# Non-orthogonal Direct Access for Small Data Transmission in Cellular MTC Networks

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4 Fig. 6. Exampe of RB distribution for B =6, M =4, and K =3. are determined by seecting a segment of continuous RBs, and spreading codes are determined by a pre-determined rue, and (c) seudo-random: RBs are determined by a UE-specific mapping matrix, and spreading codes are determined by a predetermined rue. This is the proposed scheme. A. Anaysis of Coision robabiity A coision happens when different UEs occupy the same RB with the same spreading code used. We begin with anayzing the coision probabiity of the random resource seection scheme. We seect one UE as the UE of interest (UOI) and discuss the coision scenarios caused by the remaining M 1 UEs. First, et us define the RB coision indication matrix R with entries being r i,j,i =1,...,M 1,j =1,...,K, and the RB coision number vector d =[d 1,d 2,...,d K ], where d q = M 1 p=1 r pq, 1 q K (i.e., d q indicates the number of coided RBs on the qth RB of UOI). Fig. 6 iustrates an exampe of RB distribution for six avaiabe RBs, four UEs, and three RB utiization per UE, i.e., B =6, M =4, and K =3. By assuming that UE 1 is the UOI and there are respectivey three and two RBs coiding with the second and third RBs of UE 1, as shown in Fig 6, then the RB coision indication matrix is R = and the RB coision 1 1 number vector is d =[, 3, 2]. The number of ( possibe RB ) coision number vectors, N d,is M + K 1 given by N d =. Since different permutations K of R may have the same d, we denote the RB coision number vector and the RB coision indication matrix respectivey as d (i) and R (j,i) where 1 i N d and 1 j N (i) N (i) R R ; is the number of permutations of the RB coision indication [ matrices corresponding ] to d (i). Denote t (j,i) = t (j,i) 1,t (j,i) 2,...,t (j,i) M 1 as the number of 1 s in each row of R (j,i), i.e., the tota number of coided RBs with the UOI for each UE. Then, the number of RB combinations corresponding to d (i) is derived as ( )( N (i) B K CR = K χ ) N (i) R j=1 M 1 =1 ( ) B K K t (j,i) N (j,i), (2) where χ is the number of RBs used by the UOI that are coided, and N (j,i) is the number of different permutations of R (j,i). In (2), χ can be computed as χ = G r (F rz ((d (i) ) T )), where the operator F rz ( ) is to remove the zeros in the vector and the operator G r ( ) is to count the number of rows in a matrix. Let d (i) = F rz ((d (i) ( ) T ) and R (j,i) = F ) ur R (j,i), where the operator F ur ( ) is to output the unique rows in a matrix. Then, N (j,i) can be computed as N (j,i) χ! (M 1)! = ( ) ω G s d (i)t,d ω (i) ( ),! ζ G s R (j,i), r (j,i) ζ! (3) where d (i) ω are the entries of d (i), r (j,i) ζ are the row vectors of R (j,i), and the operator G s (A, v) is to count the number of row vectors of matrix A that is equa to the vector v. Now, we consider the coision of spreading codes. From d, we construct a code coision indication matrix Z with entries being z i,j,i=1,...,n z,j =1,...,K, whose N z row vectors represent the possibe code coision scenarios under the RB coision condition indicated by d. For the exampe described in Fig. 6, the code coision indication matrix is given by Z with the row vectors [ 1 1], [ 1 ], [ 1], and []representing the four possibe code coision scenarios due to the RB coisions indicated by d =[, 3, 2]. Let ξ (i) be the number of ones in the th coumn of R (i) and η = K =1 z(i) q be the number of code coisions. Note that R (j,i) is simpified to R (i) because R (j,i) j have the same code coision indication matrix. The number of code combinations Ξ (i) q,,η according to the RB coision condition indicated by the th coumn of R (i) and the code coision condition indicated by the qth row of Z (i) can be derived as L M, if d (i) =, z (i) q =, (L 1) ξ(i) L M ξ(i), if d (i) >, z (i) q =, Ξ (i) q,,η = ξ (i) [( ξ (i) j ) (L 1) ξ(i) j j=1 ] L M ξ(i), if d (i) >, z (i) q =1. (4) Therefore, the probabiity of having η spreading codes coided can be computed as η = i Q N (i) CR q Q K =1 Ξ(i) q,,η [( B K ) L K ] M, (5) { where Q = (i, q) G r (F rz ((d (i) ) T )) η, } K =1 z(i) q = η. For the continuous and pseudo-random seection schemes, it is difficut not ony to write down a cosed form but aso to perform computer-based simuations due to the arge search space, in particuar for the pseudo-random seection scheme. Therefore, we turn to investigate the access probabiity. Fig. 7 shows the simuation resuts of access probabiity for different RB indices. The simuation parameters are: the number of UEs M is 6, the tota number of avaiabe RBs B is 15, the number of RBs occupied per UE K is 6, the spreading factor L is 3, the number of avaiabe cycic shifts for the spreading code seection N s = α max +1 is 12, and the mapping matrices V are {3 5, 4 4, 5 3}. In Fig. 7, we can find that both the access probabiities of the random and pseudo-random

5 Access probabiity RB index Size of search space Number of RBs occupied per UE (a) Fig. 7. Access probabiity of different resource seection schemes robabiity (ana.), (approx.) (ana.) (sim.) (sim.) (sim.) Fig. 9. Size of search space Tota number of avaiabe RBs (b) Comparison of compexity for different resource seection schemes Number of coisions Fig. 8. Anaytica and simuated coision probabiities of different resource seection schemes. Note that the anaytica resut of the random seection scheme is used to approximate the proposed pseudo-random seection scheme. seection schemes are uniformy distributed, but the access probabiity of the continuous seection scheme varies with the RB index. Therefore, it can be expected that the anaytica resut of the random seection scheme can approximate the resut of the pseudo-random seection scheme. Fig. 8 compares the anaytica and simuation resuts of coision probabiity for different resource seection schemes. It indeed shows that the coision probabiity of the pseudo-random seection scheme can be approximated by the random seection scheme. It aso shows that the continuous seection scheme, which has the owest compexity, has a high probabiity of zero coision but aso has a high probabiity of six coisions (note that the number of RBs occupied per UE is six). This is why the continuous seection scheme performs worse, as shown ater. B. Compexity Anaysis To understand how much detection compexity can be saved using the proposed pseudo-random resource seection scheme, we compare the compexity in this subsection. The detection compexity is measured by the size of the search space, which is the number of the combinations of RBs and spreading codes. The detection compexity of the random seection scheme is given by considering randomy choosing K ordered RBs from B avaiabe RBs and randomy picking a spreading code for B! each chosen RB, i.e., K! (B K)! K! LK = B! LK (B K)!. For the continuous seection scheme, the spreading code is determined according to (1) and the compexity is (B K +1) N s, where (B K +1) is the number of possibe continuous segments. For the pseudo-random seection scheme, we take the number of avaiabe mapping matrices V (the cardinaity of V) and the row cycic shift operation into account. The detection compexity of the pseudo-random seection scheme is (B K+1) N s β, where β is the tota number of coumns of avaiabe mapping matrices, i.e., β = V =1 N co(); N co is the number of coumns of the mapping matrix chosen by UE. Fig. 9(a) compares the compexity of the three schemes using the same parameters as we evauate the coision, except that the number of coumns of matrix N co is 5 and we ony consider one mapping matrix with size 3 5. When the number of RBs used by each UE is arge, the detection compexity of the random seection scheme is prohibitivey high whie the compexity of the proposed pseudo-random seection scheme stays at a moderate eve. The same situation appies when different number of RBs are used, as shown in Fig. 9(b). V. ERFORMANCE EVALUATION In this section, we present the performance evauation of the proposed system. We first consider the effect due to CDM and then investigate the performance of the proposed pseudorandom resource seection scheme under the EVehA mutipath channe. The performance is evauated by the bock error

6 BLER Throughput (%) UE w/o CDM (CR =.119), C 2 UEs w/ CDM (CR =.238), C 3 UEs w/ CDM (CR =.357), C 1 UE w/o CDM (CR =.119), EC 2 UEs w/ CDM (CR =.238), EC 3 UEs w/ CDM (CR =.357), EC 1 UE w/o CDM (CR =.238), C 1 UE w/o CDM (CR =.357), C (a) Bock error rate 1 UE w/o CDM (CR =.119), C 2 UEs w/ CDM (CR =.238), C 3 UEs w/ CDM (CR =.357), C 1 UE w/o CDM (CR =.119), EC 2 UEs w/ CDM (CR =.238), EC 3 UEs w/ CDM (CR =.357), EC 1 UE w/o CDM (CR =.238), C 1 UE w/o CDM (CR =.357), C (b) Throughput Fig. 1. erformance of using CDM under the EVehA mutipath channe. CR, C, and EC respectivey represent code rate, perfect channe estimation, and estimated channe. rate (BLER) and the throughput (in percentage). The 1% throughput is defined as the throughput which can be achieved by a singe UE since our goa is to increase the throughput aong with the increase in the number of UEs. As a resut, it is possibe that the resuting throughput is more than 1%. A. Effect of CDM First, we compare the performances of the systems with and without using CDM. The RB usage and spreading codes are assumed known by the receiver. The EVehA channe with speed 3 km/hr is chosen for demonstration. The simuation parameters are the foowing. Bandwidth is set to 1.4 MHz, moduation is QSK, the number of RBs per UE is 6, data is 152 bits ong, the size of DFT is 72, the size of IDFT is 128, and the spreading factors are 2 (for 2 UEs) and 3 (for 3 UEs). Three cases are considered: singe UE without CDM, 2 UEs with CDM, and 3 UEs with CDM. The bock error rates are compared in Fig. 1(a). When the same channe code rate is appied, the system with CDM outperforms the system without CDM due to the spreading BLER BLER with IC with IC with IC (a) 7 UEs with IC with IC with IC (b) 2 UEs Fig. 11. erformance comparison of different resource seection schemes with and without IC under the EVehA mutipath channe. gain. It can be found that the performance degradation due to the higher channe code rate is compensated by the spreading gain. However, the case of 3 UEs with the channe code rate.357 suffers sight performance degradation due to the mutipath effect. To understand how channe estimation affects the system performance, we aso compare the BLER performances of the case when the channe is perfecty known and of the case when the frequency domain east square is used for channe estimation and the minimum mean square error (MMSE) criterion is used for equaization. In Fig. 1(a), we observe that the imperfect channe estimation degrades the system BLER and resuts in error foors. However, the BLER is sti in the usabe range. The throughput performances are compared in Fig. 1(b). It is shown that, even under the non-perfect channe estimation, more than 1% throughput performance can be achieved (note again that the 1% throughput is defined as the throughput which can be achieved by a singe UE) and the throughput scaes amost ineary with the number of UEs.

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