Research Portal, f ctng you are agan advsed to check the publsher's webste for any subsequent correctons. General rghts Copyrght and moral rghts for the publcatons made accessble n the Research Portal are retaned by the authors and/or other copyrght owners and t s a condton of accessng publcatons that users recognze and abde by the legal requrements assocated wth these rghts. Users may download and prnt one copy of any publcaton from the Research Portal for the purpose of prvate study or research. You may not further dstrbute the materal or use t for any proft-makng actvty or commercal gan You may freely dstrbute the URL dentfyng the publcaton n the Research Portal Take down polcy If you beleve that ths document breaches copyrght please contact lbrarypure@kcl.ac.uk provdng detals, and we wll remove access to the work mmedately and nvestgate your clam. Download date: 30. Jan. 2019

2 The copyrghts of ths paper are wth the IEEE. Before use, please, consult the IEEE Copyrght Polces. The typeset verson of ths paper s avalable from IEEE Xplore. Enjoy readng!

3 1 Probablstc Rateless Multple Access for Machne-to-Machne Communcaton Mahyar Shrvanmoghaddam, Student Member, IEEE, Yonghu L, Senor Member, IEEE, Mscha Dohler, Fellow, IEEE, and Branka Vucetc, Fellow, IEEE, Abstract Future machne to machne (M2M) communcatons need to support a massve number of devces communcatng wth each other wth lttle or no human nterventon. Random access technques were orgnally proposed to enable M2M multple access, but suffer from severe congestons and access delay n a M2M system wth a large number of devces. In ths paper, we propose a novel multple access scheme for M2M communcatons based on the capacty-approachng analog fountan codes to effcently mnmze the access delay and satsfy the delay requrement for each devce. Ths s acheved by allowng M2M devces to transmt at the same tme on the same channel n an optmal probablstc manner based on ther ndvdual delay requrements. Smulaton results show that the proposed scheme acheves a near optmal rate performance compared to the optmal coordnated approach and at the same tme guarantees the delay requrements of the devces. We further propose a smple random access strategy and analyze the average amount of overhead requred n the proposed random access procedure. Smulaton results show the proposed approach sgnfcantly outperforms the exstng random access approaches n the current long term evoluton advanced (LTE-A) standard n terms of the access delay. Index Terms Analog fountan codes, machne-to-machne, message passng decoder, massve multple access. I. INTRODUCTION MACHINE-to-Machne communcatons have emerged as a promsng technology to enable trllons of multrole devces, namely machne-type communcatons (MTC) devces, to communcate wth each other wth lttle or no human nterventon [1, 2]. It has many potental applcatons, such as ntellgent transportaton systems (ITS), healthcare montorng, retal, bankng, smart grds, home automaton and so on. It s expected that n the next a few years over 2 bllon MTC devces wll become drectly attached to cellular networks to provde M2M communcatons [3]. Thus, there wll be a massve number of MTC devces wth no/low moblty [4] n each cell, whch s sgnfcantly more than the number of users n current cellular networks. Moreover, M2M traffc nvolve a large number of short-lved sessons, attemptng to delver a small amount of data (few hundred bts) to the base staton, whch s qute dfferent from those n human-to-human (H2H) communcatons. Such dfferences motvate researches around the globe to optmze the current cellular networks to effectvely enable M2M communcatons [5, 6]. M. Shrvanmoghaddam, Y. L, and B. Vucetc are wth the Center of Excellence n Telecommuncatons, School of Electrcal and Informaton Engneerng, The Unversty of Sydney, Sydney, NSW 2006, Australa (e-mal: mahyar.shrvanmoghaddam@sydney.edu.au; yonghu.l@sydney.edu.au; branka.vucetc@sydney.edu.au). M. Dohler s wth Kng s College London (e-mal: mscha.dohler@kcl.ac.uk) A. Motvaton and Related Work In most exstng wreless access networks, the frst step n establshng an ar nterface connecton, s to perform random access (RA) n a contenton manner. In fact, short-lved sessons wth small amount of data n M2M communcatons, makes t neffcent to establsh dedcated resources for data transmsson [7]. Such a random access approach wll not work effectvely when the number of nodes s very large, due to frequent transmsson collsons, leadng to network congeston, unexpected delays, packet loss, hgh energy consumpton, and rado resource wastage [7]. Thus, one of crtcal challenges n M2M communcatons s to desgn an effectve medum access scheme to support a large number of devces. In current RA approaches, when two or more devces select the same RA preamble n the frst phase of the contenton phase, a collson wll occur and the respectve devces wll not be scheduled for data transmsson. To reduce the access delay n M2M communcatons, several schemes have been proposed, such as dynamc allocaton [8, 9], slotted access, group-based [1, 10], pull-based, and access class barrng technques [11, 12]. Although these approaches can reduce the access collsons to a certan degree, however, the man dea behnd these schemes s to delay the retransmsson of the access request for a random/fxed amount of tme, thus ncreasng the access probablty wthn a relatvely short tme. Ths s however neffcent n M2M communcatons due to small short burst transmssons of devces whch manly do not requre the whole RB for ther transmsson. Ths means that for M2M communcatons wth a very large number of devces there mght not be enough RBs to be orthogonally allocated to the devces, whch sgnfcantly ncrease the access delay even f the random access requests are delvered correctly. Addtonally, dfferent MTC devces have dverse servce requrements and traffc patterns n M2M communcatons. Generally, we can dvde the traffc types nto four dfferent categores. The frst type s the alarm traffc, whch s completely random and ts probablty s very low; however, t has a very strct delay requrement. The second traffc type can be modeled by a random Posson dstrbuton wth the parameters dependng on the applcaton [13]. The regular traffc, such as smart meterng applcatons, s the thrd traffc type, and the last type s the streamng, lke vdeo survellance applcatons. Current proposals for enablng M2M communcatons, dd not consder the prortes among devces and dfferent qualty of servce (QoS) requrements. These approaches are mostly neffcent for M2M communcatons as they are generally desgned for a fxed payload sze and thus, cannot support M2M applcatons wth dfferent servce requrements.

4 2 Recently, a systematc framework has been developed n [13, 14] to understand the fundamental lmts of M2M communcatons n terms of power effcency and throughput. However, they dd not provde a systematc approach to develop an effcent communcaton protocol to approach these lmts. Here, we consder a realstc model for M2M communcatons, whch supports both regular and random traffcs wth dfferent delay and servce requrements. We develop a practcal transmsson scheme for M2M communcatons based on recently proposed analog fountan codes (AFCs) [15] to enable massve number of devces communcatng wth a common base staton (BS) whle satsfyng QoS requrements of all devces. We further show that the proposed scheme can closely approach the fundamental lmts of M2M communcatons n terms of throughput and can satsfy the delay requrements of all devces at the same tme. The man contrbutons of ths paper are summarzed next. B. Contrbutons 1) Effcent Random Access Proposal: We consder contenton-based random access n the proposed probablstc multple access for M2M communcatons. In the contenton process, each devce transmts an RA preamble to the BS to establsh a communcaton lnk wth the BS. In exstng RA schemes n M2M communcatons, the devces wll be dentfed by the BS n the contenton phase f each devce has chosen an RA preamble whch s not selected by other devces, and a resource block (RB) wll be allocated to the devce for the data transmsson. For a system wth a large number of devces, several devces may choose the same RA preamble and thus the BS cannot recognze the devces n the RA process. Moreover, even f the BS can dentfy all actve devces, the number of RBs s not suffcent to support all of them. To overcome ths problem, we propose a new contenton mechansm. We group the RA preambles nto several subsets accordng to delay requrements of MTC devces. Then, a sub-set of RA preambles s assgned for those devces whch have the same delay requrement. In the contenton perod, each devce selects a specfc RA preamble based on ts delay requrement from the assocated subset of RA preambles. By detectng the RA preamble of the devce, the BS then knows whch subset ths RA preamble belongs to and thus know ts delay requrement. The BS detects the number of devces whch have selected the same RA preamble and broadcast ths nformaton to the devces. The devces whch have selected the same RA preamble then transmt n the same RB, and ther dentfcatons wll be transmtted along wth ther payload data and wll be later recognzed by the BS after the decodng. In ths way, each avalable resource wll be effectvely used by a number of devces and RA collsons s handled n an effcent manner to smultaneously support collded devces. 2) Effcent Maxmum Throughput Transmsson: Our second contrbuton n ths work s to represent the multple access process as a specal knd of analog graph code. Ths enables us to draw on the recently proposed capacty approachng analog fountan codes [15] to desgn the optmal access protocol achevng the sum-rate capacty of multple access channel. Fountan codes have been used to facltate the multple access transmssons over erasure channels [16 19], where collded packets are used n an effectve way to ncrease the overall system throughput; however, they cannot be used for wreless channels whch are affected by fadng and nose. In [20], t has been shown that the capacty of a Gaussan multple access channel can be acheved by usng spatally coupled sparse graph mult-user modulaton wth an teratve nterference cancelaton scheme at the recever. However, ths approach performs decodng and nterference cancelaton separately and ts complexty ncreases sgnfcantly as the number of access users ncreases. Thus, t wll not be feasble for M2M applcatons wth a massve number of users. To overcome ths problem, we proposed a smple capacty-approachng analog fountan code (AFC) n [15] wth lnear complexty n both the encoder and decoder. Thanks to the nterestng lnear property of AFCs, the summaton of AFC coded sgnals of multple smultaneous transmtted users stll form an AFC code [21]. Thus the recever can represent the multple access transmsson by a specal knd of graph codes, and the BS can jontly decode them by usng a standard belef propagaton (BP) decoder. The proposed probablstc multple access AFC scheme enables the devces to transmt n a probablstc manner n a way to form an equvalent AFC code at the BS, and approach the sum-rate capacty of the multple access channel [21]. 3) QoS aware Random Transmsson: Dfferent devces n M2M communcatons have dverse traffc and servce requrements. Exstng random access schemes do not provde QoS guarantees n the random access transmssons. Ths precludes use n many practcal M2M systems, where tmng constrants are crtcal. How to allevate access congeston n massve access transmssons whle provdng delay or QoS guarantees remans a sgnfcant hurdle n M2M access network desgn. In the proposed approach the degree dstrbuton functons of AFCs and access probabltes are optmzed such that the delay requrement for each devce s satsfed. We formulate an optmzaton problem based on the densty evoluton analyss of the AFC codes to fnd the optmum degree and access probablty for each devce to satsfy ther delay requrements. We further show that the proposed approach can smultaneously satsfy the delay requrement for all devces. The rest of the paper s organzed as follows. In Secton II, we present the system model. The proposed probablstc multple access scheme for M2M communcatons s presented n Secton III. Secton IV presents the asymptotc analyss of the belef propagaton decodng of the MA-AFC scheme based on the densty evoluton analyss. In Secton V, an optmzaton problem s formulated to fnd the optmum code parameters. Smulaton results are shown n Secton VI, and fnally Secton VII concludes the paper. II. SYSTEM MODEL In ths secton, we frst ntroduce the network model and channel model n M2M communcatons. Then we dscuss the detals of the packet transmsson and delay model for MTC devces n M2M communcatons.

5 3 TABLE I NOTATION SUMMARY Fg. 1. W RA Data transmsson ττs (1 τ)τs A resource block (RB) n the proposed MA-AFC approach. A. Network Model and Random Access We consder an M2M last mle access system, where N MTC devces are unformly dstrbuted n a sngle cell of radus r 0 and communcate wth a base staton (BS) located at the orgn. In ths paper, we focus on the M2M applcatons where MTC devces are deployed at fxed locatons, such as smart meters, sensors or cameras n buldngs, roads, brdges, etc. [22]. It s assumed that the channel between each devce and BS s a slow tme-varyng block fadng channel, for whch the channel remans constant wthn one transmsson block but vares slowly from one block to the other. We consder a tme dvson duplex (TDD)-based wreless access system, where the channel gan of the uplnk s assumed to be the same as that of the downlnk [23]. Wth ths assumpton, each devce can estmate the uplnk channel gan from the plot sgnal sent perodcally over the downlnk channel by the BS. Usng the plot sgnal, MTC devces also synchronze ther tmng to that of the BS. The BS, however, does not have the knowledge of any channel state nformaton (CSI). Ths assumpton s partcularly relevant n M2M communcatons, where due to a large number of devces, t would be mpractcal for the BS to obtan CSI to every MTC devce [24]. The channel between each devce and the BS s modeled by path loss, large scale shadowng and small scale fadng effects. Thus, the receved power at the BS for the sgnals transmtted from U s gven by: P r, = P t, χ h Gr α, (1) where r s the dstance from U to the BS, P t, s the transmt power, χ s a log-normal random varable modelng shadowng gan wth standard devaton σ db, h s small scale fadng modeled by exponental random varable wth parameter 1, α s the propagaton loss factor, and G s the drecton based antenna gan. The effectve channel gan γ s then defned as γ χ h (r /r 0 ) α. The reference sgnal to nose rato (SNR), γ, s defned as the average receved SNR from a devce transmttng at maxmum power located at the cell edge. We further assume that the devces perform uplnk power control such that the average receved SNR from all devces at the BS are the same [13] and equals to γ 0. Such an assumpton has been consdered for code dvson multple access (CDMA) n [14]. Tme s dvded nto slots of duraton τ s secs and total avalable bandwdth s W Hz. Each tme slot s referred to as a resource block (RB), where a fracton τ, 0 < τ < 1, of the resource block s reserved for the random access procedure as shown n Fg. 1. Smlar to [13], we assume that the number of actve devces n each RB of duraton τ s s random and follows a Posson process wth rate λ. We also consder a contenton- Notaton Descrpton r 0 Cell radus W Total bandwdth n Hz τ s The duraton of a resource block (RB) λ Rate of the number of actve devces n each RB λ Packet arrval rate at the th deve N Total number of devces N s Number of RA preambles N d Number of dfferent delay requrements k Payload sze of each MTC devce b (j) k 1 vector of nformaton symbols of U j G (j) m k generator matrx of AFC code used n U j γ The effectve channel gan of devce U γ The reference SNR p Access probablty of the devces wth delay constrant t d c AFC code degree W s Weght set of AFC Z k 2 k 1 {k 1, k 1 + 1,..., k 2} Z for k 1 k 2 based random access strategy n M2M communcatons, where N s dfferent random access preambles, whch are orthogonal frequency dvson multplexng (OFDM) symbols n the LTE- Advanced standard [7], are selected n a random access attempt. We also assgn an access probablty to each devce accordng to ts delay requrement, where a devce wth delay constrant t wll be assgned wth access probablty p. These access probabltes wll be later optmzed n ths paper to satsfy the delay requrement of all devces. The notaton used n ths paper s summarzed n Table I for quck reference. It s mportant to note that n many M2M applcatons, M2M and human-to-human (H2H) communcaton coexsts. H2H users have hgh prorty to obtan a connecton to transmt ther data to the BS. Most of research work consders that the contenton-free random access s used for H2H users, whch the BS assgns a preamble and an RB to the target H2H user n a tmely manner [25]. Thus, n ths work we only focus on M2M devces, where opportunstcally contend for RBs through a contenton-based random access, and H2H users are assumed to have access to the BS through the allocated RBs. B. Delay Model for MTC devces In M2M communcatons, tmng constrants for MTC devces typcally range from 10 ms to several mnutes due to the nfrequent transmsson features [1]. For nstance, some M2M multmeda applcatons such as vdeo survellance systems wth strct tmng constrants have the delay requrement rangng from 10 ms to 40 ms. Such a dverse QoS requrements n M2M communcatons ntensfy the need for a practcal channel assgnment scheme to satsfy these requrements. Moreover, dfferent MTC devces have dverse traffc patterns;.e., some of them are regular and some have completely random traffcs. In Table II, we dvde dfferent M2M applcatons based on ther delay requrements and traffc patterns, accordng to 3GPP M2M standard n [1]. More specfcally, we dvde the MTC devces nto N d = 10 groups based on ther applcatons, where the maxmum affordable delay n group s denoted by t. It s mportant to note that the MTC devces wth regular traffc has predctable actvtes and can be completely coordnated by the BS. Ths means that the BS wll regularly assgn an RB to the devces wth regular actvtes and they

6 4 TABLE II SEVERAL M2M APPLICATIONS WITH THEIR DELAY CONSTRAINTS. Group Delay Constrant Example of applcaton Traffc Type Message Sze 1 10 ms Emergency Alarm Very Unlkely Very small [26] 2 20 ms Intellgent Regular/Irregular Medum transport system (ITS) 3 40 ms Vdeo streamng Regular (Streamng) Large ms Control messages Regular Very small for devces [26] ms ehealth Regular Medum 6 1 s Montorng the Regular Small Devces [26] 7 10 s ehealth Regular/Irregular Medum s ehealth Regular/Irregular Medum s Smart meters Regular Medum 10 >1000 s Smart meters Regular Medum can transmt ther packets through the assgned RB. Ths can be easly obtaned through several approaches n current LTE and LTE-A standards [22]. However, the devces wth completely random actvtes should contend for the RBs as allocatng predetermned RBs to them s not effcent [1]. Therefore n ths paper, we only consder MTC devces wth random actvtes wth rregular traffc patterns. Ths s the most challengng ssue n M2M communcatons due to the ever ncreasng number of such devces. Each actve MTC devce U, Z N 1, s assumed to have k nformaton symbols to transmt wthn a maxmum delay of t. That s, these k nformaton symbols must be delvered to the BS wthn t seconds after U starts transmttng ths message. We assume that the th devce has the packet arrval rate λ wth the delay constrant t. Ths means that n each tme unt, λ packets are generated at the th devce, where each packet has to be delvered to the BS no later than t seconds after ts generaton. Let us assume that 1/λ > t. Therefore, f a prevous packet has been delvered at the BS no later than t seconds after ts generaton at the th devce, the new packet wll be mmedately sent by the devce and there s no need to buffer t. On the other hand, f 1/λ < t, we set the delay requrement of the devce to 1/λ to avod any further delay due to queung. In other words, f the devce has no memory to buffer the packets (.e. each packet has to be successfully delvered at the BS before the generaton of the next packet), the approprate delay requrement for the devce s mn{1/λ, t }. It s also mportant to note that for devces wth lmted buffer sze, the devce can change the access probablty accordng to the number of packets n ts buffer. Moreover, a packet n M2M communcatons has a small sze (few bytes); therefore, we can assume that all the packets n the buffer of a MTC devce can be transmtted n one RB [25]. In the rest of the paper, we only use the term delay requrement for each MTC devce, and assume that the queung delay has been taken nto consderaton to calculate the approprate delay requrement of each devce. III. THE PROPOSED RATELESS PROBABILISTIC MULTIPLE ACCESS FOR M2M COMMUNICATIONS In ths secton, we develop an effcent multple access scheme for M2M communcatons based on analog fountan codes. For ths am, we frst brefly ntroduce AFC codes. Then, we present the rateless probablstc multple access for M2M communcatons, whch s referred to as multple access analog fountan codng (MA-AFC). A. Analog Fountan Codes Analog fountan codes (AFC) were orgnally proposed n [15, 27] as an effectve adaptve transmsson scheme to approach the capacty of wreless channels. In AFC, the entre message of length k bnary symbols s frst modulated usng bnary phase shft keyng (BPSK) modulaton to obtan k modulated nformaton symbols, b { 1, 1}, where Z k 1. Then accordng to the predefned degree dstrbuton functon, d c randomly selected modulated nformaton symbols are lnearly combned wth real weght coeffcents to generate one coded symbol. For smplcty, we assume that the code degree, d c s fxed and weght coeffcents are chosen from a fnte weght set, W s wth D postve real members, as follows: W s = {w R + Z D 1 }, (2) where R + s the set of postve real numbers. Let us assume that b s a BPSK modulated vector of dmenson k 1, and G s the generator matrx of dmenson m k, then AFC coded symbols, c, are generated as follows: c = Gb, (3) where m s the number of coded symbols, only d c elements of each row of matrx G are nonzero, and each nonzero element of G s randomly chosen from the weght set W s. To further enhance the performance, n [15] we proposed to use a hgh-rate precoder to encode the orgnal data before applyng the AFC code. We also use a standard belef propagaton (BP) decoder to decode AFC codes. Further detals of AFC encodng and decodng can be found n [15, 21]. B. Multple Access AFC for M2M communcatons The proposed probablstc multple access AFC (MA-AFC) scheme contans two steps. In the frst step, namely contenton phase, the random access requests are sent by the devces to the BS and a connecton s establshed between the devces and the BS. In the second phase, namely data transmsson phase, the actual payload data along wth the devce ID s transmtted by the devces to the BS. 1) The contenton phase: To apply AFC codes to M2M communcaton systems and satsfy delay requrements of all devces, we need to slghtly modfy the random access procedure n LTE-A [7]. The BS frst parttons N s RA preambles nto N d N s subsets, S 1, S 2,..., S Nd and broadcasts ths nformaton to all devces. Then, the sub-set of preambles S wll be assgned for those devces whose delay requrement fallng n the th delay group. In the contenton perod, each devce selects a specfc RA preamble based on ts delay requrement from the assocated subset of RA preambles. By detectng the RA preamble of the devce, the BS can then know whch subset ths RA preamble belongs to and thus know ts delay requrement.

7 5 Fg. 2. Preamble selecton based on the delay requrement Calculatng the length of the random seed 1. RA preamble transmsson 2. RAR (number of devces whch have selected any RA preamble) 3. Random seed selecton and transmsson Devce Estmatng the number of devces whch have selected any partcular RA preamble BS Detectng random seeds The proposed random access procedure for M2M communcatons. In the frst step, an MTC devce wth delay constrant t randomly selects a RA preamble from set S and transmts t to the BS. Let r S denote the selected RA preamble for the MTC devce of delay constrant t. Then, t s possble that more than one devces select r. We assume that the devces perform power control, such that the receved sgnals from dfferent devces wll have the same receved power, γ 0, at the BS. Thus, the receved power at the BS for the RA preamble r wll be proportonal to the number of devces whch have selected RA preamble r. Let n r denote the number of MTC devces whch have selected the same RA preamble r. The receved sgnal at the BS can the be shown as follows: y = n r γ0 r + z, (4) where z s the addtve whte Gaussan nose (AWGN) vector. The average receved sgnal power at the BS can then be calculated as n 2 rγ 0. Snce we assume that the BS knows γ 0, then t can easly estmate n r. In the second step, the BS transmts a message whch contans nformaton about the number of devces selected each random access preamble. In the thrd step of the contenton phase, each devce frst calculates the length of a random seed based on the receved nformaton from the BS, and then generates a random seed wth the determned length and sends t to the BS. We assume that the random seeds are orthogonal sequences. Once the BS and each devce has shared the same seed for the random encodng structure of AFC, they can construct the same bpartte graph to perform the AFC encodng and decodng. Fg. 2 shows the proposed random access procedure for M2M communcatons. It s mportant to note that n the second step of the proposed RA approach, the BS wll calculate the optmzed access probabltes based on the number of devces n each delay group. More specfcally, BS wll assgn the access probablty p for devces wth the delay constrant t and send ths probablty nformaton to the devces. Later n secton V, we show how the BS can optmze the access probabltes to guarantee that the delay requrements of all devces are satsfed. Let L c denote the length of the random seed that each devce sends to the BS n the contenton phase. The BS fals to detect ths random seed wth the probablty at most ɛ, gven by [13]: ( ) nr 1 1 ɛ = 1. (5) 2 Lc 1 Ths s followed from the fact that each random seed can be detected at the BS f t has been generated by only one devce. Thus, the mnmum length of the random seed L c requred to have a non-detectable probablty lower than a predefned value ɛ > 0 s as follows: L c = log (1 ɛ) nr 1, (6) where. s the cel operator. In the proposed RA scheme, even when two or more devces select the same preamble, they wll be allocated wth the same RB, thus they are transmttng n the same RB. Ths means that the proposed approach can support so many users wth a neglgble collson probablty, whch can be controlled by the random seed length. Unlke the conventonal RA schemes, the devces n our approach can send ther random access requests whenever they have data to transmt and do not need to wat for several RA attempt to get access to the network. In fact, once the devce sends a random access preamble to the BS, t wll be allocated wth a RB, no matter whether that preamble has been selected by other devces or not. Ths wll sgnfcantly decrease the access delay. 2) The data transmsson phase: In the data transmsson phase, each actve devce U j transmts ts AFC coded symbols to the BS accordng to ts access probablty, p j, whch s also known by the BS. Ths means that n each tme nstant l, devce U j generates a bnary random number, I j,l, whch s one wth probablty p j. If ths random number s one, then U j generates an AFC coded symbol, u j,l and sends t to the BS. The BS also generates the same bnary random number as the one n U j as they have shared the same random seed, thus t already knows n whch tme nstants devce U j s sendng a coded symbol. Usng ths random seed, both U j and the BS can construct the same AFC code structure, so the BS s able to perform the decodng on the receved coded symbols. For smplcty, we assume that devces use the same code degree d c and the same weght set W s to generate AFC coded symbols. Let S denote the set of devces whch are currently actve and transmttng AFC coded symbols to the BS based on ther access probabltes. Then, the receved sgnal at the BS n tme nstant l s gven by y l = I j,l γ j u j,l + z l, (7) j S where z l s the addtve whte Gaussan nose wth varance σ 2 z, I,l s an ndcator functon whch s 1 when the devce U j transmts a coded symbol at tme nstant l; otherwse t s zero, and u j,l s the AFC coded symbol from U j at tme nstant l. It s clear that p(i j,l = 1) = 1 p(i j,l = 0) = p j. As can be seen n (7), the receved sgnal at the BS s the nosy verson of the sum of coded symbols of devces n S. Snce coded symbols of each devce have been generated by a lnear combnaton of modulated nformaton symbols, the receved sgnal at the BS can also be seen as a coded symbol of an

8 6 U1's symbols U2's symbols U1's symbols U2's symbols w11 w12 g11 g12 h1w12 h1w24 h2g11 w23 w24... g23 g24... h1w11 h1w23 h2g12 h2g23 h2g24 h1... h1 h2 h2... nose nose nose nose nose nose Fg. 4. Equvalent AFC code graph at the BS. Fg. 3. Orgnal AFC code graph at the BS. analog fountan code, where modulated nformaton symbols are from devces n S. By usng (3), (7) can be rewrtten as follows: y l = k γ j I j,l g (j) l,r b(j) r + z l, (8) j S r=1 where b (j) r s the r th modulated nformaton symbol of U j and g (j) l,r s the weght coeffcent. Fg. 3 and Fg. 4 show the orgnal and equvalent bpartte graphs of the AFC codes at the BS, respectvely, when there are only two devces n S and d c = 2. As shown n these fgures, the equvalent bpartte graph can be consdered as a bpartte graph of an equvalent AFC code where the nformaton symbols are from both users. More specfcally n the frst tme nstant where I 1,1 = I 2,1 = 1, both devces transmt coded symbols to the BS. But, n the second and thrd tme nstant, only one of the devces transmts a coded symbols to the BS,.e., I 1,2 = I 2,3 = 1 and I 1,3 = I 2,2 = 0. Ths s because of the fact that the devces transmt coded symbols based on ther access probabltes. In fact, a devce U j wth access probablty p j transmt a coded symbols wth probablty p j ; otherwse t remans slent. Let us defne X (l) j,r I j,lg (j) l,r b(j) r. Then for a gven degree d, X (l) j,r s a random varable wth the followng probablty dstrbuton: p(x (l) j,r = s d) = { Thus, the mean and varance of X (l) j,r follows: 1 p jd k f s = 0, p j d 2kD f s W s or s W s. can be calculated as m j = E[X (l) j,r ] = p j d d j (s s) = 0, (9) 2kD s W s σj 2 = E[X (l)2 j,r ] = p j d d j kd s2 = 1 k p jd j σw, 2 (10) s W s where σw 2 = D 1 D =1 w2. Snce n M2M communcatons the number of devces are very large and X j,l s are ndependent random varables, accordng to the central lmt theorem k j S l=1 X j,l wll approxmately follow a Gaussan dstrbuton wth a zero mean and the followng varance: σy 2 = σw 2 p j γj 2 d j. (11) j S In other words, the receved sgnals at the BS are normally dstrbuted around the orgn wth average power σ 2 Y. As the receved coded symbols at the BS can be represented as coded symbols of an equvalent AFC code, then the standard BP decodng algorthm can be appled to jontly decode all actve devces at the BS. IV. ANALYSIS OF THE RATELESS MULTIPLE ACCESS FOR M2M COMMUNICATIONS In ths secton, we analyze the performance of the proposed MA-AFC scheme by usng a densty evoluton based approach. Specfcally, we fnd the bt error probablty (BER) at the BS for each devce as a functon of channel gans, AFC code degrees and access probabltes. These results wll be used as a bass to optmze the proposed rateless multple access for M2M communcatons. As the BS determnes the allocaton of RBs to the devces, we assume a general case, where the number of actve devces allocated to each RB s modeled by a Posson random varable wth parameter λ. We also assume that each actve devce belong to a delay group wth a unform probablty. Ths model enables us to have a far comparson wth the throughput lmt obtaned n [13]. Thus, n the rest of the paper, we only consder one RB and optmze the access probabltes for the proposed scheme to smultaneously satsfy delay requrements for all devces. A. Optmum Coordnated Multple Access Before analyzng the proposed multple access scheme, let us frst nvestgate the optmum coordnated multple access, whch wll be used as a baselne for the proposed probablstc multple access AFC scheme. We assume that the base staton has already dentfed the devces whch are transmttng n the same RB. The BS also knows all the channel nformaton and the devces are transmttng wth the same power. As shown n [13], the maxmum common rate that can be acheved by N devces transmttng n a typcal RB wth ordered effectve channel gans {γ } N 1 and reference SNR γ s gven by: R c = mn j Z N 1 1 j j log γ γ k b/s/hz, (12) k=1 whch s smply obtaned from the MAC capacty regon when the transmsson rate of all the devces are the same. Ths can

9 7 be used as an upper bound on the average system common rate for the random access and later we wll show how the proposed MA-AFC code can approach ths lmt. More specfcally, when the devces perform power control n a way to have the same receved SNR γ 0 at the BS, the common rate s gven by: R c = 1 N log 2 (1 + Nγ 0). (13) Therefore, the average system throughput ncreases wth the number of devces wth a logarthmc slope. The maxmum payload sze L opt whch can be successfully transmtted by each devce n a resource block of duraton τ s and bandwdth W s then gven by: L opt = W τs N log 2 (1 + Nγ 0 ), (14) whch s obtaned wthout consderng the overhead for the contenton phase. In fact, (14) provdes an upper bound on the maxmum payload sze whch can be delvered from each devce at the BS. B. Asymptotc Performance Analyss of Multple Access AFC based on the BP Decodng A commonly used analytcal tool for analyzng a BP decoder s densty evoluton [28], whch calculates the evolutons of the message passng n the teratve decodng process. In ths paper, we focus on the densty evoluton analyss n the asymptotc case, when the number of varable and check nodes go to nfnty. Let us refer to nformaton symbols of devce U as Type-X varable nodes n the bpartte graph of MA-AFC codes, for Z N 1. Each receved coded symbol at the BS may connect to modulated nformaton symbols of varous sets of devces. A smple way to represent coded symbols at the BS s to dvde them nto dfferent types accordng to ther connectons to dfferent sets of devces. For smplcty, we represent each non-empty set of devces by a vector V of dmenson N, where ts th entry, v, s 1 f U belongs to the set; otherwse, t s zero. Here, we refer to coded symbols whch are connected to the modulated nformaton symbols of set V as Type-V check nodes. It s easy to show that the probablty that a coded symbol s of Type-V, q V, s as follows: q V = N =1 p v (1 p ) 1 v, (15) and there are n total 2 N 1 varous types of check nodes due to the fact that the total number of nonempty subsets of devces s 2 N 1. Snce there are 2 N 1 types of varable and check nodes, we need to analyze the message between each specfc types of varable and check nodes. In [29, 30], an AND-OR tree analytcal method was proposed to analyze the decodng error probablty of LT codes [31] wth dfferent types of varable and check nodes for erasure channels. However, the AND-OR tree approach cannot be appled drectly to wreless channels. Here, we extend the conventonal densty evoluton analyss to the case that there are multple types of varable and check nodes. Lemma 1: Let us consder a M2M system consstng of N MTC devces wantng to smultaneously transmt ther messages to a common BS. Each devce U s assgned wth an access probablty p and code degree d. Let L (t) X V denote the message passed from a Type-X varable node to a Type-V check node n the th teraton of the BP decodng algorthm at the BS. Then L (t) X V can be approxmated by a normal dstrbuton wth mean m (t) and varance 2m (t), where m (t) can be calculated as follows: m (t) = h 2 σwd 2 2 v 1 + σv 2 q V, (16) where d v = md /k, σ 2 V = N =1 V v =1 ( h 2 d v σws 2 m (t) ), (17) and S(x) = 1 + 2π (1 tanh(x y x)) e y 2 2 dy. The proof of ths lemma s provded n Appendx A. The BER for the th devce after t teratons of the BP decoder, denoted by P (t) e,, can then be calculated as follows: ( ) P (t) e, = Q m (t), (18) where Q(x) = 1 2π x e z2 /2 dz. C. Dscussons on the asymptotc MA-AFC decodng performance at hgh SNR As stated before, n MA-AFC, the BS receves the sum of the coded symbols generated from actve users. The BS thus tres to decode each devce s data from the receved sgnals by performng the BP decodng. Now let us consder the asymptotc performance of MA-AFC as SNR goes to nfnty, thus gnorng the nose. The decodng problem n ths case s equvalent to solvng a system of bnary lnear equatons, where the varables are the nformaton symbols of all actve devces. More specfcally, the BS requres to solve the followng system of bnary lnear equatons to fnd b (j) l for j Z N 1 and l Z k 1, gven the value of y and matrces G (j) : y = N k j=1 l=1 I j h j g (j) l b (j) l. (19) Let us defne matrx G and bnary vector b as follows: G [G (1) G (2)... G (N) ], b [b (1) b (2)... b (N) ]. It s clear that G s the generator matrx of the equvalent AFC code at the BS and we have Y = Gb. (20) Snce we consder that dfferent devces select the weght coeffcents from the same set W s, t s possble that two dfferent devces select the same weght coeffcents for ther transmtted symbols at the same tme. More specfcally, at

10 8 tme nstant, the probablty that coded symbols of devce U l and U m have at least one common weght coeffcent, denoted by p l,m, s gven by ( ) D d l p l,m = 1 d m ( D d m ), (21) where D s the weght set sze and we assume that D d l and D d m. It s clear that when at least two columns of G are exactly the same, then (20) does not have a unque soluton. The followng lemma gves the probablty that at least two column of matrx G are exactly the same. Lemma 2: Let us consder that m coded symbols are receved at the BS and each nformaton symbol of each devce s connected to at least one coded symbol at the destnaton,.e., the set of non-zero elements n each column of G s not empty. Moreover, we assume that dfferent devces have the same access probablty p and code degree d. Let q denote the probablty that two columns of G are exactly the same, then q can be calculated as follows: q = (1+α d v) 2 (m d v+1) Dd v + (d v α) 2 ( ), (22) D dv 1 m d v 1 where α = mpd/k and d v = α. The proof of ths lemma s provded n Appendx B. Lemma 2 shows that q, denotng the probablty that two columns of G are exactly the same, exponentally decreases wth the number of receved coded symbols, m, and weght set sze D. Ths means that even the weght set sze s small, we can always unquely decode all devces nformaton symbols by transmttng more coded symbols. Moreover, when m ncreases, the average degree of nformaton symbols, α also ncreases, whch results n a lower q. Ths means that when D s small, devces are requred to transmt more coded symbols to guarantee that the BS can unquely decode all devces nformaton symbols, whch clearly decrease the overall system throughput. To acheve hgher throughput one may consder larger code degree d, whch on the other sde sgnfcantly ncreases the decodng complexty at the BS that exponentally ncreases wth d. Fg. 5 shows the probablty that at least two columns of G are the same, q, versus the number of coded symbols at the BS for varous szes of the weght set. As can be seen n ths fgure, by ncreasng D the probablty that none of any two columns of G are the same does not changes sgnfcantly. Ths shows that larger weght sets are not requred to acheve hgher throughput n nose-free cases. It s mportant to note that n MA-AFC, each coded symbol transmtted from each devce s multpled by the channel gan, whch s a functon of the dstance between the devce and the BS, as shown n (1). Due to the fact that the nodes are located n dfferent places, the channel gan between each devce and the BS s unque. In other words, MA-AFC s qute smlar to the AFC codes, but the weght set s enlarged. q D=8 D=10 D=15 D= m/k Fg. 5. The probablty that at least two columns of the generator matrx at BS are the same versus the rato of the number of coded symbols and that of nformaton symbols for dfferent weght set szes. Each devce has the access probablty of 0.1 and code degree of 4. Thus, the probablty that at least two weght coeffcents are the same can be neglgble as long as the channel gans are dfferent. Therefore, the bnary lnear equaton assocated wth each receved sgnal at the BS has a unque soluton. Ths guarantees that n the noseless case, n the proposed MA- AFC, each devce U acheves the hghest transmsson rate whch s equal to 2d. Also, when the devces perform the power control, we can assume that ther transmtted power s determned based on a random varable obtaned from the shared random seed wth the BS. Ths way, all the devces are transmttng wth dfferent powers, thus the probablty that two columns of the generator matrx s the same s zero. D. How much overhead s requred n the contenton phase? In the frst phase of the contenton phase, each actve devce sends a RA preamble to the BS. Let L cp,1 denote the length of the RA preamble. In the second phase, the BS sends the nformaton about the number of devces selected a partcular RA preamble. The average number of devces whch have selected the same RA preamble s N/N s, where N s the number of actve devces and N s s the number of RA preambles. These nformaton can be broadcasted by the BS by usng at least L cp,2 = N s log 2 (N/N s) nformaton bts. In the thrd phase of the contenton phase, the users wll select a random seed of length N c whch s calculated by (6), for a gven value of p c. Thus, at most L cp,3 = N sn c nformaton bts have to be sent to the BS n the thrd phase of the contenton perod. Therefore, the total overhead can be calculated as follows: L ov = L cp,1 + L cp,2 + L cp,3 = L cp,1 + N s log 2 (N/N s) + N s log (1 p c) 1 (N/Ns) 1 (23) As we mentoned before, the BS allocates the RB to devces, snce we assume that the devces wthn the same delay group wll transmt at the same RB, each devce then knows at whch RB t should transmt ts message based on ts delay

11 9 requrement. In ths case, the amount of overhead can be further reduced to L ov = L cp,1 + log 2 (N/N s) + log (1 p c) 1 (N/Ns) 1 (24) Let k denote the message length of each devce and R c denote the achevable common rate for a gven arrval rate λ usng the proposed probablstc multple access approach. Then, ths message can be successfully transmtted to the BS wthn a resource block of duraton τ s and frequency bandwdth W f the followng condton s satsfed: k + L ov τ sw R c. (25) In other words, the maxmum message sze (n bts) whch can be supported by the proposed approach n an RB can be approxmated by: k max = max{τ sw R c L ov, 0}. (26) V. OPTIMIZATION OF ACCESS PROBABILITIES WITH DELAY GUARANTEES In ths secton, we formulate an optmzaton problem to smultaneously satsfy the delay requrements of all the devces. The access probablty and code degree for each devce wll be optmzed n a way that delay constrants of all devces are satsfed. Here we try to mnmze the average degree of the receved sgnal at the BS to further reduce the complexty of the decoder. Therefore, the BS should perform the followng optmzaton process: subject to: N mn p d =1 (a). Q( m ( ) ) < δ (b). 1 d D, = 1, 2,..., N, (c). 0 < p 1, = 1, 2,..., N, where δ > 0 s the target bt error rate, m ( ) m (t) = γ2 σ2 wd t k V v = N j=1 γ2 j d jv j σ 2 ws = lm t m(t), and ( m (t 1) j ) q V. It s mportant to note that S(x) s very close to zero for large values of x, so we can approxmate (16) as follows: m (t) 2γ2 σ2 wd t p, (27) k for large x values. Ths means that the devce U m whch has the hghest value of γ 2 md mp m, wll be decoded sooner than other devces at the BS. Let P e, denote the bt error rate of devce U at the BS. Thus, by usng (27) we have: m (t) m (t) γ2 d p γ 2 j j d, (28) jp j P e, P e, h 2 /h 1 = 1 h 2 /h 1 = 0.42 h 2 /h 1 = 0.2 Fg. 6. BER of devce U 2 versus the BER of devce U 1 for the case that both the users have the complete access to the channel and d 1 = d 2. where we assume that σv 2 s constant whch s vald when the number of devces s very large. Therefore, accordng to (18) we have: P (t) e, Q [ ] Q 1 (P (t) 2 γ 2 e,j ) d p γj 2d. (29) jp j More specfcally, when the devces perform power control to have the same receved SNR at the BS and use the same code degree d, then (29) can be further smplfed as follows: P (t) e, Q ( [ Q 1 (P (t) e,j ) ] 2 p p j ), (30) whch clearly shows that the devce whch has a hgher access probablty s decoded sooner than those wth lower access probabltes. Fg. 6 shows the BER for devce U 2 versus the BER of devce U 1 for the case that both users have complete access to the channel,.e., p 1 = p 2 = 1. As can be seen n ths fgure, when the channel gans are the same, the BER performance s the same. Moreover, when the rato of the channel gan of U 1 and that of U 2 decreases, the BER of U 2 also decreases. By usng (30), we can smplfy the optmzaton problem as follows, assumng that all the devces use the same code degree d and perform the power control to have the same receved SNR γ 0 at the BS. subject to: N mn p =1 (a). p k[q 1 (δ)] 2 2γ 2 0 σ2 wdt (b). 0 < p 1, = 1, 2,..., N, Therefore, the optmzed access probabltes can be found as follows: { k[q 1 (δ)] 2 } p,opt = mn, 1. (31) 2dγ 0 t Accordng to (31) we have p,opt 1/t. Thus, f devce U 1 has the access probablty of p 1 = 1, then the access probablty

12 10 Odd frame RA opportunty Even frame Conventonal Backoff RA [25] MA AFC MHz Subframe (1 msec) Frame (10 msec) Blockng probablty W = 0.2 MHz RB τ s = 1 msec Number of MTC devces (N) Fg. 7. Physcal layer confguraton n LTE-A [22]. for U wll be smply p = 1/τ, where τ t /t 1. It s mportant to note that the BS and devces calculate the access probabltes from (31), whch s very smple and does not add much complexty to devces and the BS. Fg. 8. The blockng probablty for MTC devces versus the number of devces. The total number of preambles s N p = 60. All the devce n the MA-AFC case use the same code degree VI. SIMULATION RESULTS In ths secton, we nvestgate the performance of the proposed MA-AFC scheme n M2M communcaton systems. We frst compare our proposed MA-AFC approach wth the conventonal massve RA technque n the LTE-A standard [32]. Lke [22], as shown n Fg. 7 we assume that tme s dvded nto tme frames of length 10 msec and the total system bandwdth s W = 20 MHz. Each frame s further dvded nto 10 subframes of length 1 msec. A subframe conssts of 100 RBs, each wth bandwdth 0.2 MHz. We also assume a total number of N p = 60 preambles and for smplcty we assume several confguratons of RAs, whch ncludes 1 RA attempt per two tme frames, 1 RA access attempt per tme frame, and 2 RA attempts per tme frame. Each successful devce wll then be allocated wth 1000/N p RBs for the data transmsson n next subframes. We assume that the packet length of devces s small (few bytes), thus a devce can successfully transmt ts packet wthn one tme frame. The conventonal random access approach, whch s currently used n the LTE-A standard uses backoff approach [7]. In ths approach, when a random access attempt s unsuccessful, the devce wll wat for a random tme before transmttng the new access request. More specfcally, before the th random access request the devce wll wat for tme t () ra, where t () ra s randomly drawn from range [0, X 1]. The devce can send a maxmum number of N ra RA request usng ths backoff approach. More detals on the specfc values of N ra and X can be found n [22]. For the comparson, we use two metrcs, blockng probablty and average access delay. The blockng probablty s defned as the rato of the MTC devces falng to access the BS due to exceedng ther maxmum allowed random access attempts to the total number of MTC devces. The average access delay s defned as the average tme elapsed from the tme nstant when a devce sends the frst access request untl that t succeeds. Fg. 8 shows the blockng probablty for both the proposed and conventonal approaches. As can be seen n ths fgure, the blockng probablty for the conventonal Average access delay [msec] Conventonal Backoff RA [25], 1 RA per two tme frames Conventonal Backoff RA [25], 1 RA per tme frame Conventonal Backoff RA [25], 2 RA per tme frame MA AFC, Scenaro 1, 1 RA per two tme frames MA AFC, Scenaro 1, 1 RA per tme frame MA AFC, Scenaro 2, 1 RA per two tme frames MA AFC, Scenaro 2, 1 RA per tme frame Number of MTC devces (N) Fg. 9. The average access delay for MTC devces versus the number of devces. The total number of preambles s N p = 60. The access probablty for MTC devces n Scenaro 1 s N p/n and n Scenaro 2 s 10N p/n. All the devce n the MA-AFC case use the same code degree 8. approach s very hgh especally when the number of devces s large. However, devces n the proposed scheme can access to the BS wth a very small blockng probablty, due to the fact that the devces can transmt smultaneously and they do not need to wat untl they select separate preambles. Fg. 9 shows the average access delay versus the number of devces. As can be seen n ths fgure, the proposed approach outperforms the conventonal approach and have roughly 90% less access delay. In Fg. 9, we consdered two scenaros for MA-AFC. The access probablty for all devces n Scenaro 1 and Scenaro 2 s set to 1/n r and 10/n r, respectvely, where n r s the number of actve devces that have selected the same preamble r. It s mportant to note that the proposed approach n Scenaro 2 has a lower access delay due to the fact that more devces can smultaneously transmt but t has hgher complexty at the BS due to larger degrees of equvalent AFC code at the BS. We then smulate our proposed approach wthn one RB, and compare the results wth the fundamental throughput lmts n [13]. For ths am, we assume that the reference SNR s γ = 0 db. Ths s equvalent to the case that a devce transmts wth