Active User Detection of Uplink Grant-Free SCMA in Frequency Selective Channel

Acti v e User Det ection of Uplink Grant-Fre e SCMA in Fre quenc y Selecti v e Channel Feilong W ang, Y uyan Zhang, Hui Zhao, Hanyuan Huang, Jing Li Intelligent Computing and Communication Lab, BUPT , Beijing, China Ke y Laboratory of Uni versal W ireless Commun ication, Ministr y o f Ed ucation Email: flw ang@bupt.edu.cn Abstract —Massiv e machine type communication (mM TC) is one of the three fif t h generation mobile networking (5G) key usage scenarios, which is chara cterized by a ver y large number of connected dev ices typically transmitting a re latively lo w volume of non-d elay sensitive data. T o sup port the mMTC communication, an up link (UL) grant-free sparse code multiple access (SCMA) system has been proposed. In this system, th e knowledge of user equipmen t s’ (UEs’) status should b e obtained befor e decoding the data by a message passing algorithm (MP A). An existing solution is to u se the compressi ve sensin g (CS) theory to detect activ e UEs und er the a ssumed condition of flat fading channel. Bu t the assumed condition is not suitable for the frequency selective chann el and wi ll decrease the accuracy of active UE s detection. This p aper p roposes a new simple module named refined a ctive UE detector (RA UD), which is b ased on frequency selectiv e chann el gain analyzing. B y making full use of the channel gain and analyzing th e d ifference between characteristic v alues of the two status of UEs, RA UD module can enh ance the acti ve UEs detection accuracy . Meanwhile, th e addition of the proposed module has a negligible effect on the complexity of UL grant-fr ee SCMA r eceiv er . Index T erms —Sparse code mu ltiple access; Up link grant-free; Activ e user equipments detection I . I N T RO D U C T I O N Fifth gener a tio n mobile networking (5G) is expected to support a scenario with low latency and massi ve conne c ti vity , such as the one of the three key usage scenario s Massiv e machine type commun ication ( mMTC). While the current lon g term e volution (L TE) system is not ef ficient enough , e sp ecially in the uplin k (UL) multi-user access scenar io. Sparse code multiple access (SCMA) [1] as a new multip le access te c h nolog y for m assi ve conn ectivity , can en h ance the maximum nu mber o f accessible user eq uipmen ts ( UEs) in wireless channels. The incoming data streams are map ped to codewords o f different multi-dime n sional codeb ooks and these sparse codebook s can share the same time-fr equency resources of o rthogo nal frequency division multiple ac c e ss (OFDMA). Due to th e sparse char acteristic of codewords, rec eiv er can use th e message passing algorithm (MP A), which c a n achieve near-optimal detection with low complexity . T o reduce the tr ansmission latency , UL g r ant-free tran s- formation is pro posed, which also can redu c e the overhead associated with control signals for sched u ling. In UL grant- free multiple-access scen ario, UE s are allowed to tran smit d ata in pre-sch eduled resources at any time. The p re-schedu led resources is c a lled co ntention transmission un it (CTU), wh ich includes tim e, f requen cy , co deboo ks f or active UEs [2]. So this requires the receiver to b e able to detect active UE s with out the kno wledge of active codebo oks and pilots, to estimate their fading channels, and to deco de their data, . In [ 3], a n active UE d etector ( A UD) modu le has b een propo sed to detect active UEs and reduce the numb er of potential active UEs. By u tilizing the orthogo nality of pilots of different UEs an d using the rece ived pilot signal, A UD module can id entify the status of UEs. Then, an join t m essage passing alg o rithm (JMP A) was p roposed to elimin ate the false detected in activ e UEs cau sed by A UD module and dec ode th e data of acti ve UEs. Despite the A UD mo dule h a s a not very high acti ve UEs detection accuracy , but it can cut d own the complexity of JMP A. The pilots of CTU are used a s a k nown condition at the receiver , and th ey are always calculated in f orm of a matrix . Because the pilot m atrix satisfies the restricted isometr y prop- erty ( RIP) with a h igh p robab ility and the sig n al mo del h as sparse ch a r acteristic fo r A UD modu le, active UEs detectio n can be solved well through compr essi ve sensing (CS) theory . The classical CS theories are com pressiv e samplin g matching pursuit (CoSaMP) [4] and iterative support de te c tion (ISD) [5]. A modified version of the o riginal ISD algorith m called the structu red ISD (SISD) was p ropo sed in [6], which can jointly d e tect the activ e UEs and the receiv ed data in several continuo us time slots. In [7], a novel sparsity-inspired sphere decodin g (SI-SD) alg orithm was prop osed to integrate A UD into JMP A m odules, with a lower compu ta tio nal complexity av oiding the r edund a n t pilot o verhead. Howe ver , the above two algorithm s in [6] and [7] are assume that the channel gain of all potential UEs is already know witho ut th e discussion of the way to get them. Actu a lly th e receiver can n ot estimate c hannel gain of the inactive UE who transmit noting to r eceiv er . In [8], [9], a n algorithm based on the framew ork of sparse bayesian learning (SBL) is pro p osed to redu ce the requir e m ent of pilots overhead and impr ove acti ve UEs d etection performan ce f or A UD m odule. Despite the practical scen a rio is u n der f requen cy selecti ve ch annel, th e SBL algor ithms of A UD module is still realized based on th e assumptio n that active UEs go throug h a flat fading channel. So the acti ve UEs detection per f ormanc e of the A UD algorithms will become in a c curate. In this paper, a new refin ed A UD (RA UD) m odule is propo sed to enhance the acti ve UEs detection accuracy of the receiver in an UL g r ant-free SCMA system. By m a king fu ll Fig. 1. (a) De finition of CTU; (b) an example of sign aling fo r a grant-free random access user who use s 2 pilot and corresponding C 1 codebook . use of the channel gain and analyzing the dif ference between characteristic values o f th e two status of UEs, the RA UD module makes the recei ver have b etter active UEs detection accuracy and a d aptability in frequen cy selective channel. In Section II , we introduce an original scheme of the grant-fr e e SCMA acc ess mo del, then analyze th e principle, advantages and d isadvantages of A UD, chan nel estimator ( CE) and JMP A module. Section III is de voted to describ e the RA UD module and the two-step A UD receiver contain s RA UD module. Numerical results are provided in Section IV to ev aluate the perfor mance of th e proposed two-step A UD receiver in UL grant-f r ee SCMA scenario, and th e conclud ing r e marks are giv en in Section V . I I . S Y S T E M M O D E L A. UL Grant-free S CMA T ransmitter • SCMA encod e r An SCMA deco d er can be seen as a mapper fro m log 2 M bits to a codew ord in the T -dimension al complex co d ebook with size M . The T dimen sio nal codew ord of the codeb ook is a sparse vector with N non- zero elemen ts, i.e., N < T . Then, different UEs’ co d ew ords will share the same time-frequency resources to be tr ansmitted. • Codeboo ks and pilots selection In the UL grant-f ree SCMA scenario, a b asic resource called CTU is known f or tr ansmitter an d r e c eiv er , which is defined as a comb ination of SCMA codebook s for encodin g data and d etecting acti ve UEs, pilots fo r identifying UEs and estimating chan n el, an d time-freq uency resour ce. As shown in Fig. 1 (a), over a time- f requen cy resourc e, there are J group s, each of them includes on e co deboo k C and L pilots S . The codebook in each gr o up corre sponds to the same Zadoff- Chu ( ZC) seq u ence, but with different cyclic-shifts on th e sequence to generate different pilots [10] [ 11]. Th e location of the p ilot in OFDM timefrequen cy grid can ref erence L TE UL Demodula te d Reference Signal (DMRS) [12] [13], a s show in Fig. 1 ( b ). He n ce, a to tal K = J × L uniq ue pilots { s 1 , · · · , s K } , called pilo t pool, is pre- d efined. In a cell with a large n umber of UEs, if sm a ll subsets of these UEs h av e data stream s to be transmitted, each of Fig. 2. UL grant -free SCMA rece i ver structure incl uding acti v e UE detect or , channe l estimator and JMP A. them has to randomly select a pilot from the pilot pool and a correspo n ding co d ebook fro m the CTU. Then, the data stre a ms can be mapped to codew ords and tran smitted with the pilot, represented in Fig. 1 (b). These UEs who transmit data ar e called acti ve UEs, while o ther U E s are called inactive UEs. Therefo re, the receiver of the UL grant-fr ee SCMA system has to decode data of activ e UEs witho u t the knowledge of UEs’ status, codeb ooks and pilots they selected. B. UL Grant-free S CMA Receiver In [3], the UL grant-free SCMA r eceiv er structure can be shown as Fig. 2. There are th ree mod ules in the receiver structure, i.e., A UD, CE and JMP A. The inp ut are the r e ceiv ed pilot signal and the rece i ved data signal. The ou tput is the decoded data of the acti ve UEs. • Activ e UE Detector The A UD mo dule is ab le to iden tify activ e UEs/pilots and red uce the size of the potential UE list f orm K to P , P ≪ K . Th e received pilo t signal mo del for A UD is represented in Eq .(1), where y pilot = [ y 1 , y y 2 , · · · , y Q ] T is the received pilot sign al, Q is the leng th of the sequence. S is the pilot matrix containing K p o tential pilot sequences. s k = [ s k 1 , s k 2 , · · · , s kQ ] T is the k -th p ilo t sequen ce. Each element o f the spar se signal h co rrespond s to one pilot. n = [ n 1 , n 2 , · · · , n Q ] T is the noise vector f o llowing the distribution C N  0 , σ 2 I N  . y pilot = Sh + n =      s 11 s 21 · · · s K 1 s 12 s 22 · · · s K 2 . . . . . . . . . . . . s 1 Q s 2 Q · · · s K Q      ·      h 1 h 2 . . . h K      + n (1) The activ e UE s/pilots dete c tio n pro blem can be seen as compressed sensing fo r the sparse characteristic o f h in Eq.(1) . Afte r com pressed sensing algo rithm, such as foc a l underd etermined system solver (FOCUSS) [1 4], the status of k -th pilot/codeboo k can be identified by th e size of | h k | 2 . W e call | h k | 2 characteristic value of k -th UE. If | h k | 2 ≥ λ AU D , the k -th UE/pilot is declared to be active. The value of λ AU D is usually set to 0 .01. • Channel Estimator The CE module can estimate channel g a in from the re c eiv ed pilot signal y pilot and the P p otential active pilot sequen ces. The rece ived pilot sign al mo del for CE module is repre sen ted in Eq.( 2). y pilot = P X p =1 diag ( h p ) s p + n (2) Although Eq .(2) is the same as Eq .(1) in regard to the received pilot signal y pilot , there are still some difference. Firstly , there is a total of P p otential acti ve pilo t sequences left after A UD module. Secondly , ea c h pilo t sequen ce s k = [ s p 1 , s p 1 · · · , s pQ ] T correspo n ds to o n e channe l gain vector h p = [ h p 1 , h p 2 , · · · , h pQ ] in pilot lo cation of p -th UE. The mature channel estimation alg orithm, such as Minimum Mean Square Erro r (MMSE), has a better perf ormanc e . For a fr equency selecti ve chann el, the sym bols in a pilot sequence over d ifferent subcarriers will correspo nd to dif ferent fading values. Theref ore, compar ing h in Eq.(1 ) with h in Eq.(2) , the receiv ed pilo t signal mode l of CE module is mo re accurate than the mode l of A UD mo dule. But m eanwhile, there are two ad vantages th at A UD mo dule use Eq. (1) as the calculatio n model. Firstly , the mo d el can b e solved well through mature CS theory . Second ly , it makes algo rithm complexity lower than the m odel in Eq.(2) does, because the number o f p ilot sequen ces in pilot po ol K is a big or d ers of magnitud e. • JMP A On a c c ount of th e small- scale deep f ading chan nel and sig- nal noise, the inaccur a cy of A UD modu le is dif ficult to a v oid. Then, in [3], the functio n of JMP A algorithm is propo sed to identify the false detec te d inactive UEs furth e r and d e code the data of the real active UEs. The receiv ed d ata signal vector y data = [ y 1 , y y 2 , · · · , y Q ] T for JMP A is obtain ed from Eq.(3 ). y data = P X p =1 diag ( g p ) x p + n (3) where g p is the chan nel g ain in data location and x p is the codeword symbols f or p -th active UE. n is the noise vector following the distrib ution C N  0 , σ 2 I N  . JMP A alg o rithm specifically contains two steps: Step1 : Identify inactive UEs and remove them from the potential UE list. I f an inacti ve UE has n o codewords mapped from data stream to transmit, it is equ i valent to tr ansmit zero codewords, whose values are z ero. In fact, JMP A can be considered as MP A which use the ne w codebook contains zero codeword. T herefor e, JMP A can identify inactive UEs fro m the probab ility o f zero codeword and nonzero cod ew ord. W e may expect that the prob a bility of zero codeword for inacti ve UEs is much hig her than that for acti ve UE s. This gap enable JMP A to iden tify the status of UEs. Step2 : Use the MP A algo r ithm to decode the data of the real activ e UEs. In the practical simulation for JMP A module , there are some factors th at m a ke the acti ve UEs detection perf ormance n ot as ideal as the above e xpectatio n. Firstly , th e transmission power of inactive UEs, wh o transmit zero codewords, is much lower than th a t of active UEs. Secon dly , the ch a n nel gain of ina c tive UEs, whose pilot seq uence is not includ ed in the received pilot signal in Eq.(2) , is lo wer than that of activ e UEs. Meanwhile the JMP A mo dule consider that the n o ise power o f inactive UEs is same as that of acti ve UEs. So, the equiv alent signal noise ratio (SNR) of inactiv e UE s is lo wer than th at of ac ti ve UEs. For JMP A, the probability of zero codew ord of inacti ve UEs will be clo se to or e ven lower than that of active UEs. That makes it hard to id entify the status of UEs. I I I . T W O - S T E P AU D R E C E I V E R F O R U L G R A N T - F R E E S C M A S Y S T E M In Section II, the prin ciple, a d vantages and disadvantages of A UD module ha ve been analyzed. Then we intend to use the implicit informatio n in received pilot signal, which is neglected by A UD m odule. And in this w ay , the inactive UEs misinterpreted by A UD module can be selected o u t. Observing Eq.(1), the r e ceiv ed pilo t signal mo d el o f A UD module, an d E q.(2), the received signal m odel of CE module. The received p ilot signal y pilot doesn’t con ta in the pilot informa tio n of inactiv e UEs. And there is a strong cor relation between p ilots s o f different UEs. Theref ore, in A U D mo dule, the e stima te d coefficient h of s f or inacti ve UE tends to zer o. Also, in CE m odule, th e estimated coefficient h of s for inactive UE tend s to zero vector . In other word s, from the receiver’ s point of view , a n inactive U E can be con sidered as a UE who goes through an infinitely deep fading chann el. It is analyzed in Section II that h contains more su bcarrier informa tio n than h a n d can accurately reflect the chan n el informa tio n. Theref ore, h can be used to select out the inacti ve UEs that A UD mod ule misinterpreted. Then, we pr opose a RA UD module that takes the channel gain vector h as input. By using the difference betwe e n ac tive UEs and in activ e UEs about h , the RA UD m odule can outpu t a refined active UE list. In order to distinguish th e h of the two status o f UEs, we define a metric called F characteristic value. The value of F is ob ta in ed fro m 1-nor m || h || 1 or 2-norm || h || 2 . Mea nwhile, a thr eshold λ RAU D should b e set to d istinguish the F of UEs in different status. Different from the threshold λ AU D of A UD module, λ RAU D is related to SNR . As SNR increases, channel estimation err or is red uced, and the F of inactive UEs will be much m ore tends to z ero. Th en, the v alue of λ RAU D should be reduced to adapt the ne w characteristic v alue. W e do a lot of UL gr a nt-free transmission tests for UEs with known status under different SNR, and o btain a collec tio n of F cha racteristic values. By an alyzing the size of F and their corresp onding UE status, an empirical curve λ RAU D ( S N R ) related to SNR is obtained. Then th e following RA UD algorithm achieving th e cap abil- ity to identif y UEs status can be developed acco rding to the theory a n d analysis above. I t can b e seen that the algorithm has o nly a few nor m and comp arison oper ations, and the ad ded complexity of the RA UD algorith m is very low co mpared to the entire UL gr ant-free SCMA receiver . Algorithm 1 RA UD alg o rithm Input: Equiv alent fading channel gain vector of potential pilots: { h 1 , h 2 , ..., h P } Potential UE list: { 1 , ..., P } Signal noise ratio : S N R Output: Equiv alent fading channel gain vector of acti ve pilots: { h 1 , h 2 , ..., h R } Activ e UE list: { 1 , ..., R } 1: p = 1 2: while p ≤ P do 3: F p = || h p || 1 or || h p || 2 4: if F p ≥ λ RAU D ( S N R ) then 5: p → Active UE list 6: else 7: Delete h p in { h 1 , h 2 , ..., h P } 8: end if 9: p = p + 1 10: end while The improved UL grant- free SCMA re c e i ver is d epicted in Fig. 3. For th e RA UD m odule is a further operatio n on the potential UE list after A UD mod ule, the improved r eceiv er is also called two-step A UD receiver . Fig. 2 , which replaces th e JMP A module with th e MP A module, is called o ne-step A UD receiver . The o peration flow of the two-step A UD r eceiv er structure can be describ ed in the following. A UD mo dule use the receiv ed pilot signal to identity inactive UEs/pilots and reduc e the nu mber of potential active UEs/pilots fr o m K to P . Then CE modu le perfo rms cha nnel estimatio n to get P equiv alent fading chan nel plural vectors. Each poten- tial ac tive UE correspon ds to on e F characteristic v alue. F and λ RAU D ( S N R ) can be used to distingu ish the status of UEs/pilots in RA UD modu le. Then, the length of po tential UE list can be r educed from P to R . Finally , MP A d ecoder decode the data of R real acti ve UEs. I V . S I M U L A T I O N R E S U L T S In the UL gran t-free scenario, the miss detection proba bility and false alarm prob ability are important parameter s for m ea- suring receiver perfor mance. The miss detection pro bability is defined as th e ratio of the number of active UEs misinterpreted as in activ e UEs to the to ta l numb er o f active UEs. Miss detection me a ns that the lo ss of activ e UEs data. The false alarm pr obability is defined as th e ra tio of th e nu mber of inactive UEs regard ed as active UEs to the total number of Fig. 3. UL grant-fre e SCMA two-step AUD recei v er structure including acti ve UE detector , chan nel estimator , RA UD module, and MP A decoder . inactive UEs. High false alarm prob ability will lead to MP A decodin g perfo rmance d egradation a n d increased com puta- tional complexity . In order to make the perfo rmance of tw o- step A U D recei ver better than the one-step A UD receiver , we divide the function of the modules. Th e A UD modu le is mainly used to reduce the miss detection probability , while the RA UD module is aimed to r educe the false alar m pro bability with out increasing miss detection p robability . Let us consider an UL grant-free SCMA sy stem. Th e simulation p arameters are sho wn in the T able I . Ref e r to Fig. 1, there are six different co deboo ks assign ed to different g r oups in our simulation. The cod e book in each group correspond s to three pilo ts. The length o f pilot seque n ce is six resource blocks (RBs). T ABLE I S I M U L AT I O N P A R A M E T E R S Descripti on V alues Potenti al UE s 18 Acti ve UEs 6 The Number of Pilot Sequences 18 The Number of Codebooks 6 The length of Pilot Sequence 6RB Channel model EP A/EV A [15] A UD algorith m FOCUSS A. Effect of false ala rm pr ob ability High false alar m prob ability means tha t there are many inactive UEs enter th e MP A deco der . On the o ne h and, these inactive UEs will interf ere with the deco ding of acti ve user data. Fig. 4 shows the impa c t of different false alarm probab ility o n BER p e rforma n ce un der the EP A c h annel. Note that the BER perf ormanc e deteriorates with the increase of the false alar m p robab ility . One the other hand , inactive UEs could incr e a se the co mputation al co mplexity of MP A deco der, thereby increasing the transmission d elay . The co mplexity of MP A dec o ding algor ithm can b e simply expr essed by the Eq.(4) [16]. O ( N iter S F X i =1 M d ( i ) p ) (4) where N iter is the nu mber of iteration s. S F indicates the tota l number o f th e tim e - freque n cy resou rces of OFDMA u sed b y the UEs. M p is the ord er of mod ulation. d ( i ) indicates the number of UEs occupying the i -th r esource. The increase of the nu mber of in activ e UEs leads to increased d ( i ) , which makes the computa tio nal complexity of MP A decoding algo- rithm increase exponentially . Therefore, reducing false alarm probab ility is necessary for the UL gra nt-free SCMA rec e i ver . Fig. 4. Effe ct of false alarm probabilit y on BER performance . B. The characteristic value of UEs Fig. 5 shows the probability distribution ab out normalized characteristic values o f UEs. The red and blue h istog ram represent inactive and active UEs respectively . Wh e th er the A UD modu le or th e RA UD module, their working principle is to u se the difference b etween the ch a racteristic values of activ e UEs and inacti ve UEs to id entify the UEs’ status. If there is no o bvio us difference betwee n the character istic values of the two status of UEs, it is dif ficult to set a threshold to accurately d istinguish them . Comparin g Fig. 5 (a) an d Fig.5 (b), Fig. 5 (c) and Fig. 5 ( d), the overlappin g area o f the one-step A UD receiver is larger than that of two-step A UD receiver under the EP A channel and EV A chan nel. Therefore, two-step A UD recei ver can identify UEs’ statu s more accu racy than o ne-step A UD recei ver . At the same time, we can see that when the receiv er’ s channel changes from EP A to EV A, the overlapping area incr eases. T hat mean s bo th rece i vers will experience a drop in activ e UEs detection p erform ance with the enh ancement of channel frequen cy selection . Fig. 5. Histogram of the UEs’ char acterist ic v alue with/ without RA UD module under E P A/EV A channel. Fig. 6. Miss Detecti on Probability . C. P erforma nce comparison In ord e r to make the two-step A UD receiver has a lower miss detectio n pr obability than the on e-step A UD receiver . W e reduce the thr eshold λ AU D of A UD module in the two- step A UD receiv er from 0.01 to 0. 007. As shown in Fig. 6 , Fig. 7. False Alarm Probabilit y . either und er EP A cha n nel or EV A chan nel, a lower v alue of λ AU D makes lo wer miss detectio n probability . But at the same time, λ AU D =0.007 makes a hig her false alarm proba b ility , as sh own in Fig. 7. Aiming at this prob lem, the ad dition of the RA UD m odule can effectiv ely red u ce the false alarm probab ility , while almost n o t inc r easing the miss detection probab ility . Observing curve A UD( λ AU D =0.01) and c u rve A UD( λ AU D =0.007 )+RA UD(1 -norm ) in Fig. 7. Comp ared to EP A chann el, RA UD module reduces false alarm pro bability more obviou sly und er EV A chan nel. It also can b e seen that the RA UD a lg orithm has the same perfo rmance wheth er 1-norm or 2-no rm is used. From the figures above, it can b e confirmed that the two- step A UD rece i ver can bring lower miss detection proba b il- ity and false alarm proba b ility than one-step A UD receiver . Meanwhile, the RA UD modu le can redu ce the computatio nal complexity of MP A decod er and o ptimize the d ecoding per- forman ce. Actually , the RA U D m odule ca n mo re effectively reduce the false alarm pro bability und e r EV A chan nel and improves the adaptab ility of UL gr a nt-free SCMA re ceiv er in freq uency selective channel. V . C O N C L U S I O N In this paper, we intr o duce the transmitter and the original receiver of SCMA multiple access in the U L grant-free sce- nario, and analy ze the principle , advantages and disadvantages of A UD, CE and JMP A mo dule. T hen, we pr opose a two-step A UD receiver schem e contain s RA UD mo dule. B y making full use of the channel gain and analyzing the dif ference between characteristic values o f th e two status of UEs, the RA UD module c a n selected out the inactiv e UEs tha t A UD module misinterpreted . Finally , we verify that the lower false alarm probab ility is beneficial to improve th e decoding p erform a nce and r educe the com putational co mplexity of MP A decoder . The simu lation results show that the two-step A UD receiver has lower miss d etection pro bability and false alarm pr oba- bility than the one-step A U D receiver , especially und er the frequen cy selectiv e channel. Fr o m analy sis and simulation re- sults, it is co nfirmed that the pro posed two-step A UD receiver provide a way of designing an UL gran t-free SCMA system for adaptin g the frequency selecti ve channel. 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