THE ever increasing demand of industries to automate

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1 Massve Multple Access Based on Superposton Raptor Codes for M2M Communcatons Mahyar Shrvanmoghaddam, Member, IEEE, Mscha Dehler, Fello, IEEE, Sarah J. Johnson, Member, IEEE arxv:62.567v [cs.it] 8 Feb 26 Abstract Machne-to-machne (M2M) reless systems am to provde ubqutous connectvty beteen machne type communcaton (MTC) devces thout any human nterventon. Gven the exponental groth of MTC traffc, t s of utmost mportance to ensure that future reless standards are capable of handlng ths traffc. In ths paper, e focus on the desgn of a very effcent massve access strategy for hghly dense cellular netorks th M2M communcatons. Several MTC devces are alloed to smultaneously transmt at the same resource block by ncorporatng Raptor codes and superposton modulaton. Ths sgnfcantly reduces the access delay and mproves the achevable system throughput. A smple yet effcent random access strategy s proposed to only detect the selected preambles and the number of devces hch have chosen them. No devce dentfcaton s needed n the random access phase hch sgnfcantly reduces the sgnallng overhead. The proposed scheme s analyzed and the maxmum number of MTC devces that can be supported n a resource block s characterzed as a functon of the message length, number of avalable resources, and the number of preambles. Smulaton results sho that the proposed scheme can effectvely support a massve number of M2M devces for a lmted number of avalable resources, hen the message sze s small. Index Terms Internet of thngs, M2M communcatons, Raptor codes, superposton modulaton. I. INTRODUCTION THE ever ncreasng demand of ndustres to automate ther real-tme montorng and control processes and the popularty of smart applcatons to mprove our everyday lfe ll exponentally ncrease machne-to-machne (M2M) system deployments n the near future []. M2M communcatons am to enable trllons of mult-role devces, namely machnetype communcaton (MTC) devces, to communcate th each other and the underlyng data transport nfrastructure th lttle or no human nteracton [2, 3]. M2M communcatons have potentally dverse applcatons across dfferent ndustres, ncludng healthcare, the smart cty market, logstc, manufacturng, process automaton, energy, and utltes [4]. Ths makes M2M communcatons one of the fastest-grong technologes n the feld of telecommuncatons. Accordng to an updated market forecast from ABI Research, the number of devces ll more than double from the current level, th 4.9 bllon forecasted for 22 [5]. Furthermore, Gartner estmates that the Internet of Thngs (IoT) ll nclude 26 bllon unts nstalled by 22, and by that tme, IoT product and servce The materal n ths paper as submtted n part to IEEE Internatonal Symposum on Informaton Theory (ISIT), 26. M. Shrvanmoghaddam and Sarah. J. Johnson are th School of Electrcal Engneerng and Computer Scence, The Unversty of Necastle, NSW, Australa (e-mal: {mahyar.shrvanmoghaddam; sarah.johnson}@necastle.edu.au). M. Dohler s th Kng s College London, UK (emal: mscha.dohler@kcl.au.uk). supplers ll generate ncremental revenue exceedng $3 bllon n servces [6]. Ths demonstrates the strong motvaton for cellular reless technology provders to partcpate n ths market [7]. On the other hand, the ubqutousness of cellular netorks s a major ncentve for M2M applcaton developers to adopt cellular netorks for ther numerous applcatons [8]. The latest cellular communcaton standard developed by the thrd generaton partnershp project (3GPP) s Long-Term Evoluton (LTE), hch provdes a flexble communcaton archtecture to enable relable communcaton at a loer cost per bt and to accommodate the contnuous groth n reless cellular demand [7]. Hoever, LTE cellular netorks, hch are orgnally desgned and engneered for human-to-human (H2H) communcatons, have been consdered not sutable to handle the unque characterstcs of M2M applcatons [8]. Many M2M applcatons and devce types share a set of key attrbutes that have to be consdered n the desgn of future reless netorks. These nclude, sporadc transmsson of small data bursts (only fe kbs), massve number of devces, and lo poer consumpton to extend battery lfe. Moreover, M2M devces and applcatons have dverse qualty-of-servce (QoS) requrements and traffc patterns [9]. For these reasons, leadng standardzaton bodes, such as 3GPP, have commenced ork on satsfyng these and other constrants hle not sacrfcng current cellular system usage for human-based applcatons []. For example, 3GPP has already specfed the general requrements for MTC applcatons and dentfed ssues and challenges related to them, and several netork and devce modfcatons have been consdered n the future release of LTE, referred to as LTE-Advanced (LTE-A) []. Hoever, a dramatc mprovement n effcency requres major changes to the ar nterface and core netork [4]. The random access channel (RACH) of LTE and LTE-A has been dentfed as a key area n hch an mprovement for MTC traffc s necessary []. In fact, the connecton-orented communcaton n the current LTE standard can nduce excessve sgnallng overhead n the case of transmttng smallszed data for M2M communcatons, especally hen a large number of M2M devces attempt to access cellular netorks at the same tme [8]. Moreover, many M2M devces stay out of connecton to save energy except for communcatng th the netork and transmttng a small amount of sgnallng data. Therefore, cellular netorks should focus on ho to deal th a massve number of connecton requests to ntate the netork connecton before data transmsson, rather than data traffc from numerous devces [2]. In the current LTE standard, the uplnk channel s dvded nto to sub-channels, namely the physcal random access channel (PRACH) for preamble transmsson and sgnallng overhead and physcal uplnk shared channel (PUSCH) for

2 2 data transmsson. Random access (RA) s the frst step n establshng an ar nterface connecton to access the cellular netork, here multple users/devces transmt random access preambles n PRACH. In M2M communcatons, due to a massve number of MTC devces, a preamble s usually selected by more than one devce, hch are then allocated th the same PUSCH for the data transmsson by the base staton (BS). Ths s the frst problem n RA for M2M communcatons hch s called preamble collson on PRACH and results n PUSCH astage as the BS cannot decode any data packet due to the co-channel nterference. The frequent preamble collsons n M2M communcatons also leads to netork congeston, unexpected delays, packet loss, hgh energy consumpton, hgh sgnalng overhead, and rado resource astage [3]. The second problem s that even f each MTC devce selects a preamble thout collson, there may not be enough resource blocks (RBs) to be allocated to the devces by the BS to the respectve PUSCH [4]. The focus of exstng studes on RA for M2M communcatons s mostly lmted to the frst problem. In ths ven and to reduce the access delay n M2M communcatons, several overload control mechansms have been proposed, ncludng dynamc allocaton [5, 6], slotted access, groupbased [2, 7], pull-based, and access class barrng [8, 9]. Moreover, the authors n [2] proposed a novel RA scheme, here a cell coverage s spatally parttoned nto multple group regons based on ther delay and addtonal preambles can be provded by reducng the cyclc shft sze n RA preambles. A further mprovement on [2] can be acheved for fxed locaton MTC devces based on fxed tmng algnment and predcton of the possble occurrences of collsons [2]. A reve of several RA overload control mechansms can be found n [3]. Although these approaches can reduce the access collsons to a certan degree, most of them stll suffer from very hgh access delays n hghly dense netorks. Unfortunately, only fe studes have consdered the second problem. More specfcally, [4] proposed a ne RA strategy by attachng the devce ID to the preamble sent by the MTC devce, enablng the BS to detect the collson n the the RA process. Moreover, the devce s message s sent as part of the scheduled message n the RA phase of the LTE standard, hch reduces the sgnallng overhead. A Hybrd RA and data transmsson protocol has also been proposed n [8], here the avalable resources are dynamcally allocated for the PRACH and PUSCH accordng to the perodc estmaton of the number of actve M2M devces by the BS. Although, the proposed approach can reduce the sgnallng overhead, hch s sutable for M2M applcatons th small data szes, t cannot solve the preamble collson problem hen a massve number of devces are attemptng to access the netork. In ths paper, e propose a novel RA strategy for M2M communcatons hch provdes major mprovements n terms of access delay and QoS, by shftng from conventonal dentfcaton/authentcaton based RA strateges. The proposed strategy ams to ) mnmze the access delay by enablng the collded devces to transmt at the same data channel, consstng of several RBs, 2) mnmze the sgnallng overhead by sgnalng once for each group of devces hch have selected the same preamble, and 3) mnmze the resource astage due to effcent usage of avalable resources. The proposed scheme contans to phases, the RA phase and the data transmsson phase. The devces do not need to be dentfed by the BS n the RA phase; nstead, the devce ID s sent along th ts message n the data transmsson phase and later s decoded by the BS. In the proposed scheme, collded devces are transmttng at the same data channel by usng the same Raptor code [2]. More specfcally, a sngle degree dstrbuton s used for Raptor codes n all the devces, hch sgnfcantly smplfes the system desgn as the code s not dependent on the number of devces or netork condton. The BS ll need to kno only the number of actve devces n a data channel to perform the decodng and devce dentfcaton. In fact, the receved sgnal at the BS can be realzed as a superposton of coded symbols sent from the devces, hch s then shon to be capacty approachng, hen an approprate successve nterference cancellaton (SIC) s used for the decodng. Ths s partcularly sutable for M2M communcatons th strct poer lmtatons, especally hen the data sze s very small and the number of devces s very large; thus, lo rate Raptor codes n the lo SNR regme can be effectvely used for ther data transmsson. The maxmum number of M2M devces hch can transmt at the same resource block s then characterzed as a functon of the data sze and the avalable banddth. The proposed scheme shos an excellent performance n hghly dense M2M netorks, hch makes t an excellent choce for future reless technologes. The rest of the paper s organzed as follos. Secton II represent the system model. Secton III represents the proposed random access scheme. An overve on Raptor codes and the proposed data transmsson strategy s presented n Secton IV. The rate performance analyss of the proposed scheme and the eght coeffcent desgn are studed n Secton V. In Secton VI, e shed lght on some of mportant practcal ssues of the proposed scheme. Secton VII shos the smulaton results, folloed by some concludng remarks n Secton VIII. II. SYSTEM MODEL We consder a sngle-cell centered by a BS n a cellular reless netork, here M2M and H2H devces coexst and share rado resources. The number of M2M devces s assumed to be far greater than that of H2H devces. Smlar to the LTE system, e consder the uplnk of an orthogonal frequency dvson multple access (OFDMA) system, here the rado resources are dvded nto unts of resource blocks (RBs), each th tme duraton τ s and banddth W s. The tme s dvded nto tme frames of length T f, here the number of actve M2M devces n each tme frame s random and follos a Posson process th rate λ [22]. Fg. shos the tme-frequency model of the uplnk rado resource for M2M communcatons. We also consder a contenton-based random access strategy n M2M communcatons, here N s dfferent random access preambles are selected n a random access attempt [3]. The notaton used n ths paper s also summarzed n Table I for quck reference. We assume that the rado resources for M2M and H2H communcatons are separately managed. The rado resource

3 3 Frequency Resource block for M2M PRACH Resource block for H2H PRACH Resource block for M2M PUSCH Resource block for H2H PUSCH PRACH A set of RBs for a preamble A data channel Tme frame t Tme frame t + PUSCH Fg.. Tme-frequency doman model of uplnk rado resource for the proposed scheme. manager can determne the number of requred resources for M2M communcatons based on the nformaton on the traffc loads of M2M and H2H communcatons. Traffc load nformaton of H2H communcatons can be obtaned n LTE based on the buffer status report and for M2M communcaton by usng a load estmaton algorthm [8]. The detals of the rado resource manager s out of the scope of ths paper. In fact, our am n ths paper s to maxmze the number of M2M devces hch can be supported by a gven number of rado resources and the proposed scheme can be combned th any dynamc resource management scheme to optmze the system-de performance. Moreover, H2H users have hgh prorty to obtan a connecton to transmt ther data to the BS. Most research to date has consdered contenton-free random access for H2H users, that s the BS assgns a preamble and a data channel to the H2H user n a tmely manner [23]. In ths ork, e only focus on M2M devces, hch opportunstcally contend for data channels through a contenton-based random access, and H2H users are assumed to have access to the BS through the allocated data channels. It s assumed that the channel beteen each M2M devce and the BS s a slo tme-varyng block fadng channel, for hch the channel remans constant thn one transmsson block but vares sloly from one block to the other. We consder a tme dvson duplex (TDD)-based reless access system, here the channel gan of the uplnk s assumed to be the same as that of the donlnk [24]. Wth ths assumpton, each devce can estmate the uplnk channel gan from the plot sgnal sent perodcally over the donlnk channel by the BS. The BS, hoever, does not have knoledge of any channel state nformaton (CSI). Ths assumpton s partcularly relevant n M2M communcatons th fxed locaton devces here, due to a large number of devces, t ould be mpractcal for the BS to obtan CSI to every MTC devce [25]. Moreover, e assume that the devces perform poer control n such a ay that the receved poer from all the devces at the BS s the same. III. THE PROPOSED RANDOM ACCESS STRATEGY FOR M2M COMMUNICATIONS In ths secton, a novel massve access strategy for M2M communcaton s proposed. Unlke the conventonal RA strategy n LTE here only the exstence of preambles are detected by the BS, n the proposed scheme the BS can effectvely Tme Notaton W s τ s T f γ γ γ max γ,max λ N N s N t N ZC γ th k T s τ TABLE I NOTATION SUMMARY Descrpton Total banddth of an RB n Hz The duraton of an RB Tme frame duraton The total receved SNR at the BS Receved SNR at the BS after poer control per MTC devce Maxmum total receved poer at the BS Maxmum receved SNR at the BS from each MTC devce Average number of actve devces n an RB Total number of devces Total Number of RA preambles Total number of tmng groups Length of the ZC sequence Threshold SNR n the load estmaton algorthm Payload sze of each MTC devce Basc tme unt hch s equal to ns mnmum tme dfference beteen to tmng groups detect the preambles and estmate the number of devces hch have selected each preamble usng conventonal Zadoff-Chu sequences [2] as RA preambles. A. The Contenton-Based RA Phase We assume that MTC devces perform poer control such that the sgnal transmtted by each MTC devce s receved at the BS th the same poer P. The steps of the proposed RA strategy are as follos: ) PRACH schedulng: Before each tme frame begns, the BS decdes the number of RBs for a PRACH and broadcast the confguraton of RBs for a PRACH va a donlnk control channel. In ths paper, e assume that the number of RBs for the PRACH of M2M and ther confguraton s fxed. More specfcally, e assume N s preambles are allocated for RA of MTC devces. 2) Preamble transmsson: Each MTC devce hch has data to transmt, randomly chooses a preamble out of N s avalable preambles th equal probablty. The chosen preamble s then sent to the BS va the PRACH. 3) Preamble detecton and data channel schedulng: The BS detects all the preambles transmtted on the PRACH by the MTC devces and determnes the total number of actve MTC devces. Then the BS broadcasts the schedulng nformaton along th the nformaton about the eght coeffcents to all devces va a donlnk control channel n the form of a random access response (RAR). The detals of ths step ll be dscussed n the next subsecton. It s mportant to note that n the thrd step of the proposed RA strategy, the BS broadcasts the nformaton regardng the eght coeffcents to all the devces. The eght coeffcents are used n the data transmsson phase and are desgned such that the BS can accommodate all the detected devces thn the avalable resource channels. We ll dscuss dfferent eght desgns and ther respectve rate performances n Secton V. B. Load Estmaton Algorthm The load estmaton algorthm runs on Step 3 of the RA procedure and ams to determne the number of devces hch

4 4 have selected each preamble and been receved th the same delay at the BS. In the conventonal RA procedure n LTE, a set of nformaton s sent as a RAR message n the thrd step of the RA phase. More specfcally, the RAR message n LTE contans, ) a number to dentfy the RA slot, 2) the ndex of the receved preamble, 3) the tmng advance command, and 4) the resource allocaton nformaton [26]. The tmng advance command s used to adjust the uplnk transmsson tme n such a ay that the data s receved at the BS at the antcpated tme. Ths command takes an ndex value by a multple of 6 T s, here T s denotes the basc tme unt and s equal to ns [26]. Smlar to [26], e assume that to propagaton delays are quantzed to the same ndex hen ther dfference s less than or equal to τ = 8T s. Furthermore, the propagaton delays of MTC devces to the BS are quantzed and take values of multple of τ. Therefore, the propagaton delay s modelled by an ndex takng values from to N t, here N t s the maxmum tmng ndex hch s determned by the cell coverage radus, R. More specfcally, N t = R/(cτ), here c = 3 8 m/s s the lght speed and. s the cel operator. The cell coverage area can then be vrtually parttoned nto multple regons, here the devces n each regon have the same tmng ndex. That s an MTC devce at dstance r from the BS belongs to the l th tmng group f (l )τ < r/c < lτ. Each MTC devce determnes ts on group based on ts dstance nformaton beteen the BS and tself, hch can be obtaned by several dstance estmaton algorthms [2]. Thus, e assume that each MTC devce knos ts on tmng ndex. Fg. 2 shos ths cell parttonng based on tmng ndexes. As shon n Fg. 2, the transmtted preambles by MTC devces are receved th dfferent delays (.e., tmng ndexes) due to dfferent propagaton dstances from MTC devces to the BS. In LTE, the BS determnes the presence of any preamble by calculatng the dscrete cross correlaton of the receved sgnal th each of the N s preambles. The Zadoff-Chu (ZC) sequences are used to generate RA preambles hch are defned as z r[n] = exp[ jπrn(n + )/NZC ] for n =,, N ZC, here N ZC s the sequence length and r {,, N ZC } s the root ndex [2]. The magntude of the cyclc correlaton of each ZC sequence th tself s a delta functon,.e., NZC c rr[σ] = n= zr[n]z [n + σ] = N ZC δ[σ], here (.) denotes the complex conjugate. Usng ths property, e can determne by ho much the receved sequence s shfted. Multple RA preambles are then generated from the ZC sequence by cyclcally shftng the sequence by a factor of N SC, hch s determned by the system parameters. The th preamble can be generated as z r, [n] = z r[ mod (n + N CS, N ZC )]. More detals on the ZC sequences and ther desgn parameters n LTE can be found n [27 29]. No, e explan the proposed load estmaton algorthm based on tmng advance and dfferent poer levels of receved preambles. Let n(, j) denote the number of devces belong to the j th tmng group that have selected the th preamble. We denote by P,j the th receved preamble at the BS hch s sent by the devce n the j th tmng group. Ths preamble s shfted by (j )τ due to the propagaton delay of the j th group. The receved sgnal at the BS at the end of the frst T = T 2 = τ P, T Nt =(N t )τ P,2 P3,2.. P2,Nt P2,Nt Inactve MTC devce Actve MTC devce Base staton cτ. (N t )cτ N tcτ = R Fg. 2. Vrtual cell parttonng based on tmng advance nformaton of MTC devces and the respectve random access process n the RA phase. step of the RA phase can be rtten as follos: N s N t Y = n(, j)p,j + Z, () = j= here Z s addtve hte Gaussan nose (AWGN) th zero mean and varance σ 2 z. The BS then calculates the crosscorrelaton beteen the receved sgnal Y and each preamble th dfferent tmng ndexes. Unlke the preamble detecton strategy n the LTE standard that only one tmng advance s detected for multple copes of each preamble receved by the BS, the BS n the proposed scheme can detect all the tmng ndexes of all the copes of each preamble, thanks to the same receved poer from all the devces at the BS. Algorthm shos the steps of the proposed teratve load estmaton strategy at the BS. Algorthm Load Estmaton Algorthm : Intalze ˆn = 2: hle Y 2 2 > γ th do 3: for {,, N t } do 4: for j {,, N s} do 5: f N ZC n= Y [n]p j,[n] > γ th then 6: ˆn(, j) + +, 7: Y = Y P j,, 8: end f 9: end for : end for : end hle It s mportant to note that γ th n Algorthm can be changed and optmzed for dfferent loads. Fg. 3 shos the estmaton accuracy of the proposed scheme under dfferent loads. Here, the estmaton accuracy s defned as the dfference beteen the estmated and actual number of devces dvded by the actual number of devces. As can be seen n ths fgure the proposed approach can accurately estmate the total number of devces from the preambles sent over the PRACH. The desgn and adjustng the parameters of the proposed algorthm can be done n such a ay to maxmze the accuracy of the estmaton. Ths s hoever beyond the scope of the paper. In the rest of the paper, e assume that the BS alays detects the preambles and accurately determnes the number of devces hch have selected each preamble and have the same tmng ndex. It orth notng that a smlar algorthm s used n the current LTE standard to only detect each preamble. As several devces mght have chosen each preamble the dscrete cross correlaton

5 5.8 N=2 N= N=3 N=5 b () C c BPSK d t x Estmaton accuracy γ th Fg. 3. Estmaton accuracy for dfferent number of devces hen N s = N t = 2, N ZC =, and SNR = db. of the receved sequence and a cyclcally shfted preamble contans several mpulses n the tme doman. These mpulses determne the propagaton delay of the devces that has selected the respectve preamble. Hoever, the BS only consder the mpulse th the shortest delay/hghest ampltude, and broadcast the respectve tmng advance n the RAR message. Ths s neffcent as the BS only schedules a data channel for the devce th the shortest propagaton delay hen multple devces have selected the same preamble. Moreover, f more than one devces have the same tmng advance and have selected the same preamble, ther scheduled messages ll collde and the respectve data channel ll be unused. IV. THE PROPOSED DATA TRANSMISSION PHASE FOR M2M COMMUNICATIONS A. An Overve on Raptor Codes n the Lo SNR Regme A Raptor code [2] s a smple concatenaton of a hghrate lo densty party check (LDPC) code and a Luby transform (LT) code [3]. A k-bt nformaton sequence s frst encoded by usng a hgh-rate LDPC code to generate k LDPC coded symbols, also referred to as nput symbols. Usng an LT code, a potentally lmtless number of coded (output) symbols can then be generated. The encodng process of LT codes contans to mportant steps. Frst, an nteger d, called degree, s obtaned from a predefned probablty dstrbuton functon, called a degree dstrbuton. Second, d dstnct nput symbols are unformly selected at random and then XORed to generate one output symbol. The encodng process ll be termnated hen the sender receves an acknoledgement from the destnaton or a pre-determned number of coded symbols are sent. Let Ω d denote the probablty that the degree s d. Then, the degree dstrbuton functon can be represented n a polynomal form as follos: Ω(x) = D Ω d x d, (2) d= here D s the maxmum code degree. A sum product algorthm (SPA) s usually used for the decodng of Raptor codes, here log-lkelhood ratos (LLRs) are passed as messages along edges from varable to check nodes and vce versa n an teratve manner. More detals of ths decoder can be found n [3]. The desgn of Raptor codes Fg. 4. Encoder structure at the th MTC devce th Raptor component code C. t s an..d. random bnary sequence and s the eght coeffcent selected by the th devce. over AWGN channels n the lo sgnal to nose rato (SNR) regme has been studed n [32], here an exact expresson for the degree dstrbuton polynomal n the lo SNR regme as found. More specfcally, the asymptotc degree dstrbuton polynomal n the lo SNR regme hen the maxmum code degree goes to nfnty s gven by [32]: Ω ( ) (x) = 4 ln(2) x ϕ (t)dt, x [, ], (3) here ϕ (x) s the nverse of ϕ(x), hch s defned as follos for x > : ϕ(x) = 4πx ( u ) tanh e (u x)2 4x du. (4) 2 A set of practcal degree dstrbutons th lmted maxmum degree as also desgned n [32], hch have shon excellent rate performance n very lo SNRs (belo - db). More specfcally, a rate effcency of.95 as acheved for a Raptor code th maxmum degree 3 n the hole SNR range belo - db. Here, the rate effcency s defned as the rato of the achevable rate and the channel capacty. Ths s an nterestng property for Raptor codes, here a sngle degree dstrbuton can be used for all SNRs belo - db to acheve a near capacty performance over AWGN channels. B. Encodng at MTC devces In the data transmsson phase, each MTC devce appends ts unque ID to ts message and then encodes t by usng a Raptor code. Each devce uses ts preamble ndex and tmng ndex as the seed for ts random generator n the Raptor encoder, thus the BS and the devce can buld the same generator matrces for ther Raptor codes. The same degree dstrbuton s used for all the devces. Ths ll sgnfcantly reduce the system desgn complexty as the devces do not need to change ther code structure every tme accordng to the system load. Moreover, as the MTC devces are assumed to have small packets to transmt, the effectve code rate of each devce can be very small. Ths allos to use the degree dstrbuton optmzed for Raptor codes n the lo SNR regme [32], for all the devces. All the actve devces hch have successfully receved the RAR message n the RA phase are transmttng at the same data channel, hch conssts of multple RBs determned by the BS n the RA phase. Fg. 4 shos the encoder structure at each MTC devce. As can be seen n ths fgure, each encoded symbol c s XORed th a bnary random symbol t. We refer to ths bnary random source as the channel adaptor as t forces the symmetry condton for each equvalent bnary nput AWGN channel of each devce. The resultant symbol, d, s then BPSK modulated and multpled by the selected eght and transmtted over the scheduled data channel. The seed for the random generators of

6 6 CHANNEL ADAPTER t L t...d. source L..d. source. 2 (.) 2 (.) b () b (L) C C BPSK c d.. Σ Σ c L d L BPSK L ENCODER x z AWGN y APP ˆd L ˆdL APP u v DEC... u L v L DECODER DEC ĉ ĉ L Fg. 5. Encoder and decoder structure of the proposed code th Raptor component codes. the channel adaptors at the devces are shared th the BS n the RA phase through the RAR message or at the begnnng of the data transmsson phase. Ths ll be dscussed n Secton VI. The detals of the eght coeffcent desgn ll also be dscussed n the next secton. C. Decodng at the BS Let x denote the output of the BPSK modulator of the th devce, here e gnore the tme ndex for the smplcty of representaton. Then, the receved sgnal at the BS, denoted by y, s shon as follos: L y = x + z, (5) = here L s the number of actve MTC devces, z s zero mean addtve hte Gaussan nose th varance σ 2 z. Fg. 5 shos the encoder structure of the mult-layer realzaton of the proposed scheme, here each layer corresponds to one MTC devce transmttng at the same data channel. For the decodng of the devces messages, e use the ell-knon multstage decodng (MSD). More specfcally, the decoder for the th stage,.e., a decoder for the th MTC devce at the BS, removes all coded symbols from all prevous stages, and treats the coded symbols of stages + to L as addtve nose. Let y denote the effectve nput of the th stage of the decoder, t can be shon as follos: y = x + z, (6) here z = j> jx j + z s the effectve nose of the th decoder stage. It can be easly verfed that z has zero mean and ts varance, denoted by σ 2 can be calculated as follos: σ 2 L = j=+ 2 j + σ2 z. (7) The nput of the th stage of the decoder can then be realzed as the output of an equvalent BI-AWGN channel, here ts effectve SNR s gven by: γ = 2 Lj=+ j 2 +. (8) σ2 z It s mportant to note that by usng..d. channel adapters, e can force the symmetry of the equvalent bnary-nput component channels [33]. Generally, a bnary nput channel s symmetrc f [33] p(y = y C = ) = p(y = y C = ) here c and y are nput and output of the bnary-nput channel, respectvely. As shon n Fg. 5, the sgn of the channel output ll be adjusted by v = u ( 2t ), here u s the LLR of the APP module output, and v s the nput of the th stage decoder. More specfcally, the APP module at stage ll subtract the coded symbols of the prevous stages from the channel output y, and calculate the output LLR, u, of the equvalent BI-AWGN channel (6) as follos: LLR = 22 y σ 2. (9) As shon n [33], for any ne bnary-nput output symmetrc component channel, f e use a channel code C through ths channel, the decodng error probablty s ndependent of the codeord. It as also shon that the capacty of the bnary nput channel th..d. equprobable nput dstrbuton s equal to the capacty of the equvalent bnary-nput output symmetrc channel th the..d. channel adapter. Ths means that no rate loss s ntroduced n the system due to use of the channel adapter. V. ANALYSIS OF OF THE PROPOSED SCHEME AND WEIGHT A. Achevable Rate COEFFICIENT DESIGN Wth the ell-knon mult-stage decodng and the mutual nformaton chan rule, e have I(C,, C L ; Y ) = I(C ; Y ) + I(C 2 ; Y C ) + + I(C L ; Y C,, C L ), () hch shos that the transmsson of vector (c,, c L ) can be separated nto the parallel transmsson of c over L equvalent bnary nput channels [33]. More specfcally, the mutual nformaton for the th equvalent bnary nput channel can be shon as follos: I(C ; Y C,, C ) log 2 ( + γ ), ()

7 7 hch s vald snce e assume that the equvalent SNR for all layers s very small. By usng (8), () can be rertten as follos: L I(C,, C L ; Y ) = log Lj=+ = j 2 + σ2 z L Lj= 2 = log 2 j + σ2 z Lj=+ = j 2 + σ2 z Lj= 2 = log 2 j + σ2 z σz 2 = log 2 ( + γ), (2) hch can be further smplfed accordng to (): L log 2 ( + γ) = = log 2 ( + γ ). (3) As e assume that the devces contnue ther transmsson over all the allocated RBs,.e., the BS does not send acknoledgement to each ndvdual devce upon successful decodng of each stage, the achevable rate for each devce s upper bounded by the rate of the devce th the mnmum effectve SNR. Let R denote the effectve rate of each devce, then e have: R log 2 ( + γ mn ), (4) here γ mn = mn {γ } and R mn log 2 ( + γ mn ). Let k denote the message length of each MTC devce, ncludng the devce ID. The number of RBs requred for the successful transmsson of the message can be calculated as follos: V k. (5) τ sw sr mn The RB load, defned as the average number of devces per RB, can be easly obtaned as V/N. B. Desgnng the Weght Coeffcents As can be seen n (3), the effectve rate for each devce s characterzed by the eght coeffcents. In ths secton, e propose three eght coeffcent desgns and dscuss ther respectve rate performances. ) Equal Weght Selecton: In the equal eght (EqW) selecton strategy, all the devces select the same eght coeffcent. Let denote the eght coeffcent selected by all devces, then, t can be calculated as follos: = L, (6) hch s due to the fact that the overall receved sgnal poer at the BS s assumed to be. The effectve SNR of the th devce can then be calculated as follos: 2 γ = =, (7) (L ) 2 + σ 2 z L + Lσ 2 z and the mnmum SNR for MTC devces s gven by γ mn = L + Lσz 2. (8) The maxmum achevable rate for MTC devces s then upper bounded by the rate of the devce th the mnmum SNR. It can be characterzed as follos: R (EqW) mn = log 2 ( + L + Lσz 2 ). (9) 2) Exponental Weght Selecton: In the exponental eght (ExW) selecton strategy, the eght coeffcents are desgned n such a ay that the effectve SNR at the BS for each devce s the same. Lemma : Let L denote the number of actve MTC devces and γ denote the target effectve SNR at the BS for every MTC devce. Then, the overall receved SNR at the BS s gven by: γ = ( + γ ) L, (2) and the optmal eght coeffcents can be calculated as follos, for =,, L : L = ( + γ ) γ γ. (2) Proof: Snce the eght coeffcents are desgned such that the effectve SNR of each equvalent BI-AWGN channel s γ, accordng to (3) e have: L log 2 ( + γ ) = log 2 ( + γ), (22) hch drectly results n (2). Also from (8), t s clear that for the L th layer, e have 2 L = γ /γ, hch proves (2) for =. We assume that (2) holds for =,, j for j, e then sho that t also holds for j +. As e assume that the effectve SNR for all layers s γ, then for layer L j e have: L j 2 L j 2 γ = L=L j 2 + = σ2 j z = 2 L + σ2 z = = 2 L j j = ( + γ ) γ γ γ 2 L j ( + γ ) j+, + σ 2 z hch s equvalent to (2) for j +. Ths completes the proof. In ths scheme, the devces randomly select the eght coeffcents from the set of optmal eght coeffcents. Therefore, t s hghly probable that more than one devce ll select the same eght coeffcent. Let r denote the number of devces hch have selected the eght coeffcent. It s clear that L= r = L and = j for + j l= n l j l= n l. Accordng to (8), t s easy to verfy that γ < γ j for every < j here + j l= n l, j j l= n l. Ths s because γ = < 2 Lj=+ 2 j + σ2 z 2 j Ll=j+ 2 l + σ2 z = 2 Lj=+ 2 j + σ2 z = γ j, (23) hch s vald hen < j. Accordngly, the mnmum effectve SNR for MTC devces can be calculated as follos: γ mn = mn {:r } (r ) L j=+ r j 2 j + σz 2. (24) In the follong, e fnd the probablty dstrbuton functon (pdf) of γ mn. For ths am, e defne ξ =

8 8 2 (r ) 2 + L j=+ r j j 2+σ2 z for { : r }; otherse t s set to. Then accordng to Lemma and (2), e have: L = (r ) + r j ( + γ ) j + ( + γ ) L. ξ γ j=+ Snce the devces randomly choose from the L avalable eght coeffcents, for a suffcently large L, r can be modelled by a bnomal dstrbuton th a success probablty of /L,.e., p(r ) = ( L (/L) r ( /L) L r, (25) r) Probablty N= N= N= and ts mean and varance are E[r ] = and var[r ] = ( /L), respectvely. It s also easy to sho that p(r = ) = ( /N) N. When L goes to nfnty and r, /ξ can be modelled by a Gaussan dstrbuton accordng to the Central Lmt Theorem, th mean m and varance S, hch are gven by: L m = E[/ξ ] = r j ( + γ ) j + ( + γ ) L =, γ j=+ γ S = var[/ξ ] = ( L L ) ( + γ ) 2( j). j= The complete pdf of /ξ can then be characterzed as follos: ( ) p ; ( z =, p = z = ξ 2πS p exp (z m ) 2 ) 2S ; z, here p = ( /N) N. The cumulatve dstrbuton functon (cdf) of γ mn, denoted by F γ(x L), hen the number of devces s L, can be found as follos: F γ(x L) = p(γmn < x) = p(mn ξ < x) = p(max > ξ x ) = p(max < ξ x ) = p( < ξ x,, < ξ L x ) L = p( < ξ x ) = ( ( L = p + ( p ) Q = here Q(x) = 2π x ( x ))) m, (26) S ( ) exp u 2 /2 du. As L follos a Posson dstrbuton th mean λ, the complete cdf of γ mn s calculated as follos: F γ(x) = e λ λj Fγ(x L). (27) j! j The pdf of γ mn s smply the dervatve of F γ(x). Fg. 6 shos the hstogram of the mnmum SNR dvded by the target effectve SNR, γ, hen the total SNR at the BS s γ = 2 db. As can be seen n ths fgure, th ncreasng the number of devces, and accordngly the number of avalable eght coeffcents, the probablty that the mnmum SNR s closer to γ s ncreased. Ths s because by ncreasng the number of devces, the probablty that the devces choose separate eght coeffcents s ncreased, hch accordngly leads to a hgher mnmum achevable rate. It s mportant to note that the proposed approxmaton of the pdf shos around % to 5% msmatch n the mean value to the smulated pdf. Ths fgure also shos the approxmaton of the pdf of γ mn γ mn / γ Fg. 6. Hstogram of the mnmum devce SNR for dfferent number of devces, hen the total SNR at the BS s γ = 2 db. Sold lnes shos the smulaton results and dashed lnes sho the approxmated results by usng (26). R mn /R o γ γ = db γ = db γ =2 db γ =3 db Number of devces Fg. 7. Average mnmum achevable rate of MTC devces versus the number of devces for dfferent target SNRs at the BS. Sold lnes shos the smulaton results and dashed lnes sho the approxmated pdf usng (26). by shftng the mean value by about 3%, hch s n a close agreement th the smulaton results. Fg. 7 shos the mnmum achevable rate for MTC devces versus the number of devces. As can be seen n ths fgure, th ncreasng the number of devces, the mnmum achevable rate gets closer to the desgned rate. Moreover, th decreasng the target SNR at the BS, the mnmum achevable rate gets closer to the desred rate. Ths s because, accordng to Lemma (), th decreasng total SNR at the BS, the effectve target SNR per devce, γ, s decreased. More specfcally, the rato of eght coeffcents for the th and j th devce, hch s gven by ( + γ ) j, gets closer to. Ths leads to less rate loss as the eght coeffcents are no close to each another. It s also mportant to note that the approxmaton of the average mnmum achevable rate usng (26) shos excellent agreement th smulaton results, especally hen the number of devces s relatvely large. 3) Grouped Weght Selecton: Let us assume that the BS can determne the number of devces hch have a partcular tmng advance and have selected a partcular preamble. Ths ay the devces can be parttoned nto N st = N s N t dfferent groups, here the devces n each group have the same tmng ndex and have selected the same preamble. The devces n each group are then assumed to have the same eght coeffcent. We refer to ths strategy as the group eght

9 9 (GrW) selecton strategy. The eght coeffcents are then desgned n such a ay that the mnmum effectve SNR for the devces s maxmzed. Let r denote the number of devces n the th group, here =,, N st. We defne the follong optmzaton problem to maxmze the mnmum effectve SNR for MTC devces: max mn 2 W {:r } (r ) 2 + N st j=+ r j j 2, + σ2 z s.t. () N st r 2 =, = (), for =,, N st, here e assume that the BS alays starts the decodng from the group th the largest eght coeffcent. To further smplfy the desgn of the eght coeffcents, e defne a target mnmum SNR γ, and determne the eght coeffcents such that the mnmum devce SNR s at least γ. For ths am, e fnd the eght coeffcents such that the effectve SNR of the frst devce of each group s at least γ. Ths s because the frst devce of each group has the loest effectve SNR amongst other devces n the group, hch can be easly proven by usng the same strategy as n (23). Therefore, for the frst devce of the th group, e have: γ = For = N st, e have: 2 (r ) 2 + N st j=+ r j 2 j + σ2 z N 2 γ = st (r Nst ) N 2 + σ 2 st z = γ. (28), (29) and the eght coeffcent for the Nst th group,.e., Nst, can be calculated as follos: 2 N st = γ γ γ (r Nst ). (3) The eght coeffcent for the th group can then be calculated as follos: 2 = γ ( + γ ) N st γ N st l= γ (r l ). (3) As e assume that the total receve poer at the BS s, then e have: N st r 2 = and by substtutng (3), e have: N st r γ = γ ( + γ ) N st N st = [ γ (r )] l= =, (32). (33) It s clear from (33) that for a gven γ, the order of the number of devces n each group affects the total receved SNR at the BS. The BS then performs an optmzaton to fnd the optmal order of the eght coeffcents to maxmze the average receved SNR at the BS. For smplcty, e assume that r r j for > j. Average throughput per RB 3 GrW, γ = - db 2 - ExW, γ = - db GrW, γ = -2 db ExW, γ = -2 db -2 Arrval Rate (λ) 2 3 Fg. 8. Average throughput per RBs for the proposed scheme th dfferent eghtng strateges thout adaptve poer management at the devces. The message length of MTC devces s k = 24, N s = N t = 2, W s = MHz, and τ s = ms. Sold and dashed lnes sho smulaton and analytcal results, respectvely. C. Comparson Beteen Weght Selecton Strateges Fg. 8 shos the RB load versus the number of devces for dfferent target SNR values at the BS. Fg. 8 shos the average throughput per RB for the proposed scheme th dfferent eghtng strateges. The analytcal results are also plotted n Fg. 8 hch sho a good match th the smulaton results. As can be seen n ths fgure, the grouped based eght selecton can accommodate more devces per RB compared to the exponental eght selecton strategy. Ths s because of non-deal eght selecton n the ExW scheme, hch reduces γ mn and accordngly the mnmum achevable rate per MTC devce decreases. Hoever, n the GrW scheme, the eght coeffcents are desgned to maxmze the loest effectve SNR, hch can sgnfcantly ncrease the achevable rate per MTC devce, especally n hgher loads. Moreover, as can be seen n Fg. 8, th ncreasng the arrval rate the number of MTC devces hch can be supported by each RB s lnearly ncreasng. Ths s due to the fact that the eght selecton strateges are desgned n such a ay that the mnmum receved SNR per devce remans constant at the BS. Thus, by ncreasng the number of devces the mnmum achevable rate remans constant, therefore the BS can support a larger number of devces per RB. VI. PRACTICAL CONSIDERATIONS A. Overhead due to the Weght Selecton n the Data Transmsson Phase In the data transmsson phase, the devces should select the eght coeffcents and the BS must kno hch eghts are selected and ho many devces have selected the same eght. The devces then need to nform the BS of ther selected eght coeffcents. For ths am, e assume that devces randomly select a eght coeffcent among N coeffcents and send the ndex of the eght to the BS. Ths can be done by sendng a bnary sequence of an approprate length to the BS. The selected sequences should be orthogonal, so the BS can detect them. The nformaton about these orthogonal sequences can be sent va the RAR message. Then a smlar strategy as Algorthm can be performed to detect the sequences and estmate the number of devces hch have selected the same

10 Probablty Probablty γ = -2 db Rate effcency (η) Rate effcency (η) γ =- db Fg. 9. Hstogram of the rate effcency of a Raptor code th a message length of kb and optmzed degree dstrbuton n the lo SNR regme. sequence. More specfcally, e assume that the length of the eght sequences s δn, here δ. δ s determned such that the probablty that the BS cannot detect any sequence s mnmzed. The desgn of bnary orthogonal sequences for synchronous and asynchronous CDMA systems has been dely studed and e do not dscuss them here as t s out of scope of ths paper. Interested readers are referred to [27] and the references theren for further detals. The devces perform tmng adjustment and poer control to transmt the selected sequences to the BS, thus the BS performs Algorthm th a slght modfcaton that the sequences are receved thout delay. Ths hoever ncreases the amount of overhead for the proposed scheme, as extra RBs have to be allocated for transmttng orthogonal eght sequences. The number of RBs requred to successfully transmt orthogonal eght sequences n the data transmsson phase can be characterzed as follos: δn N RB =, (34) R Wsτs here R = log2 ( + γ ) and e assume that the devces perform poer control and the receved SNR for each devce at the BS s γ. Wth an adequate number of RBs allocated for the random eght transmsson n the data transmsson phase, e assume that the BS can successfully detect the eght sequences and determne the number of devces hch have selected the same eght. B. Rate Loss Due to the Small Packet Sze of MTC Devces The capacty approachng degree dstrbuton of Raptor codes n the lo SNR regme as desgned n [32] for messages of nfnte length, here the tree assumpton of the bpartte graph of the Raptor code easly holds. Hoever, one could use ths degree dstrbuton for fnte message szes th slght rate losses n the lo SNR regme. Fg. 9 shos the hstogram of the rate effcency of a Raptor code th the optmzed degree dstrbuton desgned n [32] for dfferent SNR values, hen the message sze s 24 bts. As can be seen n ths fgure, the rate effcency of the fnte message length Raptor code can be as small as.6 hen the SNR s - db. Ths hoever has a negatve effect on the overall rate effcency of the mult-layer Raptor code, as the overall rate effcency s characterzed by the mnmum rate effcency over all the layers. In the next secton, e sho that even th ths mperfect rate effcences, the proposed scheme sgnfcantly outperforms the exstng massve access strateges for M2M communcatons n terms of throughput and access delay. In fact the superorty of the proposed code over exstng schemes comes from the smultaneous multple devce transmsson over the same data channel, hch sgnfcantly reduces the access delay and resource astage. C. Adaptve Poer Management at MTC Devces As can be seen n Fg. 8, the throughput per RB n the proposed scheme reduces hen the number of actve devces s small. Ths s because the desgned target SNR has been set to a very small value, so several RBs are needed for an MTC devce to successfully transmt ts message at the very lo rates requred at very lo SNRs. Ths leads to very lo effcences f the arrval rate s lo. To overcome ths problem, the BS sends a poer update message n the RAR message to nform the devces to update ther transmsson poers. Ths ay hen the number of actve devces s lo the devces transmt th hgher poers such that each RB can support at least one MTC devce. To mnmze the number of RBs requred n the data transmsson phase, e adjust the target SNR based on the number of actve devces such that the total receved SNR at the BS s less than a threshold value, denoted by γ max. At the same tme, and to lmt the maxmum transmsson poer of each devce, e put a lmt on the maxmum alloable target SNR per MTC devce. The target SNR, γ, can then be updated and nformed to the devces by the BS as follos: γ = mn{ L + γ max, γ,max }. (35) The BS then needs to control the number of devces hch are transmttng n the data transmsson phase. For ths am, the BS estmates the maxmum number of devces that can transmt at the same data channel for a gven maxmum alloable SNR at the BS, and then sends a not-to-transmt message to the devces hch have selected some of the preambles. Ths ay the BS can alays effectvely delay some of MTC devces for transmsson at future tme frames. In fact, conventonal massve access management technques can be combned th the proposed scheme to manage a large number of devces n M2M communcatons n an adaptve manner. VII. SIMULATION RESULTS For the smulatons, e assume that the message sze of each MTC devce s k = 24 bts, ncludng the devce ID. Each devce uses a Raptor code th a degree dstrbuton functon th maxmum degree 3 from [32], hch has been optmzed for Raptor codes n the lo SNR regme and s gven by Ω(x) =.74x x x x x 5 +.2x x 7 +.4x 8 +.9x +.58x x x x x x 3. A rate.98 LDPC code s also used as the precoder for the Raptor code. We also assume that each RB has banddth W s = MHz and tme duraton τ s = ms.

11 Average throughput per RB GrW ExW Arrval rate (λ) 2 3 Fg.. Average throughput per RBs for the proposed scheme th dfferent eghtng strateges th adaptve poer management at the devces. The message length of MTC devces s k = 24, N s = N t = 2, W s = MHz, and τ s = ms. The maxmum receved SNR at the BS s γ max = 3 db. Sold and dashed lnes sho smulaton and analytcal results, respectvely. Fg. shos the average throughput per RB hen a poer adaptaton strategy s used at the MTC devces such that the maxmum receved SNR at the BS s 3 db. As can be seen n ths fgure n hgh load cases each RB can support up to 7 and 5 MTC devces per RB n GrW and ExW eghtng strateges, respectvely. We compare the proposed scheme th the optmal access class barrng (ACB) scheme [26], hch uses tmng advance nformaton n the random access phase to ncrease the MTC access probablty. In ths scheme, the BS can detect the tmng advance nformaton of multple devces hch have selected the same preamble. The BS then randomly selects one of these tmng advances and ncludes t n the RAR message. If only one of the MTC devces, hch have chosen the same preamble, has the selected tmng advance, then t can send ts message thout collson. Ths scheme can slghtly mprove the random access effcency, but s stll lmted by the number of preambles, as the devces cannot smultaneously transmt at the same RB. In the ACB scheme, a parameter called ACB parameter, s broadcasted by the BS to nform the devces to transmt th a certan probablty. Let p denote the ACB parameter, then an MTC devce hch has data to transmt ll dra a random number n the range [, ], and partcpate n the random access procedure only f the random number s less than p. The optmal value for p for the orgnal ACB scheme [34] s p = mn{, N/N s} and that for the ACB th tmng advance nformaton [26] s p = {,.7Ns ln(ρ) N(ρ ) }, here ρ = 4d(R d) R 2. Smlar to [26], e assume that the cell has radus R =.5 km, τ =.26 µs, and d = cτ = 75 m. Ths results n N s = 2 dfferent tmng groups. Wthout loss of generalty, e assume that each RB carres exactly k r symbols, here k r k, hch means that n the ACB scheme, each devce hch has been granted access to the BS, ll be allocated one RB. Fg. shos the average number of MTC devces hch can be supported by dfferent massve access technques hen RBs are allocated for M2M communcatons n the data transmsson phase. As can be seen n ths fgure the ACB scheme [34] can support at most 25 MTC devces hle the ACB th tmng advance nformaton can support up to 55 Average number of successful MTC devces 3 2 Proposed scheme, ExW, γ max = db Arrval rate (λ) ACB only [34] ACB th tmng advance nfo [26] Proposed Scheme, GrW, γ max =3 db Proposed Scheme, ExW, γ max =3 db Proposed scheme, GrW, γ max = db Fg.. Average number of MTC devces that can be supported n each tme frame for dfferent massve access strateges. The message length of MTC devces s k = 24, N s = 64, N t = 2, W s = MHz, and τ s = ms. Delay [tme frame] ACB th tmng advance nfo [26] ACB only [34] Proposed scheme, ExW, γ max =3 db Proposed scheme, GrW, γ max =3 db Proposed scheme, GrW, γ max = db Proposed scheme, ExW, γ max = db Arrval rate (λ) Fg. 2. Average delay versus arrval rate. The message length of MTC devces s k = 24, N s = 64, N t = 2, W s = MHz, and τ s = ms. MTC devces thn each tme frame. The proposed scheme sgnfcantly outperforms the ACB schemes by supportng up to 2 and 5 MTC devces hen the maxmum SNR at the BS s db and 3 db, respectvely. Fg. 2 shos the average delay versus the arrval rate for dfferent massve access strateges. As can be seen n ths fgure the proposed scheme can support a sgnfcantly larger number of devces th almost zero delay compared to ACB schemes. It s mportant to note that n the ACB scheme, e assume that a devce can successfully delver ts message to the BS n ts correspondng data channel, hen t has successfully completed the RA phase; thus, the only lmtng factor for the ACB scheme s the preamble collson n the RA phase. In ACB and to accommodate more devces n gven number of RBs, each devce should be allocated only fe number of RBs and transmt at hgh poer to guarantee that ts message can be decoded. On the other hand n the proposed scheme, RBs are shared among all the devces and they are transmttng at mnmum poer over relatvely large number of RBs. As the devces ll only perform random access once n the proposed scheme and also accordng to Fg. here a larger number of MTC devces can be supported n each RB n the proposed scheme th loer transmsson poer, e can clam that the proposed scheme ll sgnfcantly mprove energy effcency n M2M communcatons compared to exstng ACB approaches.