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IEEE COMMUNICATIONS LETTERS, VOL. 20, NO. 11, NOVEMBER 2016

Cellular-Aided Device-to-Device Communication: The Benefit of Physical Layer Network Coding Sang-Woon Jeon, Member, IEEE, Sang Won Choi, Member, IEEE, Juyeop Kim, Member, IEEE, and Won-Yong Shin, Senior Member, IEEE Abstract— We introduce a cellular-aided device-to-device (D2D) communication model in which two D2D transmitters (Txs) send independent messages W1 and W2 to their intended D2D receivers (Rxs) with the help of a base station (BS). Specifically, at the first phase, two Txs send their signals to both the BS and two Rxs and then at the second phase the BS sends its signal to the Rxs. We consider a feasible channel assumption that D2D channels are not always available at the BS and each Tx, thus resulting in an outage. For the proposed cellular-aided D2D scheme, the Txs send their messages via physical layer network coding, and thus, the BS is able to decode W1 ⊕W2 and broadcasts it to the Rxs. In consequence, from the fact that an outage does not occur if each Rx can decode W1 or W2 from its D2D links, the outage probability is significantly reduced compared with the D2D only communication where each Rx needs to decode its own message Index Terms— D2D communication, physical layer network coding, outage capacity, cellular networks.

I. I NTRODUCTION ECENTLY, device-to-device (D2D) communications in cellular networks have been actively studied as a promising solution for improving spectral efficiency [1] and offloading data [2] for future cellular systems. Most works in the literature have considered in-band D2D communication strategies in which D2D pairs share licensed cellular spectrum allocated for legacy cellular users instead of using unlicensed spectrum (i.e., out-band), in order to mitigate interference in a more controllable manner. In-band D2D communications are in general partitioned into two categories: underlay D2D communications and overlay D2D communications. For the underlay D2D model [3], [4], D2D pairs opportunistically utilize the cellular spectrum such that interference to legacy cellular users can be minimized or below a certain threshold level. Hence the key technical challenge is to establish efficient scheduling and power

R

Manuscript received May 2, 2016; revised June 17, 2016 and August 5, 2016; accepted August 11, 2016. Date of publication August 24, 2016; date of current version November 9, 2016. This work was supported by ICT R&D program of MSIP/IITP [B0101-16-1361, Development of PS-LTE System and Terminal for National Public Safety Service]. The associate editor coordinating the review of this letter and approving it for publication was N. Pappas. (Corresponding author: Won-Yong Shin.) S.-W. Jeon is with the Department of Information and Communication Engineering, Andong National University, Andong 36729, South Korea (email: [email protected]). S. W. Choi is with the ICT Convergence New Technology Research Team, Korea Railroad Research Institute, Uiwang 16105, South Korea (e-mail: [email protected]). J. Kim is with the Advanced Signaling and Communications Research Team, Korea Railroad Research Institute, Uiwang 16105, South Korea (email: [email protected]). W.-Y. Shin is with the Department of Computer Science and Engineering, Dankook University, Yongin 16890, South Korea (e-mail: [email protected]). Digital Object Identifier 10.1109/LCOMM.2016.2602332

allocation strategies for D2D pairs satisfying such regulation. For the overlay D2D model [5]–[7], on the other hand, a subset of cellular resources such as subcarriers or time slots are dedicated to D2D communications, which eliminate interference issues between cellular users and D2D pairs. In this letter, we consider in-band overlay D2D communications. Assuming that a given cellular resource ( e.g., subcarrier or time slot) is dedicated to D2D communications, D2D pairs can communicate with each other with the help of base stations (BSs). For this case, BSs can be solely used to support D2D communications, i.e., acting as relays, so that cooperative transmissions using BSs might be more beneficial than in-band underlay D2D communications where BSs have their own cellular traffic. A similar relay-aided adaptive communication method has been studied in [8]. As a fundamental building block, we consider two D2D pairs communicating with the help of a single BS. We establish an efficient cooperative communication strategy using adaptation based only on cellular channels, which results in a reduced outage probability compared to the D2D only communication. In particular, the main contributions of this letter are as follows: • A new physical layer cooperative communication framework based on physical layer network coding is established for in-band overlay D2D communications. • An efficient transmission rate adaptation method is proposed under the practical channel state information (CSI) assumption, i.e., each D2D transmitter (Tx) only knows legacy cellular channels and does not know D2D channels. • It is numerically shown that the proposed cellularaided D2D scheme outperforms the conventional noncooperative schemes in terms of throughput and outage performance. II. P ROBLEM F ORMULATION A. Cellular-Aided D2D Networks We consider a cellular-aided D2D network depicted in Fig. 1, in which two D2D pairs wish to communicate with the help of a single BS. We assume that communication takes place into two phases. At the first phase, two Txs simultaneously transmit to both the BS and two receivers (Rxs). Then, at the second phase, the BS transmits to two Rxs. Let be the transmit signal of Tx j at the first phase and x [1] j x [2] be the transmit signal of the BS at the second phase,   2 ≤ 1 satisfying the average power constraint, i.e., E (x [1] ) j   and E (x [2] )2 ≤ 1. Then, the received signals of the BS and

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JEON et al.: CELLULAR-AIDED D2D COMMUNICATION: THE BENEFIT OF PHYSICAL LAYER NETWORK CODING

Fig. 1.

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Cellular-aided D2D networks. Fig. 2.

Proposed cellular-aided D2D scheme.

Rx i ∈ {1, 2} at the first phase are respectively given by y [1] =

2  √ [1] snru f j x [1] j +z , j =1

yi[1] =

2  √ [1] snrh i j x [1] j + zi

(1)

j =1

and the received signal of Rx i ∈ {1, 2} at the second phase is given by √ yi[2] = snrd gi x [2] + z i[2] , (2) where f j , gi , and h i j are channel coefficients from Tx j to the BS, from the BS to Rx i , and from Tx j to Rx i , respectively. We assume block fading in which each channel coefficient is drawn independently from a continuous distribution with zero mean and unit variance, but remains fixed during the entire communication block. The additive noises z [1] , z i[1] , and z i[2] follow N (0, 1). It is worthwhile to mention that D2D communication pairs can be regarded as legacy cellular users capable of acquiring cellular uplink and downlink channels. On contrary, it might be quite challenging for most practical cellular systems to acquire D2D channels at the BS and each Tx due to the lack of D2D feedback links. For this reason, we assume that { f i }i∈{1,2} and {gi }i∈{1,2} are revealed at the BS and each Tx and Rx but {h i j }i, j ∈{1,2} , i.e., D2D channels, are only revealed at each Rx (available only at the receiver side). For notational convenience, denote i = 3 − i , F j = f i2 , G i = gi2 , and Hi j = h 2i j for i, j ∈ {1, 2}. Define C(x) = 1 1 1 + 2 log2 (1 + x) and C (x) = max( 2 log2 ( 2 + x), 0). B. Throughput For analytical convenience, we focus on the symmetric rate, i.e., each Tx transmits its message with the same rate R. Notice that R is a function of { f i }i∈{1,2} and {gi }i∈{1,2} , which are available at each Tx so that R can be adjusted based on them. Due to the lack of {h i j }i, j ∈{1,2} at the BS and each Tx, however, an outage might occur depending on the realization of {h i j }i, j ∈{1,2} . Specifically, when { f i }i∈{1,2} and {gi }i∈{1,2} are given the outage probability is defined as       ˆ Pr i∈{1,2} ( Wi  = Wi ){ f i }i∈{1,2} , {gi }i∈{1,2}

(3) := Pout { f i }i∈{1,2} , {gi }i∈{1,2} ,

where the probability is taken over {h i j }i, j ∈{1,2} . Hence, the throughput is given by 

T = E R { f i }i∈{1,2} , {gi }i∈{1,2}

· 1 − Pout { f i }i∈{1,2} , {gi }i∈{1,2} , (4) where the expectation is taken over { f i }i∈{1,2} and {gi }i∈{1,2} . Similarly, is given by Pout = the outage probability

E[Pout { f i }i∈{1,2} , {gi }i∈{1,2} ]. The primary aim of this letter is to improve the throughput of D2D communication with the help of legacy cellular uplink and downlink transmission. III. P ROPOSED S CHEME In this section, we propose a cellular-aided D2D scheme and analyze its throughput. Figure 2 illustrates a high level description of the proposed approach, which utilizes the benefit of physical layer network coding [9], [10]. At the first phase, each Tx sends its message via the same lattice code with the rate of R, which will be specified later on, and the BS decodes W1 ⊕ W2 .1 At the second phase, the BS then broadcasts W1 ⊕ W2 to the Rxs. Hence each Rx is able to use W1 ⊕ W2 as side information for decoding its intended message. In conclusion, an outage does not occur if each Rx is able to decode W1 or W2 based on the received signal of the first phase, i.e., D2D links. A. Rate Adaptation Now we show how to adapt the transmission rate R based on { f i }i∈{1,2} and {gi }i∈{1,2} , but not on {h i j }i, j ∈{1,2} . From [10], the BS is able to decode W1 ⊕ W2 at the first phase if R ≤ C+ (min(F1 , F2 )snru ). In summary, each Rx is able to finally decode W1 ⊕ W2 if

R ≤ min C+ (min(F1 , F2 )snru ), C(min(G 1 , G 2 )snrd ) := R⊕

(5)

is satisfied. We first define some fixed Rmin and Rmax satisfying Rmin ≤ Rmax and then adapt R based on cellular channel gains, represented by R⊕ , only in the range of [Rmin , Rmax ]. 1 For simplicity, we assume that W and W are linear finite field sources. 1 2 We refer to [10] for the detailed conversion from discrete sources to the corresponding linear finite field sources.

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IEEE COMMUNICATIONS LETTERS, VOL. 20, NO. 11, NOVEMBER 2016

The two parameters will be numerically optimized for maximizing the throughput in Section IV. Specifically, we set R = max(Rmin , min(R⊕ , Rmax )).

(6)

Remark 1 (Role of Rmin and Rmax ): By setting R = R⊕ , each Rx can always decode W1 ⊕ W2 from cellular uplink and downlink transmission. Nonetheless, this might not be optimal if D2D links are relatively good enough compared to cellular uplink and downlink. In this case, setting R greater than R⊕ can be better, i.e., decoding the intended messages only from D2D links. Hence Rmin prevents R from setting R = R⊕ when R⊕ is relatively small. Similarly, Rmax prevents R from setting R = R⊕ when R⊕ is relatively large (in this case, Rxs might ♦ not decode W1 or W2 from D2D links).

T = Pr(R⊕ ≤ Rmin )E[T |R⊕ ≤ Rmin ] + Pr(Rmin < R⊕ ≤ Rmax )E[T |Rmin < R⊕ ≤ Rmax ] + Pr(Rmax < R⊕ )E[T |Rmax < R⊕ ] = Pr(R⊕ ≤ Rmin )Rmin (1 − Pout,1 ) + Pr(Rmin < R⊕ ≤ Rmax ) ·E[R⊕ (1 − Pout,2 (R⊕ ))|Rmin < R⊕ ≤ Rmax ] + Pr(Rmax < R⊕ )Rmax (1 − Pout,3 ), (11) where Pout,1 , Pout,2 (R⊕ ), and Pout,3 are given by (8), (9), and (10), respectively. In the same manner, the expected transmission rate E[R] can be derived. C. Throughput Upper and Lower Bounds

B. Throughput Analysis Let us now analyze the throughput of the proposed cellularaided D2D scheme. For notational convenience, denote

 Hii snr Rtin,i := C 1+H , ii snr 

Hii snr . (7) Rid,i := C 1+H ii snr Note that Rx i can decode Wi via D2D links if R ≤ Rtin,i . Similarly, Rx i can decode Wi if R ≤ Rid,i . From (6), we consider three regimes and derive the throughput for each regime. 1) Regime I (R⊕ ≤ Rmin ): For this regime, R = Rmin and each Rx cannot attain W1 ⊕ W2 from cellular links. Hence by attempting to decode the intended message at each Rx, Rmin is achievable with the outage probability Pout,1 defined by    

 1 − Pr (8) Rmin ≤ Rtin,i  R⊕ ≤ Rmin . i∈{1,2}

The throughput for Regime I is then given by Rmin (1− Pout,1 ). 2) Regime II (Rmin < R⊕ ≤ Rmax ): For this regime, R = R⊕ and each Rx decodes W1 ⊕ W2 from cellular links. Hence each Rx can attain its intended message if at least one of W1 and W2 is decoded, provided that   

R⊕ ≤ max(Rtin,i , Rid,i ) . Pout,2 (R⊕ ) = 1 − Pr i∈{1,2}

(9) Hence, the throughput for Regime II is given by E[R⊕ (1 − Pout,2 (R⊕ ))|Rmin < R⊕ ≤ Rmax ], where the expectation is taken over R⊕ for given the event that Rmin < R⊕ ≤ Rmax . 3) Regime III (Rmax < R⊕ ): For this regime, R = Rmax and each Rx decodes W1 ⊕W2 from cellular links. Hence, similarly as in (9), Rmax is achievable with the outage probability Pout,3 defined by    

  Rmax ≤ max(Rtin,i , Rid,i )  Rmax < R⊕ . 1 − Pr i∈{1,2}

(10) The throughput for by Rmax (1 − Pout,3 ).

4) Throughput: Finally, from the throughput for each regime derived above, we have

Regime

III

is

then

given

For better understanding on the throughput improvement of the proposed cellular-aided D2D scheme, we provide intuitive upper and lower bounds on T in (11) by setting Rmin = 0 and Rmax → ∞. We further assume that snru = snrd in this subsection. Then, from (9) and (11), we have    

T = E R⊕ Pr R⊕ ≤ max(Rtin,i , Rid,i ) i∈{1,2} 

2 = E R⊕ Pr R⊕ ≤ max(Rtin,1 , Rid,1 ) 



= E R⊕ Pr R⊕ ≤ Rtin,1 + Pr R⊕ ≤ Rid,1

2 − Pr R⊕ ≤ min Rtin,1 , Rid,1 

(b) = E R⊕ 2 Pr R⊕ ≤ Rtin,1

2 − Pr R⊕ ≤ min Rtin,1 , Rid,1 , (12)

(a)

where (a) follows since max(Rtin,i , Rid,i ) are independent and identically distributed (i.i.d.) for i ∈ {1, 2} and (b) follows from the fact that the probability density functions of Rtin,1 and Rid,1 are the same. For notational simplicity, denote P(R ) = Pr ⊕

R⊕ ≤ Rtin,1 . By assuming that Pr R⊕ ≤ min Rtin,1 , Rid,1 = 0 in (12), the following upper bound is obtained: 

2  (13) T ≤ 4E R⊕ P(R⊕ ) . Furthermore, by assuming that Rtin,1 and Rid,1 are independent in (12), the following lower bound is obtained: 

2  T ≥ E R⊕ 2P(R⊕ ) − (P(R⊕ ))2  

2 

3  − 4E R⊕ P(R⊕ ) = 4E R⊕ P(R⊕ ) 

4  (14) +E R⊕ P(R⊕ ) . IV. S IMULATION R ESULTS In this section, we simulate the performance of the proposed cellular-aided D2D communication scheme and compare it with the conventional cellular only and D2D only schemes. In the case of the cellular only scheme, there is no outage

JEON et al.: CELLULAR-AIDED D2D COMMUNICATION: THE BENEFIT OF PHYSICAL LAYER NETWORK CODING

Fig. 3.

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Throughput with respect to snr u = snrd (dB) when snr = 10 dB. Fig. 5. Throughput upper and lower bounds with respect to snr (dB) when snru = snrd .

Fig. 4. Outage probability with respect to E[R] when snr = 10 dB and snru = snr d = 8 dB.

because the BS and each D2D pair knows cellular channels, i.e., { f i }i∈{1,2} and {gi }i∈{1,2} . Hence the transmission rate R can be adjusted as the minimum of the symmetric rates achievable by uplink and downlink transmissions. Whereas, each Tx sends its message with a fixed R for the D2D only scheme, which results in an outage if R > min(Rtin,1 , Rtin,2 ). We perform Monte Carlo evaluations to attain the throughput T or the expected transmission rate E[R] by assuming that each channel coefficient follows N (0, 1). Specifically, for each channel realization, the transmission rate R is determined from (6) and then outage events can be checked depending on three operating regimes in Section III-B.1 to Section III-B3. Then we can evaluate the outage probabilities and the ergodic rates in (11) from large enough channel realizations. In simulation, we numerically optimize Rmin and Rmax to maximize T based on exhaustive search for the cellular-aided D2D scheme. Similarly, we numerically optimize R for the D2D only scheme. Figure 3 plots T in (11) with respect to snru = snrd when snr = 10 dB. For comparison, we also plot T of the cellular only scheme and the D2D only scheme. As seen in the figure, the proposed scheme provides an improved T compared to the D2D only scheme and the gap increases as the strength of the cellular links (snru and snrd ) increases. As the strength of the cellular links increases, however, T of the cellular only scheme also increases and eventually outperforms the proposed scheme. Hence the benefit of the proposed scheme tends to be maximized when the performances of both cellular only and D2D only schemes are comparable. When snr = 10 dB and snru = snrd = 8 dB, for instance, the proposed scheme improves T about 10% over the cellular only D2D only schemes. Figure 4 plots the outage probability Pout with respect to E[R] when snr = 10 dB and snru = snrd = 8 dB. Recall that the ergodic rate E [min(Rmac , Rbc )] is achievable with no outage for the cellular only scheme, where

Rmac and Rbc are the symmetric rates achievable by uplink and downlink transmissions, respectively. Hence, the regime where E[R] > E [min(Rmac , Rbc )] is only meaningful. For this regime, the proposed cellular-aided D2D communication scheme provides a smaller outage probability compared to the D2D only scheme, which leads to an improved T as seen in Fig. 3. Figure 5 plots T in (12), i.e., the achievable throughput of the cellular-aided D2D scheme when Rmin = 0 and Rmax → ∞, and its upper and lower bounds in (13) and (14) with respect to snr. As seen in the figure, due to some mutually exclusive relation between the events R⊕ ≤ Rtin,i and R⊕ ≤ Rid,i , T in (12) is larger than the lower bound in (14), which assumes that they are independent. As the same reason, T in (12) is smaller than the upper bound in (13), which assumes that they are mutually exclusive. R EFERENCES [1] A. Asadi, Q. Wang, and V. Mancuso, “A survey on device-to-device communication in cellular networks,” IEEE Commun. Surveys Tuts., vol. 16, no. 4, pp. 1801–1819, 4th Quart. 2014. [2] S. Andreev, A. Pyattaev, K. Johnsson, O. Galinina, and Y. Koucheryavy, “Cellular traffic offloading onto network-assisted device-to-device connections,” IEEE Commun. Mag., vol. 52, no. 4, pp. 20–31, Apr. 2014. [3] H. Min, J. Lee, S. Park, and D. Hong, “Capacity enhancement using an interference limited area for device-to-device uplink underlaying cellular networks,” IEEE Trans. Wireless Commun., vol. 10, no. 2, pp. 3995–4000, Dec. 2011. [4] H. ElSawy, E. Hossain, and M. S. Alouini, “Analytical modeling of mode selection and power control for underlay D2D communication in cellular networks,” IEEE Trans. Commun., vol. 62, no. 11, pp. 4147–4161, Nov. 2014. [5] M. N. Tehrani, M. Uysal, and H. Yanikomeroglu, “Device-to-device communication in 5G cellular networks: Challenges, solutions, and future directions,” IEEE Commun. Mag., vol. 52, no. 5, pp. 86–92, May 2014. [6] Y. Cao, X. Chen, T. Jiang, and J. Zhang, “SoCast: Social ties based cooperative video multicast,” in Proc. IEEE INFOCOM, Toronto, ON, Canada, Apr./May 2014, pp. 415–423. [7] Y. Cao, T. Jiang, and C. Wang, “Cooperative device-to-device communications in cellular networks,” IEEE Wireless Commun., vol. 22, no. 3, pp. 124–129, Jun. 2015. [8] F. Wang, S. Wang, Q. Song, and L. Guo, “Adaptive relaying method selection for multi-rate wireless networks with network coding,” IEEE Commun. Lett., vol. 16, no. 12, pp. 2004–2007, Dec. 2012. [9] B. Nazer and M. Gastpar, “Reliable physical layer network coding,” Proc. IEEE, vol. 99, no. 3, pp. 438–460, Mar. 2011. [10] B. Nazer and M. Gastpar, “Compute-and-forward: Harnessing interference through structured codes,” IEEE Trans. Inf. Theory, vol. 57, no. 10, pp. 6463–6486, Oct. 2011.