Deep Learning Based Fast Multiuser Detection for Massive Machine-Type Communication

1 Deep Learning Based F ast Multiuser Detect ion for Massi v e Mac hine-T ype Co mmu nication Y anna Bai, Bo Ai, Senior Me mber , IEEE , and W ei Chen*, Senior Member , IEEE Abstract —Massiv e machine-type communication (MTC) with sporadically transmitted small p ackets and low data rate requires new designs on the PHY and MA C laye r with light transmission ov erhead. Compressi ve sensing based mul tiuser detection (CS- MUD) is designed to d etect activ e users through random access with low o verhead by exploiting sparsity , i.e., the nature o f sporadic transmissions in MTC. Ho wev er , the high computational complexity of con ventional sparse r econstruction algorithms prohibits the i mplementation of CS-MUD in rea l communication systems. T o ov erco me this drawback, i n th is paper , we propose a fast Deep learning based approa ch for CS-MUD in massive MTC systems. In particular , a novel bl ock restrictiv e activ ation nonlinear unit, is proposed to capture the block sp arse structure in wid e-band wireless communication systems (or multi-antenna systems). Our simulation r esults sho w that the proposed appro ach outperfor ms various existing algorithms f or CS-MUD and allows fo r ten-fold decrea se of the computing time. Index T erms —Massiv e machine-type communication, random access, deep learning. I . I N T RO D U C T I O N R ECENT years observe a growing interest in massive machine-ty pe communica tio n (MTC) owing to the rapid development of In ternet of Things and 5G [1]. In a typical MTC com munication scene, a massi ve numb er of nod es spo- radically transmit small packets with a low da ta rate, which is quite different to curren t cellu lar systems that are d esigned to suppo rt high data rates an d reliable conne c tions o f a small number of user s per cell. Commu nication overhead takes up a larger portio n of r esources in the MTC scene, and thus more efficient access method s are need ed. One po tential ap proach to redu ce the co mmunicatio n overhead is to av oid or r educe control sign aling overhead regarding the a c ti vity o f devices before tran smission. An im p ortant issue in massive MTC is acce ss cong e stion owing to the large num ber of MTC devices. In [2], f our approa c h es, i.e. , backoff-based scheme, access class barring based scheme, separating ran d om access ch annel (RA CH) resources and dyanam ic allocatio n of RA CH resource s, are introdu c ed to deal with acc e ss congestion. Howev er , th o se approa c h es does not effectiv ely redu ce sig naling overhead. In massi ve MTC with sporadic commu n ication, a comp ressiv e sensing (CS) based multiuser detectio n (MUD) [3], [4] is propo sed to joint detect u ser activity and data with a k nown channel state informa tion (CSI), wh ich redu ces commu nica- tion overhead by elimin ating contr o l signaling. In p ractical systems where CSI is unknown, a CS b ased joint activity and Y anna Bai, Bo A i and W ei Chen are w ith the Stat e Ke y Lab of Rail Tra f fic Control and Safet y , Beijing Jiaotong Uni versity , Beijing, China (e- mail: 16125001,boai,mmni,weich@bj tu.edu.cn). Correspondi ng author: W ei Chen. channel detection metho d is proposed in [5], where each nod e is assign ed a uniqu e pilot sequence f o r chann el estimation. The cost brou ght by the CS-MUD approach is the effort in solving a sparse estimation problem , which requ ires iterati ve algorithm s, e.g., ortho g onal matching pursuit (OMP) [6]. How- ev er , these iterative algorithm s are designed and optim ized for achieving a hig h er accur a cy and/or theoretically guar anteed conv ergence and fail to consider time constraints. Apply - ing iterative steps in trad itional sparse estimation algo rithms until a c hieving convergence would increases co mmunica tio n latency ( especially when the nu mber of nod es is large), wh ich is critical in some applications. It then naturally begs the question: can we red uce the sign aling overhead for MTC without sign ificantly sacrifice o n the laten cy . In this paper, we pr opose a fast Deep Learning (DL) based approa c h for MUD in massi ve MTC systems. As on e of the most h ig hly soug ht-after skills in technolo gy , DL [ 7] has been applied to various fields including comp uter vision [8], speech reco gnition [9], and langua ge translation [10] and got great success. As a branch of mach ine learnin g, DL, which usually refers to deep neur al networks (DNNs), con sumes a large amo unt of train ing data to learn param eters in a neural network. Whe n the neur a l ne twork has a suf ficient n u mber of hidden units, it can appr o ximate a large class of piecewise smooth f u nctions [1 1]. Altho ugh the training process o f the propo sed DL based app roach is time con suming, it can be condu c te d o ff-line with synthe tica lly gener ated data. For the inference task, i. e., MUD, the computing complexity of the trained DNN is low , as it only inv olves a nu mber of vector- matrix multiplication s/summations and eleme n t-wise no nlinear operation s. In addition , for wid e-band wireless commu nication systems or multi-a n tenna systems, the tra n smitted signal ar r iv es at the receiv er with multiple paths or multiple links, wh ich leads to a block sp a rse CSI vector . Capitalizing on the blo ck sparse structure, we furth er propose a novel b lock restricti ve activ atio n nonlin ear un it, which is distinct to existing a c ti vation function s in DNNs [12], [13]. Experim ents de monstrate the efficiency an d effecti veness of the pro posed bloc k-restrict neural network (BR NN) in compared with existing me thods. I I . B A C K G RO U N D A. System Description In this paper , we consider a massi ve MTC scenario where multiple devices communic a te with a b ase station (BS), a s shown in Fig. 1. W ithout lo ss o f ge nerality , o nly n devices out of K d evices hav e data to b e transmitted to the BS in one frame. For simp licity , we assume that all frames are received 2 Fig. 1. A star-t opology for the massiv e MT C scenario. synchro n ous at the BS. Each user is assigned a unique pilo t sequence s k ( k = 1 , . . . , K ) with the length N s for ch annel estimation. E ach symbol of the pilot sequ ence is ch osen fr o m the modulation alpha bet A . The channel vector h k of user k is d enoted by h k ∈ C L , wh e r e C denotes th e set of comp lex number s. Th e conv olution o f the chann el vector and the pilot sequence s k can be expressed as the matrix multiplication by rewriting th e conv o lution matrix of the tra n smitted pilot sequence of user k as ˆ S k =           s k, 1 0 · · · s k, 2 s k, 1 . . . . . . . . . s k,N s s k,N s − 1 0 s k,N s 0 0 . . .           ∈ C N , where N = ( N s + L − 1) × L . Then the sign a l received at the BS is gi ven by y = K X k =1 a k ˆ S k h k + n , (1) where n den otes add iti ve wh ite Gaussian noise, and a k ∈ { 0 , 1 } denotes the activity of user k . a k = 1 an d a k = 0 indicate active user and silen t user , respecti vely . Now we con struct th e pilot matrix of all user as ˆ S = [ ˆ S 1 , . . . , ˆ S K ] ∈ C ( N s + L − 1) × K L , th e ch annel vector of all user as h = [ h T 1 , . . . , h T K ] T ∈ C K L , and the user activity matrix as A = d iag ( a 1 I , . . . , a K I ) ∈ R K L × K L , where diag ( · ) denotes the transformatio n of a vector in to a d iagonal m atrix. Then the eq uation (1) can be reexpressed as y = ˆ SAh + n = ˆ Sx + n , (2) where x = Ah is a b lock sparse vector with n non zero b locks correspo n ding to acti ve users. By r econstructin g x fr o m y , we simultaneou sly detect active u sers and estimate their ch a n nel. Therefo re, the p r oblem boils down to solve the following optimization pr oblem min x    y − ˆ Sx    2 2 , s.t. k x k 0 ≤ n L, (3) where k · k 0 denotes the ℓ 0 norm th at cou nts the number of nonzer o elem ents. Note that the optim iz a tion pro blem in (3) is NP-hard, and po pular a p proxim ations with v arying degrees o f co mputation al overhead include con vex relaxation methods [14] and iterative algo r ithms [15]. B. Deep Neural Network From th e perspec ti ve o f DL, the p rocess that solves the optimization problem in (3) could be seen as a black box, which is e xpressed as a functio n g ( y , ˆ S , θ ) = a rg min k x k 0 ≤ nL    y − ˆ Sx    2 2 , (4) where θ denotes a set of parameter s. Giv en a set of training examples D = { x ( i ) , y ( i ) } i , a DNN is learned to m a p each input y ( i ) to a desired outco me by sev eral succ essi ve layers of lin ear transfor m ation interleaved with element- wise non - linear transforms. For an ord inary f eedforward n e ural network (FNN), the t th layer can be expressed as x t +1 = f ( W t x t + b t ) , (5) where the weig ht matr ix W t and the bias vector b t are parameters to be learned, an d f ( · ) denotes some non-linea r operator, e.g . , rectilinear un its (RELU). V arious DNN designs f o r th e sp a r sity enforcin g problem as (3) h ave be e n pro posed in literature. For example, in compariso n to the ordinar y FNN layers as defined in (5), a learned iterativ e shr inkage and thresho lding algo rithm (LIST A) is propo sed in [16], wher e different layers share same p a- rameters, i.e., W and b . Fu r thermor e, the no nlinear u nit f [ · ] adopted in LIST A is the elem e n t-wise soft-threshold ing func - tion f [ x ] = sig n ( x ) max { 0 , | x | − δ } , where δ is the shr inkage parameter . An IHT -net is proposed in [12], which is th e same as LIST A except fo r using a hard thr esholding function f [ x ] = sig n { x } max { 0 , | x |} as the nonlinear unit. While both L IST A and I H T -net use sha red weig h ts among layers, au th ors in [13] propo se to use or dinary FNN where layers do not have shared weights, and incorp o rate batch no rmalization [ 17] and residual connectio n [8] to reasonably initialize the neural network and to prevent v anishing/explod ing gradie n ts, respectiv ely . I I I . P RO P O S E D A P P R O AC H A. Network Structure The mo st straightfor ward DNN d esign for tacklin g a regre s- sion problem as in (3 ) is to map the rec e i ved sign al y to some outcome x . In v iew of the fact that a spar se x can be obtain e d by the least sq u are e stima to r g iven its suppo rt, it is would be mor e capacity- efficient to u se a D NN to app r oximate the mapping from y to the support o f x . Ther efore, we co n sider to use DNN for detecting acti ve users, which leads to a multi- label classification problem. Furthermo re, in wideband wireless communicatio n systems, x b ecomes a block sparse vector 1 with the block size L . It would be beneficial to incorpo rate this prior inform ation into the structure of the designed DNN. Here, we propo se to use a new block acti vation unit f ( x 1 , . . . , x L ) = sign (max { 0 , x 1 , . . . , x L } ) · [ x 1 , . . . , x L ] , (6) 1 For narro wband systems ( L = 1 ) with multiple antenna s at the BS, x is also a block sparse vecto r , where the block length is the number of antenna s. 3 Fig. 2. The structu re of the proposed BRNN. where a block of e le m ents are jointly acti vated if one elemen t is g reater than zero. Here sign ( · ) denotes th e sign fu n ction. Batch normalization is added for reasonable in itialization and residual connec tion is used to prevent vanishing/explod in g gradients. Furth ermore, we ad opt a p o oling layer b efore the last sof tmax layer to for c e the ou tput of the n etwork to indica te the acti ve users. R ELU is employed in the first a fe w layers, while the block activation unit is used in th e remaining lay ers. The last layer of BRNN employs th e softmax cross entro py loss functio n. This proposed network is named a s BRNN, and its stru cture is illustrated in Fig. 2 . B. T raining Data Gen eration A comm o n issue in app lying DL to wir e le ss c ommun ic a tion is the difficulty of collec tin g massive real data. Fortun ately , for solving the o p timization pro blem in (3) by a DNN, we cou ld use synthetically g enerated d ata fo r train ing. In specific, to obtain each training data, we first g enerate a r andom no ise vector n and a ran dom block sparse vector x whose support is used as the label, and then gener ate y by simply applyin g (1). Ma ssi ve training d a ta can be gen erated in this way , and the tr a ining pr ocess can be d o ne in an o ff-line manner . Once parameters of BRNN is learned, u sing this neura l network for inference, i.e., de te c ting active users in ne w d ataset, is compu tational inexpensive, as it only in volves a nu m ber of vector-matrix mu ltiplications/summa tio ns and elemen t- wise nonlinear o perations. W e would also like to emp hasize that the r e q uired amou nt of training data depen ds o n the numb er of n o des and the nu mber of acti ve nod es. W ith K nodes in total, there are  K n  different labels f or n active nodes. This number increa ses qu ick ly with the g row of n . T herefor e, in stead of generating the training data with a random activ e user nu mber, we fix the nu mber o f activ e node close to the lim it of traditional iterative algorithms for solv in g (3). I V . E X P E R I M E N T S In this section , we inv estigate the perfo r mance of the propo sed BRNN fo r MUD in MTC. In the experim ents, we co nsider K = 1 00 users in to tal, an d the activ e users transmit N s pilot sym bols with binary p hase shif t keying (BPSK) mod ulation. The chann el is modeled by L = 6 indepen d ent identically Ray le ig h distributed taps. Th e receiver noise n is generated b y a zero mean Gaussian vector with variance ad ju sted to have a desired value of the signal to noise ratio ( SNR). As K > N s + L − 1 L , the MUD p roblem is underd etermined . The propo sed BRNN is comp ared with several iterative sparse estimatio n alg orithms, in cluding o rthogo nal matching pursuit (OMP) [6], iterative hard th resholding (IHT) [1 5] and their extensions for block structur e, i.e., BOMP [18] and BIHT [19]. The DNN pro posed in [13] is also comp ared to emph a size the g ain brough t by BRNN. The detection o f multiuser is considered to be successful if er ror occur s. In our experimen ts, we g enerate 8 × 10 6 different samples for training, 10 5 samples for verification and 10 5 samples for testing. For a ll the generated data samples, we ad d ad ditiv e white Gaussian noise with a signal-to-noise ratio (SNR) o f 10 dB. In the trainin g data and verification data, we ran domly activ ate 6 no des, while in the test data, n ≤ 6 acti ve users a r e random ly selected. The optimizer adopte d for training neura l networks is stocha stic grad ient descen t with a m omentum 0 .9 and a learning rate 0.0 1. The batch size is fixed to 250. A. Con ver gence P erformance an d Comp utation Efficiency W e fir st inv estigate the co n vergence pe r forman ce of DNN and the pro posed BRNN in the train ing proc e ss. Th e pilot length of eac h u ser is fixed as N s = 40 . W e use the same initialization for DNN and BRNN as suggested in [2 0] and train the two neura l networks with the same learning r a te . The cross-entropy loss in the training proce ss is calculated for ev ery 100 b atches, and the r e sults are sho wn in Fig. 3( a). In addition to the cross-entropy loss, Fig. 3(b) shows the ratio o f successfully de te c te d users in the training proce ss. As shown in Fig. 3, be nefited from the block activ ation unit (6), BRNN conv erges mu c h faster and achieves a lower training lo ss than DNN, which fails to inco rporate the pr ior knowledge on the structure of the signal supp o rt. Then we investigate the computatio n efficiency o f in ference using testing data. The averaged computin g tim e for testing one d ata samp le is given in T able I. Note that altho ugh we use GPU to sp e ed up the training process for BRNN and DNN, for a fair comp a r ison of compu tational complexity we u se CPU for th e testing data for all the compared app r oaches includ ing OMP , BOMP , IHT , BIHT , DNN an d BRNN. These simulations are performed on a computer with a quad-core 4 .2GHz CPU 4 0 1 2 3 Batch index 10 5 18 20 22 24 26 28 Cross-entropy loss BRNN DNN (a) Cross-entr opy loss 0 1 2 3 Batch index 10 5 0 0.2 0.4 0.6 Ratio of successfully detected users BRNN DNN (b) Ratio of succe ssfully dete cted users Fig. 3. The con verg ence performance of DNN and BRNN. T ABLE I A V E R A G E D C O M P UT I N G T I M E F O R M ULT I U S E R D E T E C T I O N ( I N S EC O N D S ) . ( N s , n ) DNN/BRNN IHT BIHT OMP BOMP (30 , 3) 2 . 57 × 10 − 4 0 . 162 0 . 173 0 . 007 0 . 007 (30 , 6) 2 . 57 × 10 − 4 0 . 009 0 . 163 0 . 007 0 . 009 (40 , 3) 2 . 56 × 10 − 4 0 . 183 0 . 159 0 . 009 0 . 006 (40 , 6) 2 . 56 × 10 − 4 0 . 021 0 . 177 0 . 010 0 . 010 (50 , 3) 2 . 58 × 10 − 4 0 . 193 0 . 141 0 . 011 0 . 006 (50 , 6) 2 . 58 × 10 − 4 0 . 085 0 . 183 0 . 0136 0 . 012 0.01 0.02 0.03 0.04 0.05 0.06 n/K 0 0.2 0.4 0.6 0.8 1 Success Rate DNN BRNN OMP BOMP IHT BIHT (a) Success rate vs. n K ( N s = 40 ) 30 35 40 45 50 55 60 Ns 0 0.2 0.4 0.6 0.8 1 Success Rate DNN BRNN OMP BOMP IHT BIHT (b) Success rate vs. N s ( n = 4 ) Fig. 4. Performance of activ e users detection. and 16 GB RAM, ru nning under the Micr osoft W in dows 1 0 operating system. As shown in T able I, for various settings of pilot leng th and user a c ti vation probab ility , deep learning approa c h es, i.e., DNN and BRNN, allo w for mor e than 1 0 -fold decrease of the compu ting time. This significant improvement regarding to the com puting comp lexity is owing to th e fact that DNN and BRNN use a fixed n umber of matrix pro ductions and nonlinear th resholding , while both OMP an d BOMP in volve computatio nal co mplex matrix inv erse o peration , and bo th IHT and BIHT requ ire a relativ ely large num ber of iterations to conv erge. B. Active User Detection Accuracy In this experim ent we stud y how the propo sed approa c h perfor ms with different numbers of active user and d ifferent lengths of pilot. In Fig. 4(a), the pilot length of each user is fixed as N s = 40 . It is ob served that the p roposed BRNN achieves the highest activ e user de te c tion success rate among the com pared method s in cluding OMP , BOMP , IHT , BIHT and DNN. Fig. 4 (b) shows the active user detectio n success rate with d ifferent pilot leng th s, where the n umber of active users is set to b e 4 . It is also observed that BRNN outperfo rms other appr o aches in most of the cases. Here, we would like to emph a size that there are various way to furth er improve 0.01 0.02 0.03 0.04 0.05 0.06 n/K 0 0.5 1 1.5 2 MSE DNN BRNN OMP BOMP IHT BIHT (a) MSE vs. n K ( N s = 40 ) 30 35 40 45 50 55 60 Ns 0 0.5 1 1.5 MSE DNN BRNN OMP BOMP IHT BIHT (b) MSE vs. N s ( n = 4 ) Fig. 5. Performance of channel estimate. perfor mance of BRNN and DNN, e.g., using a larger size of training d ata and/or in creasing the numb er of layers in the neural n etwork, wh ile the perfo rmance of OMP , BOMP , IHT and BIHT would not improve with more iterations. C. Cha nnel Estimation Accuracy In this experimen t we show h ow do es th e prop o sed ap p roach affect th e chan n el e stima tio n perfo rmance under different number s of acti ve user an d different lengths of pilot. Th e channel is estimated by m in imum m ean squa re erro r estimator with the r e sult of active user detec t. In Fig. 5(a), the pilot length of each u ser is fixed as N s = 40 . It is o bserved that the pr oposed BRNN ach iev es the smallest mean squ a re error (MSE) amon g the comp a red methods including OMP , BOMP , IHT , BIHT and DNN. Fig. 5(b ) shows the MSE of channel estimation with different pilot len gths, whe r e the number of active users is set to be 4 . It is o bserved that BRNN outperf orms all the oth er appr oaches. V . C O N C L U S I O N In this pap er , we propose a novel de ep neural network, called BRNN, for m u ltiuser detection in m assi ve MTC com - munication with with sporad ically tr ansmitted small p a ckets and a lo w data rate. A new bloc k activ ation layer is pr oposed in BRNN to capture the block sparse structur e in the multiu ser detection p roblem. In comparison with existing appr oaches, significant red uction of compu tin g time and imp r ovement of multiuser detection accu racy are ac h iev ed by the p roposed approa c h . R E F E R E N C E S [1] C. Bock elmann, N. Pratas, H. Nik opour , K. Au, T . Sve nsson, C. 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