Asynchronous Detection for Machine-to-Machine ...

Asynchronous Detection for Machine-to-Machine Systems with Code Division Multiple Access Zhaohui Yang, Ming Chen, Yijin Pan, Hao Xu and Jianfeng Shi National Mobile Communications Research Laboratory, Southeast University, Nanjing 211111, China E-mail: [email protected]

Abstract—In this paper, we study multiuser detection for asynchronous uplink machine-to-machine systems with code division multiple access. We formulate the maximal logarithmic likelihood problem for asynchronous multiuser detection via joint channel gains, time delays and transmission symbols detection. We present the design for pilot sequence and propose an adaptive step-size method with low complexity to estimate time delays based on the estimated time delays of the past times. Numerical results are shown to illustrate the effectiveness of the proposed method. Index Terms—Asynchronous detection, code division multiple access (CDMA), machine-to-machine (M2M) systems.

I. I NTRODUCTION Machine-to-machine (M2M) communications have been considered as one of the promising technologies to realize the Internet of Things (IoT) in the future 5th generation network. M2M communications can be applied to many IoT applications, which mainly involve new business models and opportunities, such as smart grids, environmental monitoring and intelligent transport systems [1]. Different from the conventional human type communications, M2M communications have unique service features [2]. Specially, the unique features of M2M communications include the massive transmissions from a large number of machine type communication devices (MTCDs), small bursty natured traffic (periodically generated), high requirements of energy efficiency and security, etc. One major challenge for M2M communications is access control, which manages the engagement of massive MTCDs to the core network. To tackle this challenge, various solutions have been proposed, e.g., by using wired access (cable, DSL, etc.) [3], wireless short distance techniques (WLAN, Bluetooth, etc.), or wide area cellular network infrastructure (Long Term Evolution-Advanced, WiMAX, etc.) [4]. Among all these solutions, an effective approach is to deploy machine type communication gateways (MTCGs) to act as relays of MTCDs [2]. To enable multiple MTCDs to transmit data to the same MTCG, time division multiple access (TDMA) was adopted in [5]. Since there are vast amount of MTCDs to be served, TDMA leads to large transmission delay and synchronization overhead. By splitting users in the power domain, non-orthogonal multiple access (NOMA) can simultaneously serve multiple users at the same frequency or time resource [6]. Consequently, the NOMA based access scheme yields a significant gain in spectral efficiency over conventional orthogonal TDMA [6]–[11]. This favorable characteristic makes NOMA

an attractive access solution for supporting massive MTCDs in M2M networks. Considering NOMA, [12] investigated an M2M enabled cellular network, where multiple MTCDs simultaneously transmit data to the same MTCG and multiple MTCGs simultaneously transmit the gathered data to the base station (BS). The above works [2], [5], [12] all considered the deployment of MTCGs, which require additional cost. Instead of deploying MTCDs, the uplink transmission for M2M communications is scheduled by the BS in a requestgrant procedure [13], where MTCDs can randomly transmit data. In grant-free system, the BS cannot acquire the device activity information before information transformation. For multiuser detection problem, there are some traditional detection methods: linear minimum mean square error method [14], maximum a posteriori probability method [15], and maximum likelihood (ML) method [16], [17]. Specially, the ML method is not practical in many situations due to the heavy computation in large scale systems. In order to overcome the high computation problem and utilize the unique properties of M2M systems, the compressive sensing method was applied to M2M systems by using the priori information of MTCDs [18]. There are two major differences between the detection problems in M2M systems with compressive sensing and conventional wireless communication systems with compressive sensing, different value spaces of the variables and whether the transmission signal contains error correction coding information. Based on these two differences, a weighted group orthogonal matching pursuit method with low complexity was proposed in [19]. The compressive sensing methods in [18] and [19] were applied to multiuser detection in different discrete time slots. The authors in [20] investigated joint user activity and data detection based on compressive sensing in continuous time slots. Considering the sporadic feature of M2M communications, [21] proposed a low-complexity dynamic compressive sensing based multiuser detection to jointly realize user activity and data detection. Recently, approximate message passing method was adopted in [22] and [23] for an uplink massive device communication scenario with massive multiple-input multipleoutput. However, the above works [18]–[23] all assumed synchronous transmission for M2M systems. Since the time accuracies of MTCDs are not the same and the physical locations of MTCDs are different, the uplink transmissions from the MTCDs are always not perfectly synchronized in reaching the BS. For the multiuser detection problem in asynchronous M2M systems, it is required to joint

II. S YSTEM M ODEL AND P ROBLEM F ORMULATION A. System Model Consider an machine-to-machine (M2M) system with one base station (BS) and K machine type communication devices (MTCDs), as shown in Fig. 1. The MTCDs need to transmit the collected data with fixed length to the BS periodically. During transmission time T , each MTCD transmits M symbols to the BS and the symbol period is Ts . Since the time accuracies of MTCDs are not the same and the physical locations of MTCDs are different, the uplink transmissions from the MTCDs are not perfectly synchronized in reaching the BS, i.e., different MTCDs have different time delays. Due to massive number of MTCDs, the number of orthogonal spreading codes is not enough for all MTCDs. To tackle this trouble, we assign the same spreading code to the MTCDs with distinctive time delays. Specially, K MTCDs can be classified into N groups according to the locations. The MTCDs in the same group are assumed to have similar time delays to the BS since their locations are near to each other. Note that we have utilized the property of asynchronous transmission, since different MTCDs with the same code can

MTCD

BS

……

MTCD

MTCD

Fig. 1.

11 21 0

System model.

 1N Tb

…

detect of channel gains, time delays and transmission symbols of all MTCDs, which differs from synchronous detection problems in [18]–[23]. Due to the distinction of massive number of MTCDs, it is important to develop a detection method with low complexity. The benefit of asynchrony when multiple users are sending data simultaneously to a common receiver was investigated in [24]. An iterative method was proposed to solve the multiuser detection problem in an asynchronous M2M system [25]. According to [18], the rate requirement of MTCD in M2M systems is low, which allows the application of code division multiple access (CDMA). Since orthogonal frequency division multiplexing is considered in [25], the method in [25] cannot be directly applied to the detection problem in M2M system with CDMA. Besides, due to massive number of MTCDs, the orthogonality of different MTCDs cannot be strictly satisfied, which means that the conventional multiuser detection methods [14]–[16] for CDMA cannot be directly used to solve the detection problem in asynchronous M2M systems. In this paper, we investigate the multiuser detection problem for an asynchronous M2M system with CDMA. By using the benefit of asynchronous transmission, different MTCDs with similar time delays are assigned with different spreading codes, while MTCDs with distinctive time delays can be allocated with the same spreading code. We first design the pilot sequence, which is used for detecting channel gains and time delays. Then, a data detection method with given channel gains and time delays is proposed. This paper is organized as follows. In Section II, we introduce the system model and provide the formulation of asynchronous multiuser detection problem. Section III provides the multiuser detection with pilot sequence. Some numerical results are displayed in Section IV and conclusions are finally drawn in Section V.

( N  1)Tb

 2N NTb

t

Ts

Code 1 Code 2

Group 1 …

…

Group N …

Fig. 2.

…

Time delay distribution of users in different groups.

be identified by using sampling diversity in asynchronous transmission according to [24]. In the n-th group, there are Kn MTCDs. Obviously, we have K = K1 + · · · + Kn . Owing to the fact that the MTCDs in the same group share similar time delays, we set that MTCDs in the same group are allocated with different spreading codes and MTCDs in different groups can utilize the same spreading codes. Letting Ka = max{K1 , · · · , Kn } be the maximal number of MTCDs in a group, we only need a small number of Ka spreading codes to support the uplink data transmission of K MTCDs. As illustrated in Fig. 2 and Fig. 3, the relative time delay between the k-th MTCD in group n and the BS is denoted by τkn ∈ [(n − 1)Tb , nTb ), where Tb is the maximal time delay uncertainty of each MTCD, n = 1, · · · , N , k = 1, · · · , Kn . Assume that N Tb < Ts , which means that the maximal time delay does not exceed one symbol period. Time Tc in Fig. 3 is the spreading chip period, which is given in the following equation (1). It should be noted that τkn ≥ 0, and this can be realized by the searching method for the initial point of data. A signature waveform sk (t) based on spreading code is assigned to the k-th MTCD in each group. Defined in [0, Ts ],

with different transmission delays as follows: Group n 1-th MTCD

……

2-th MTCD

 2n

 1n

r(t)=

Kn N X X

Akn xkn (t n=1 k=1 Kn M N X −1X G X X

Kn-th MTCD

K n n

− τkn ) + n(t) (m) (g)

Akn bkn ck π(t−(g−1)Tc −mTs −τkn )

=

n=1k=1 m=0 g=1

Tc

Tc

Tc

……

Tc

……

+z(t)

Tb

Fig. 3.

where Akn is the channel gain between the k-th MTCD in group n and the BS, and z(t) is white Gaussian noise with zero mean and variance of σ 2 . Assume that all K uplink channels are of single path and the channel gains remain unchanged in each block transmission time T .

Time delay distribution of users in the same group.

Channel and Delay Estimation

(4)

Data Estimation

C. Sampling Signal Expression

Pilot Sequence Fig. 4.

At the BS side, the received signal r(t) is sampled in single chip, which yields the following data vector

Transmission Symbols

Two-phase transmission design.

r=

Kn N X X

(0)

(1)

(M −1)

Akn Dbτkn /Tc c (bkn c k , bkn c k , · · · , bkn

ck ) + z

n=1 k=1

sk (t) can be expressed as sk (t) =

G X

(g)

ck π(t − (g − 1)Tc )

(1)

g=1

where G is the spreading gain, Tc denotes the spreading chip period, π(t) is the pulse waveform with finite support (1) (2) (G) [0, Tc ], and (ck , ck , · · · , ck ) = c k is the spreading code, of which each element is binary valued in ±1. According to code division multiple access (CDMA) system, the spreading codes satisfy < cj , ck >= Gδjk

(2)

where δjk = 1 for j = k, and δjk is a very small number for j 6= k. The transmission signal of the k-th MTCD in group n can be written as xkn (t) =

M −1 X

(m)

bkn sk (t − mTs )

(3)

m=0 (m)

where bkn is the m-th transmission data modulated with binary phase shift keying for the k-th MTCD in group n. As depicted in Fig. 4, a two-phase transmission scheme is adopted, where joint channel and delay estimation is conducted by using pilot sequence in the first phase, and transmission data detection is performed in the second phase. B. Received Continuous Time Signal Expression From (1) and (3), the received signal at the BS can be expressed as a sum of transmission packets from K MTCDs

(5) where b·c means rounded down, Dbτkl /Tc c is an operator which performs operation on an vector to add bτkl /Tc c zeros in the front and adding G − bτkn /Tc c zeros in the end such that the length of new vector is (M + 1)G. By using operator Dbτkl /Tc c , the operated vector can be transformed as (0)

(M −1)

(1)

Dbτkl /Tc c (bkn c k , bkn c k , · · · , bkn =

(0) (1) (00bτkl /Tc c , bkn c k , bkn c k , · · ·

ck ) (M −1) , bkn c k , 0 G−bτkn /Tc c ) (6)

where 0 bτkn /Tc c = (0, 0, · · · , 0), | {z } bτkn /Tc c

0 G−bτkn /Tc c = (0, 0, · · · , 0 ) | {z } G−bτkn /Tc c

(7) D. Problem Formulation Denote a = (A11 , · · · , A1K1 , · · · , AN KN )

(8)

(0) (M −1) b kn = (bkn , · · · , bkn ), ∀k, n

(9)

b = (bb11 , · · · , b K1 1 , · · · , b KN N )

(10)

τ = (τ11 , · · · , τK1 1 , · · · , τKN N ),

(11)

(0) (1) (M −1) d kn (bbkn , τkn ) = Dbτkn /Tc c (bkn c k , bkn c k ,· · · ,bkn c k ), ∀k, n (12) and

D (bb, τ ) = (dd11 (bb1 , τ1 ); · · · ; d K1 1 (bb1K1 , τ1K1 ); · · · ; d KN N (bbN KN , τN KN ))

(13)

Based on the above abbreviations, equation (5) can be rewritten as r = aD (bb, τ ) + z (14)

To solve the asynchronous multiuser detection problem, we need to calculate the logarithmic likelihood function ln L(rr ), which is given by 1 krr − aD (bb, τ )k (15) σ2 Now, it is ready to formulate the maximal logarithmic likelihood problem for asynchronous multiuser detection as ln L(rr ) = −σ 2 −

(ˆ a , bˆ, τˆ) = arg

= arg

min

krr − aD (bb, τ )k2

min

D (bb, τ )T a T −2rrD (bb, τ )T a T aD (bb, τ )D

0 a ≥0 b ∈{±1}M K τ ∈[0,Ts ]K 0 a ≥0 b ∈{±1}M K τ ∈[0,Ts ]K

(16) The asynchronous multiuser detection problem (16) can be described as how to obtain the channel gains, time delays and transmission symbols from the single-chip sampled data r in (5). Obviously, it is hard to detect channel gains, time delays and transmitted symbols at the same time. In the following, we investigate the multiuser detection with pilot sequence. The BS estimates the channel gains and time delays by using pilot sequence. With the obtained channel gains and time delays, the transmission symbols are estimated. III. M ULTIUSER D ETECTION WITH P ILOT S EQUENCE In this section, we present the design of pilot sequence, which can be used to estimate channel gains and time delays. Having obtained channel gains and time delays, we present a detection method to estimate the transmission symbols. A. Design of Pilot Sequence To estimate the channel gains and time delays, we design the pilot sequence. As an example, the pilot sequence can be described as 1, −1, · · · , 1, −1, 0, which is a repeat of sequences 1, -1 ended with a 0. Note that all the MTCDs share the same pilot sequence, due to the fact that MTCDs with similar time delays are allocated with different spreading codes and MTCDs with distinctive time delays can be distinguished by using sampling diversity. The last symbol 0 in the pilot sequence is used to eliminate the interference caused by pilot sequence when detecting transmission data. Denote L + 1 as the number of symbols in the pilot sequence. Based on the received signal r , interference cancelation method is adopted to estimate the channel gains and time delays. Denote the s-th data to (LG+s−1)-th data of vector r as [rr ]LG+s−1 , s = 1, 2, · · · , G + 1. Without loss of generality, s we set d TTcb e = C, i.e., the ratio of the maximal time delay uncertainty Tb of each MTCD and the spreading chip period Tc is C, where d·e is rounded up and C ≥ 1. Taking into account the pilot sequence, we define s u ⊗ c k )T Skn = [rr ]LG+s−1 (u s

(17)

where u = (1, −1 · · · , 1, −1) is the pilot sequence with length s L, and ⊗ is Kronecker product. From (17), Skn can be viewed

as the sliding sum for detecting the k-th MTCD in group n. We can calculate the maximal sliding correlation sum of received data and pilot sequence of the k-th MTCD in group n as Skn =

max s∈{1+(n−1)C,··· ,nC}

s Skn

(18)

According to (18), we find that the calculation of Skn involves a number of C searching times. When C is large, the exhaustive method of obtaining Skn needs high complexity. Instead of using exhaustive search method, we adopt adaptive step-size rule based on the estimated time delays of the past t times. The key idea of the adaptive step-size rule is that the initial delay is a weighted mean of the past delay values. Based on the initial value, the delay is either increased, or decreased, or unchanged according to the sliding correlation sum. The details of this adaptive step-size rule can be found as follows: 1) Denote the initial point as s = s0 , which is the weighted average value of the time delays in the past t block transmission times. Set the initial step size δ = 1. s+δ s−δ s 2) If Skn > max{Skn , Skn }, set s = s + δ; If s−δ s+δ s s Skn > max{Skn , Skn }, set s = s − δ; If Skn ≥ s−δ s+δ max{Skn , Skn }, terminate. 3) Repeat step 2) until find the locally optimal s. If the value of s continuously increases or decreases for twice, double the step size, i.e., δ = 2δ. If the the value of s increases (or decreases) in the last time and s cannot increase (or decrease) in the next time, half the step size, i.e., δ = δ/2. To effectively estimate the time delays of these K MTCDs, we investigate the required length of the pilot sequence. Denote Qjk = max < c j , Rs (cck ) > (19) s∈{1,··· ,N C}

where Rs (cck ) represents that vector c k is s elements cyclic shifted to the right. To detect the time delay of the k-th MTCD in group n, we can obtain that the maximal inter user interference is Ikn =

max l=1,··· ,N,j=1,··· ,Kl ,(j,l)6=(k,n)

Ajl Qjk .

(20)

Assuming that the accuracy of the sliding correlation sum is α, the minimal required number of pilot symbols for the k-th MTCD in group n is1   α (21) Lkn = Akn G − Ikn To ensure that the time delays of all MTCDs can be successfully detected, the minimal required number of pilot symbols is L= max {Lkn } (22) n=1,··· ,N,k=1,··· ,Kn

Having obtained all Skn , we arrange Skn in a decreasing order. Without loss of generality, we assume that S11 ≥ Skn , 1 In equation (21), we only consider the strongest inter user interference. A more detailed analysis about the required length of pilot sequence is out of the scope of this paper.

0

10

Correlator Bank

Z1

r

BER

c1

−1

10

Z2

c2 … …

bk  sgn(Z k )

Select Maximal

−2

10

Zk

ZK

−3

10

0

cK Fig. 6.

ck

k

Fig. 5.

Partial Interference Factor

Serial interference cancelation method [17].

τˆk1 = Tc arg

max s∈{1,2,··· ,C}

s (Sk1 − 1)

(23)

for k = 1, 2, · · · , K1 . When the channel gains and time delays of the first n groups of MTCDs are obtained, data r with reduced pilot sequence of the first n groups of MTCDs can be expressed as r0 = r −

Kn n X X

10

15

u ⊗ c k )) Dτˆkj /Tc (Aˆkj (u

Asynchronous multiuser detection with Tb = 2.

detecting the symbol of user k + 1, the output signal should subtract the estimated m-th symbols of k users multiplied with corresponding partial interference factors as well as the the estimated (m − 1)-th symbols of all users multiplied with corresponding partial interference factors due to asynchronous transmission.

Decoded Signal

∀n = 1, · · · , N, k = 1, · · · , Ka . By using the successive interference cancellation method to estimate the channel gains and time delays, the channel gains and time delays of K1 MTCDs in group 1 can be respectively estimated as S11 , Aˆk1 = LG

5 SNR

—

Eliminator

K=8, ZF K=16, ZF K=8, SIC K=16, SIC

(24)

j=1 k=1

With new data r 0 , we can obtain the estimated channel gains and time delays of Kn+1 MTCDs in group n + 1 as (23). B. Data Detection with Given Channel Gains and Time Delays After obtaining the time delays and channel gains of all MTCDs, we use the serial interference cancelation method to estimate the transmission symbols of all MTCDs, as shown in Fig. 5. Firstly, the BS estimates the 0-th symbol of the MTCD with the highest channel gain. After having estimated the 0-th symbol of k MTCDs with k highest channel gains, the BS then estimates the 0-th symbol of MTCD k + 1 by subtracting the estimated 0-th symbols of k users multiplied with corresponding partial interference factors. To estimate the m-th symbol, 1 ≤ m ≤ M − 1, the same serial interference cancelation method is used, the only difference is that before

IV. N UMERICAL R ESULTS In this section, we evaluate the performance of the proposed method. In all simulations, channel coefficients are independent Rayleigh fading with variance one as in [24]. There are M = 1024 symbols for each MTCD to upload, and MTCDs are classified into two groups with equal number of MTCDs in each group. It should be noted that the length of pilot sequence is large (L = 1024) such that the channel gains as well as the time delays can be accurately estimated. In Fig. 6, we present bit error rate (BER) performance of different asynchronous multiuser detection methods versus signal-to-noise ratio (SNR) for different number of MTCDs, where zero forcing method is labeled as “ZF” and the serial interference cancelation method is labeled as “SIC”. Both ZF and SIC are used to estimate the transmission symbols, while the channel gains and time delays are estimated by pilot sequence according to Section III-A. From Fig. 6, the BER performance for small number of MTCDs outperforms that for large number of MTCDs especially for high SNR regime. This is because that the inter user interference increases with the number of MTCDs due to asynchronous transmission. It is also observed that the SIC method always outperforms the ZF method. The BER performance of different asynchronous multiuser detection methods versus SNR for different maximal time delay uncertainties is shown in Fig. 7. For both ZF and SIC, it can be seen that the BER performance for small maximal time delay uncertainty outperforms that for large maximal time delay uncertainty. This is due to that large maximal time delay uncertainty leads to large inter user interference. It can be also

0

10

−1

BER

10

Tb=1, ZF −2

10

Tb=2, ZF Tb=1, SIC Tb=2, SIC

−3

10

0

5

10

15

SNR

Fig. 7.

Asynchronous multiuser detection with K = 16.

found that the performance of the SIC method is sensitive to the maximal time delay uncertainty, which shows that the SIC method suits well for small maximal time delay uncertainty. V. C ONCLUSION In this paper, we have provided a new multiuser detection method for asynchronous uplink machine-to-machine systems with code division multiple access. The the maximal logarithmic likelihood problem for asynchronous multiuser detection with joint channel gains, time delays and transmission symbols detection is formulated. The pilot sequence is designed, and multiuser detection method is accordingly proposed. Numerical results have been shown that serial interference cancelation method always outperforms the zero forcing method. The bit error rate performance of both serial interference cancelation and zero forcing is well for small number of MTCDs and low maximal time delay uncertainty. ACKNOWLEDGMENTS This work was supported by National Nature Science Foundation of China (Nos. 61372106, & 61221002), NSTMP under 2016ZX03001016-003, the Six Talent Peaks project in Jiangsu Province under GDZB-005, the Fundamental Research Funds for the Central Universities under grant 2242016K41080, Science and Technology Project of Guangdong Province under Grant 2014B010119001, and the Scientific Research Foundation of Graduate School of Southeast University under Grant YBJJ1650. R EFERENCES [1] G. Wu, S. Talwar, K. Johnsson, and N. Himayat, “M2M: From mobile to embedded internet,” IEEE Commun. Mag., vol. 49, no. 4, pp. 36–43, Apr. 2011. [2] K. Zheng, F. Hu, W. Wang, and W. Xiang, “Radio resource allocation in LTE-advanced cellular networks with M2M communications,” IEEE Commun. Mag., vol. 50, no. 7, pp. 184–192, Jul. 2012. [3] M. Hasan, E. Hossain, and D. Niyato, “Random access for machineto-machine communication in LTE-advanced networks: Issues and approaches,” IEEE Commun. Mag., vol. 51, no. 6, pp. 86–93, Jun. 2013.

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