Adaptive Rate Transmission with Opportunistic ... - IEEE Xplore

2nd IEEE International Workshop on Densely Connected Networks

Adaptive Rate Transmission With Opportunistic Scheduling in Wireless Networks Yufeng Wang, Ismail Butun, Ravi Sankar and Salvatore Morgera Dept. of Electrical Engineering, University of South Florida, Tampa, FL, 33620. Email: {ywang2,ibutun}@mail.usf.edu,{sankar,sdmorgera}@eng.usf.edu Abstract—In this paper, we study the adaptive rate transmission with opportunistic scheduling in two-hop relaying networks, in which only channel state information (CSI) at receivers are available. Previous work [5] that proposed an opportunistic relaying scheme has focused on the fixed rate transmission. We develop an adaptive rate transmission scheme according to instantaneous channel connections. The scheme operates with cooperative relays and opportunistic scheduling for adaptive rate transmission, to improve the throughput performance. We obtain the exact throughput expression and we show that the advantage using adaptive rate transmission over fixed rate transmission is the multiplicative factor of log log n, where n is the number of users. Furthermore, we prove that the throughput achieved by the adaptive rate transmission scheme is actually the optimal throughput for two-hop relaying networks. Numerical results are presented, indicating the alignment with our theoretical analysis.

I. I NTRODUCTION The demand for ever larger, more efficient and reliable communication networks necessitates new network architectures, such as ad hoc networks, cognitive radio (CR), relay extensions for cellular networks, sensor networks, and wireless mesh networks. Initiated by Gupta and Kumar in their seminal work [1], focusing on the study of system throughput, numerous schemes have been proposed corresponding to different assumptions on the channel state information (CSI) and levels of cooperations among communicating nodes [2]–[5]. The above works have made great strides on improving the system throughput performance in wireless networks, one common aspect is the fact that they all study the scaling law of the system throughput with fixed rate transmissions. For some new network architectures, such as ad hoc, sensor and CR networks, using adaptive resource allocation may provide better system performance due to its ability of changing transmission parameters. In particular, the transmit power and modulation level can be adjusted according to instantaneous channel connections with adaptive resource allocation policy [13], to provide better system performance or longer lifetime of the ad hoc or sensor nodes. The line of work on studying adaptive transmission schemes have been focused on different rate transmission and power allocation in wireless networks, under numerous fading models, power and quality of service (QoS) constraints [6]–[8]. In this work, we develop the adaptive rate transmission scheme based on the previous work on two-hop opportunistic relaying scheme [5]. In [5], the transmission rate is fixed as 1 bit/s/Hz, so that as long as the signal-to-interference-plus-noise

U.S. Government work not protected by U.S. copyright

ratio (SINR) is greater or equal to one, the fixed transmission rate is adopted. For fixed rate transmissions, there is a waste on transmission resources for the users with strong channel connections which could support higher transmission rates. With adaptive rate transmission, it is expected that the transmitter has the ability to further explore the wireless channel and adjust transmission rate according to instantaneous channel connections to improve the average system throughput, while still under the constraints of practical cooperative relaying and only CSI at receivers. These constraints are imposed due to the fact that for a large network, setting up cooperation among all the ad hoc nodes need lots of overhead which may reduce the useful throughput and obtaining CSI at transmitters is not feasible in practice [9], [10]. We assume the cooperation is not among neither source or destination nodes, but among the relay nodes. This approach is motivated by a type of networks known as hybrid networks, in which relays are infrastructure nodes connected to a wired backbone [11]. Hybrid networks act as a bridge between the infrastructure supported networks [12]. Furthermore, we assume the cooperative relays only exchange their CSI. In this paper, we restrict ourselves to these assumptions and propose the adaptive rate transmission scheme. Specifically, we first develop our opportunistic scheduling policy, in which only the nodes that benefit from the multiuser diversity1 are scheduled for transmission and low rate feedback from receivers are employed. Then we propose the adaptive rate transmission scheme, in which only independent encoding and decoding are needed, we obtain the throughput expression as m 2 log log n and compare its performance with the fixed rate transmission scheme in [5]. Furthermore, we prove that the achieved system throughput by our adaptive rate transmission is actually the optimal throughput for two-hop relaying networks. Note that in this work, we focus on the scheme of adaptive rate transmission and only constant transmitting power is assumed. The rest of the paper is organized as follows. In section II, the system model is presented. Section III shows the opportunistic scheduling policy for the adaptive rate transmission scheme. In section IV, we investigate the throughput of the adaptive rate transmission and analyze the gain over the fixedrate transmission scheme. Numerical results and conclusion are provided in section V and section VI, respectively. 1 Multiuser diversity gain is obtained by scheduling the best user among all the candidate nodes according to the qualities of each channel connection for communicating in each time slot.

445

II. S YSTEM M ODEL

By assumption of CSI at the receivers, relay r knows the channel connections of hi,r , i = 1, ..., n and selects the source node ir , which has the strongest channel connection, i.e., ir = arg maxi hi,r . • By cooperation, relay r exchange the channel information and selected source nodes with other relays. After obtaining the CSI from other relays, relay r is able to calculate Ph the corresponding SIN RiPr1,r = N0 + ir ,rP hk,r , where k=ir P is the fixed transmission power and N0 is the Gaussian noise power. Then relay r feedback the SIN R to the selected source node ir . • Upon receiving the feedback information, source node ir starts transmitting data at the rate of RiPr1 =  log(1 + SIN RiPr1,r ),  < 1 to relays. Since the transmission rate is less than log(1 + SIN RiPr1,r ), relay r is able to decode the received data from information-theory point of view. The decoded data is then buffered for forwarding in Phase 2. The scheduling in Phase 2 works as follows, • First, destination node j measures the channel connections gr,j from all the relay nodes and calculates its P gr ,j SIN RrPj2,j = N0 + j P gl,j , then feedback this infor•

Consider a wireless network in which n source nodes having data traffic to send to their designated destination nodes, through the help of m relay nodes. We assume relays do not generate their own traffic. The communication protocol is restricted to two-hop decode-and-forward transmissions, in which the source nodes communicate with their destination nodes only through the half-duplex relays. Specifically, in the first hop (Phase 1), a subset of source nodes are scheduled to transmit data to m relays. After decoding and buffering the received signals, the relays forward the data to a subset of destination nodes in the second hop (Phase 2). We consider simultaneous transmission in each hop, i.e., all nodes are operating in the same frequency band, with the presence of fading. We assume the channel connections from source nodes to relays and from relays to destination nodes experience independent and identically distributed (i.i.d.) Rayleigh fading. Accordingly, we assume the channels to be constant during each phase of the two-hop communication protocol. We denote the channel connections between source nodes i, 1 ≤ i ≤ n, and relay nodes r, 1 ≤ r ≤ m, as hi,r and the connections between relay nodes r and destination nodes j, 1 ≤ j ≤ n, as gr,j . According to our assumption, the channel gains follow an i.i.d. exponential distribution, i.e., |hi,r | ∼ Exp(1) and |gi,r | ∼ Exp(1). This model is appropriate in the sense of a dense networks in a rich scattering environment, where the distance between transmitters and receivers has only a marginal effect on channel fading [5]. The scheduling process for each hop is of opportunistic nature, that is, in each hop, only a subset of nodes that can benefit from multiuser diversity are scheduled for transmission. Specifically, in Phase 1, the m relay nodes cooperate by exchanging their CSI and each relay selects a source node with the strongest channel connection; the selected source nodes then transmit packets to the relay nodes. In Phase 2, each destination node measures the signal to interference and noise ratios (SINR) of all m relays and feedback the index of the relay (if exists) that has SINR ≥ 1 and the SINR information. Upon receiving the feedback and SINR, the relay nodes then forward the packets to the destination nodes. Note that the system delineated here is operating in a decentralized fashion, i.e., there are no cooperation among source/destination nodes. Only CSI at receivers are assumed at each hop. Transmitters have access to the CSI only through low-rate feedback from the receivers and relays cooperate only by exchanging their CSI in Phase 1. The details of the scheduling policy is presented in the next section. III. O PPORTUNISTIC S CHEDULING P OLICY In this section, we present details of our scheduling policy for the two-hop adaptive rate transmission scheme. Since all the relays operate independently, we may select any specific relay without loss of generality, i.e., relay r, to show our scheduling policy. We start with Phase 1:

l=rj

mation to the relay rj , which that has SINR ≥ 1. P2 • Upon receiving the SIN Rrj ,j information, relay rj start transmitting data at a rate of RrPj2 = ε log(1+SIN RiPr2,r ), ε < 1. Since the transmission rate is less than log(1 + SIN RiPr2,r ), destination node j is able to decode the data. Note that the difference between Phase 1 and 2 is that, in Phase 1, the relays have no knowledge which source nodes are the transmitters (they can be any subsets of n), while in Phase 2, the transmitters are known by the destination nodes as all the relay nodes will be transmitting. The overhead of the feedbacks in Phase 1 from each relay is an integer of the source node index plus a real number of its channel gain. While since in Phase 2, the transmitters are known (all the relays), only a real number of the channel gain is needed to feedback from the destination node to relays. IV. A DAPTIVE R ATE T RANSMISSION

In this section, we analyze the throughput of the adaptive rate transmission scheme. We show that the scheme achieves m 2 log log n throughput and we also prove that the achieved throughput is actually the optimal throughput for two-hop relaying communications. A. Throughput in Phase 1 We now derive the throughput in Phase 1. We first select a specific relay r for analysis. According to the opportunistic scheduling policy in Phase 1, relay r selects the source node ir for transmission via feedback of its index and channel gain. After receiving all the feedback signals and SIN RiPr1,r from the relays, source node ir starts transmitting data at a rate of RiPr1 , (1) RiPr1 = ir log(1 + SIN RiPr1,r ),

446

where ir < 1, in order to guarantee that the transmitted signal can be successfully decoded at relay r. Similarly, all the other m − 1 relays schedule their corresponding source nodes. We denote the scheduled source nodes constitute a set Γ ⊂ 1, ..., n, and γ as the elements (scheduled source nodes) in Γ. Since with m relays, there can be up to m source nodes can be scheduled, hence, |Γ| ≤ m. Specifically, when same source nodes are scheduled by different relays, | Γ |< m; when each of the m relays schedules a different source node, |Γ| = m. After the scheduled source nodes receive all the feedback, they start transmitting data according to the instantaneous channel connection (SINR) accordingly, which leads to the sum-rate throughput in Phase 1 as  γ log(1 + SIN RγP 1 ), (2) R1 = γ∈Γ

in which SIN RγP 1 denotes the SINRs calculated by each of the scheduled source node γ and γ has to be less than 1. For Rayleigh-fading, it is well studied that the term h SIN Rir ,r = N0 +ir ,r hi,r scales as log n due to multiuser i=ir diversity gain with a pool of n nodes. Hence, the sum rate throughput can be written as  R1 = γ log(1 + log n) (3) γ∈Γ

≥

mP r[Nm ] log(log n),

(4)

in which the term P r[Nm ] is the probability of each of the m relays schedules a different source node. The equation (3) is based on the multiuser diversity gain, the the inequality (4) is because of the fact the considering only the case of |Γ| = m. According to the opportunistic scheduling scheme, the probability for each source node to be scheduled (with the strongest channel connection) is n1 , the probability for m relays schedules a different source node, can be written as P r[Nm ] = n(n − 1) · · · (n − m + 1)/nm . Hence, R1 can be finally obtained as R1

≥

m

n(n − 1) · · · (n − m + 1) log log n. nm

(5)

Remark 1: For fixed rate opportunistic relaying scheme in [5], the throughput in Phase 1 is R1f ixed = n(n−1)···(n−m+1) P r[SIN R ≥ 1]. Comparing with our m nm adaptive rate transmission scheme, it is obvious to find that the adaptive rate transmission achieves the gain of log log n/P r[SIN R ≥ 1] over the fixed rate transmission. B. Throughput in Phase 2 As noted earlier in Section III, the difference between Phase 1 and 2 is that the receivers in Phase 1 have no knowledge of who are transmitters, while in Phase 2 the receivers know all the transmitting nodes (the relays). Hence, in Phase 2, focus on any specific destination node j, it first measures the channel connections from all the relays, select the best relay rj and calculate the corresponding SINR, then feedbacks the index of the best relay and the SINR value. Upon receiving the all

feedback from destination nodes, relay rj start transmitting data at the rate of RrPj2 with its best SINR, RrPj2 = εrj log(1 + SIN RrPj2,j ),

(6)

where εrj < 1, in order to guarantee that the transmitted signal can be successfully decoded at destination node j. Accordingly, all the other m − 1 relays receive their corresponding SINRs information and start adaptive transmissions according to the instantaneous channel connection. Hence, the sum-rate throughput in Phase 2 can be written as R2 =

m 

εr log(1 + SIN RrP 2 ),

(7)

r=1

in which SIN RrP 2 denotes the SINRs from each of the relays and εr has to be less than 1. Similarly as in Phase 1, we may further calculate R2 as follows, R2 =

m 

εr log(1 + log n) = m log log n.

(8)

r=1

Remark 2: Compare with the fixed rate transmission, which has R2f ixed = mP r[relay receives a f eedback], the adaptive rate transmission scheme achieves a minimum gain of log log n. C. Throughput of Adaptive Rate Transmission From the previous analysis, considering the penalty by two-hop transmissions, the overall system throughput can be obtained as, 1 min{R1 , R2 } (9) R = 2 m n(n − 1) · · · (n − m + 1) = log log n. (10) 2 nm Note that it is shown in [5] that the above achieved throughput is actually the optimal throughput for two-hop opportunistic relaying schemes. Because it is reasonable to say that the optimal throughput can be achieved with full cooperation among the nodes and full CSI knowledge at both transmitters and receivers and this case is equal to MIMO with multipleaccess channels of Phase 1 and MIMO Broadcast Channel in Phase 2, which have been proven in [14] and [15] that the throughput to be m log log n. Taking into the 21 factor due to two-hop transmission, the optimal throughput is m 2 log log n. V. S IMULATION R ESULTS In this section, we present the numerical results of the proposed adaptive rate transmission scheme with opportunistic scheduling under Rayleigh-fading. Fig. 1 plots the average throughput in Phase 1 and in Phase 2, as well as the corresponding system throughput R, with n = 500 S-D pairs. As shown in the figure, R1 and R2 increases with the number of relays m at the beginning, because more relays provides more simultaneous transmissions. However, increasing relays also increases the interference, after exceeding a certain number, the interferences become dominant

447

with more nodes in the network, the multiuser diversity gain becomes larger. From the comparisons in the figure, clearly that the adaptive rate transmission performs better than fixed rate transmission, which agrees closely with our previous theoretical analysis.

10

average R1 9

average R2 average R

Throughput [bits/s/Hz]

8 7 6 5 4 3 2 1

1

2

3

4

5

6

7

8

9

10

Number of Relays m

Fig. 1. Throughput R1 , R2 and R as a function of the number of relays m, with n = 500 S-D pairs.

VI. C ONCLUSION In this paper, we have studied the adaptive rate transmission scheme with opportunistic scheduling in a two-hop relaying networks. Our contributions are three-fold. We have developed an opportunistic scheduling scheme, which operates with cooperative relays and a practical CSI assumption. Our second contribution is to propose the adaptive rate transmission scheme for two-hop relaying networks and obtain the exact throughput of the proposed scheme. Our third contribution is to prove that the achieved throughput is actually the optimal throughput for two-hop relaying networks and compare with the fixed-rate transmission scheme. The delay related issues of the proposed scheme and the effect of adaptive power allocation are left for future work.

5

4

Throughput [bits/s/Hz]

R EFERENCES

Adaptive−Rate with n = 100 Fixed−Rate with n = 100 Adaptive−Rate with n = 500 Fixed−Rate with n = 500

4.5

3.5 3 2.5 2 1.5 1 0.5 1

2

3

4

5

6

7

8

9

Number of Relays m

Fig. 2. Throughput Comparison between Adaptive Rate Transmission and Fixed Rate Transmission, as a function of the number of relays m, with different number of n = 100 and n = 500 S-D pairs.

and decrease the throughput. The corresponding simulated R behaves similarly, which is consistent with the theoretical analysis of R = 12 min{R1 , R2 }. Also note that since the receivers have more knowledge of the transmitters in Phase 2 than in Phase 1, as analyzed in Section IV, as a consequence, R2 is larger than R1 . The throughput comparison between adaptive rate transmission and fixed rate transmission is shown in Fig. 2. Presented are throughput as a function of the number of relays m, with n = 100 and n = 500 S-D pairs. The plotted curves increase first, then start decreasing with the increasing number of relays m, which is similar as in Fig. 1, when increasing relays the number of simultaneous transmissions also increases, however, the interference may become dominant after a certain value of the number of relays, which leads to a decrease on the throughput. The throughput with n = 500 nodes is larger than the throughput with n = 100 nodes, that’s because

[1] P. Gupta and P. R. Kumar, “The capacity of wireless networks,” IEEE Trans. Inf. Theory, vol. 46, no. 2, pp. 388-404, Mar. 2000. [2] M. Grossglauser and D. N. C. Tse, “Mobility increases the capacity of ad hoc wireless networks,” IEEE/ACM Trans. Networking, vol. 10, no. 4, pp. 477-486, Aug. 2002. [3] R. Gowaikar, B. M. Hochwald, and B. Hassibi, “Communication over a wireless network with random connections,” IEEE Trans. Inf. Theory, vol. 52, no. 7, pp. 2857-2871, July 2006. [4] A. F. Dana and B. Hassibi, “On the power efficiency of sensory and ad hoc wireless networks,” IEEE Trans. Inf. Theory, vol. 52, no. 7, pp. 2890-2914, July 2006. [5] S. Cui, A. M. Haimovich, O. Somekh, and H. V. Poor, “Opportunistic relaying in wireless networks,” IEEE Trans. Inf. Theory, vol. 55, no. 11, pp. 5121-5137, Nov. 2009. [6] M. S. Alouini and A. J. Goldsmith, “Capacity of Rayleigh fading channels under different adaptive transmission and diversity-combining techniques,” IEEE Trans. Veh. Tech., vol. 48, no. 4, pp. 1165-1181, Jul. 1999 [7] S. L. Gong, B. G. Kim, and J. W. Lee, “Opportunistic Scheduling and Adaptive Modulation in Wireless Networks with Network Coding,”in Proc. IEEE Vehi. Tech. Conf. (VTC’09), pp. 1-5, Apr. 2009 [8] T. Nechiporenko, K. T. Phan, C. Tellambura, and H. H. Nguyen, “On the capacity of Rayleigh fading cooperative systems under adaptive transmission,” IEEE Trans. Wireless. Comm., vol. 8, no. 4, pp. 16261631, Apr. 2009 [9] Y. Wang, S. Cui, R. Sankar, and S. Morgera, “Delay-Throughput Tradeoff With Opportunistic Relaying in Wireless Networks,” in Proc. IEEE Global Telecommun. Conf. (GLOBECOM), Houston, Dec. 2011. [10] Y. Wang, M. Ert¨urk, H. Arslan, R. Sankar, I. Ra and S. Morgera, “Throughput and Delay Analysis in Aeronautical Data Networks,” in Proc. International Conference on Computing, Networking and Communications (ICNC), Hawaii, Jan. 2012. [11] B. Liu, Z. Liu, and D. Towsley, “On the capacity of hybrid wireless networks,” in Proc. IEEE INFOCOM, vol. 2, Apr. 2003, pp. 15431552. [12] B. Niu and A. M. Haimovich, “Optimal Throughput of Two-Hop Relay Networks with Different Relay Cooperation,” in Proc. IEEE Military Communication Conference (Milcom), Boston, Oct. 2009. [13] V. Asghari and S. Aissa, “Adaptive Rate and Power Transmission in Spectrum-Sharing Systems,” IEEE Trans. Wireless. Comm., vol. 9, no. 10, pp 3272-3280, Oct. 2010 [14] H. Weingarten, Y. Steinberg, and S. Shamai (Shitz), “The capacity region of the Gaussian multiple-input multiple-output broadcast channel”, IEEE Trans. Inf. Theory, vol. 52, no. 9, pp. 3936-3964, Sep. 2006 [15] N. Jindal, S. Vishwanath, and A. Goldsmith, “On the duality of Gaussian multiple-access and broadcast channels”, IEEE Trans. Inf. Theory, vol. 50, no. 5, pp. 768-783, May 2004

448