Performance Evaluation of n-throughput andk-throughput in a Hierarchical Cooperation Scheme

Eunmi Chu, Inkyu Bang, Taehoon Kim, and Dan Keun Sung

CNR Lab., Dept. of Electrical Engineering, KAIST,291 Daehak-ro, Yuseong-gu, Daejeon, 305-701, Korea

E-mail:femchu,ikbang,thkimg@cnr.kaist.ac.kr, dksung@ee.kaist.ac.kr

AbstractWe evaluate the throughput performance of a k-node Virtual-MIMO (V-MIMO) transmission with k fixed coop-erative nodes (k-throughput, k < n), compared with that of ann-node V-MIMO transmission (n-throughput) in which all nodesparticipate in a hierarchical cooperation scheme.

I. INTRODUCTIONA virtual multiple-input multiple-output (V-MIMO) technol-

ogy enables us to achieve a MIMO gain through cooperation ofnodes with a single antenna per node. Ozgur et al. [1] recentlyproposed a hierarchical cooperation (HC) scheme using long-range V-MIMO which achieves almost O(n) throughput incase of n nodes in a cluster. The basic idea of the HCis to reduce transmission time by increasing the number ofcooperative nodes. It is commonly called the n-throughputwhich consists of the following three phases. In phase 1,each source node broadcasts its own data frame, Ld, to allnodes in a cluster in a round-robin manner. Each node inthe cluster divides the received data frame into n cooperativenodes in a cluster and obtains a segment with Ld=n. After oneround-robin cycle, i.e, after broadcasting n data frames, eachnode maintains n segments from n broadcasted data frames.In phase 2, all nodes in the source cluster form a V-MIMOtransmitter, while all nodes in a target cluster form a V-MIMOreceiver. The n nodes in the source cluster transmit theirown segments simultaneously though V-MIMO. One clusterperforms n times of V-MIMO. In phase 3, n nodes in the targetcluster decode their own segments in phase 2 and forwardsegments toward a destination node.Ozgur and Leveque [2] showed a tradeoff between the

aggregate throughput and delay of n-throughput. Ghaderi etal. [3] analyzed the optimal number of nodes in a unit clusterand the optimal number of nodes in a merged cluster combinedunit clusters. Niesen et al. [4] showed the regime of achiev-able throughput. Thus, studies of n-throughput have shownremarkable performance from the viewpoint of informationtheory on physical (PHY) layer since the transmission timebecomes short for varying the number of cooperating nodes.However, in practical V-MIMO transmission, cooperating

nodes at the receiver side should know channel state infor-mation (CSI) to decode their own signal from the superposedreceived signal. In order to estimate channel state, cooperatingnodes at the transmitter side need to send a data frame includ-ing pilot signals. Thus, as the number of cooperative nodes

: Cluster

head

: Node : Central

coordinator

C#1 C#2

C#3 C#4

: Fixed

node

C#1 C#2

C#3 C#4

(a) n-throughput (b) k-throughput

Fig. 1. Network topology

increases, pilot overhead and system complexity increase. Inour previous work [5], we designed time division multipleaccess (TDMA) frame structure for a practical HC scheme.In this paper, we model and compare an n-node V-MIMOtransmission (n-throughtput, Fig. 1 (a)) and a k-node V-MIMOtransmission with k fixed cooperative nodes (k-throughtput,Fig. 1 (b)) with consideration of overhead from the viewpointof aggregate throughput.

II. NETWORK MODELIn V-MIMO transmission, cooperating transmitters mainly

send data frames including pilot signals to estimate channelinformation. Data frames use data sub-carriers (SCs) with thesame time-frequency resource, while pilot signals use pilotSCs with a dedicated time-frequency resource. When a nodeuses pilot SCs, other nodes put a null symbol on the SCsby a null subcarrier (NS) method [6]. Thus, the number ofpilot sub-carriers (SCs) depends on the number of cooperativenodes and channel conditions.

A. n-throughput ModelNp pilot SCs are arranged in every block of OFDM sym-

bols. Block size is determined by the interval of pilot SCsacross sub-carriers, Mf , and the interval of pilot SCs acrosssymbol times, Mt. As the block size increases, the pilotoverhead decreases. V-MIMO transmitters should send pilotSCs whenever the channel condition varies. Thus, Mf shouldbe less than coherence bandwidth, Bc, which is the inverse ofdelay spread and is expressed as follows:

Mf < dBc=fe = d1=(2Tdf)e = dNc=2Lcpe ;where f(= B=Nc), Nc, Td(= Lcp=B), B, and Lcp denotethe interval of SCs, the total number of SCs, delay spread,bandwidth, and the length of cyclic prefix (CP), respectively.On the other hand, Mt should be less than coherence time,

Tc, which is the inverse of doppler spread, and is expressedas follows:

Mt < dTc=Tsyme = d1=(4DsTsym)e = dc=(8fcvTsym)e,where Ds(= 2fcv=c), fc, v, Tsym, and c denote the dopplerspread, operating frequency, the velocity of nodes, symbolduration, and the speed of light, respectively. Generally, sinceTc is the order of tens to hundreds of Tsym depending onmobility of nodes, the pilot density per node in n-throughput,"n, is as expressed as "n = Np=(MtMf ).Let bti represent the data frame length including MAC

overhead per node in phase i (i 2 f1,2,3g), then it is calculatedas Ld=n + hmac where Ld and hmac denote the informationbit and MAC overhead, respectively. The number of symboltimes used to transmit one data frame including pilot SCs,Nreq sym, is expressed as follows:

Nreq sym = d(Nsc d +Nsc p)=Nce ;where Nsc d (= dbt2=bme) is the number of SCs used totransmit a data frame and Nsc p (= dn"nNsc de) is thenumber SCs used to transmit pilot SCs.

B. k-throughput ModelThe k-throughput utilizes k fixed nodes instead of the total

nodes i.e., n nodes in a cluster. Fixed nodes between a sourcecluster and a target cluster form a virtual MIMO in phase2. Since fixed nodes could be installed in the place with abest channel environment by a network operator, Mf and Mtincrease. Thus, Np pilot SCs per node are sufficient duringa data frame transmission. The V-MIMO transmission withk fixed nodes could be equivalent to a V-MIMO transmissionwith k nodes out of n nodes in a cluster when k nodes maintaina good channel condition without mobility and delay variationduring a data frame transmission.The number of pilot SCs of k-fixed cooperative nodes is

little related to the transmission duration of a data frame, andis as follows Nsc p k Np:

III. PERFORMANCE EVALUATIONTable I lists the detailed system parameter set. We com-

pare the k-throughput utilizing k fixed nodes with the n-throughput utilizing all nodes in a cluster by using an aggre-gate throughput metric. The aggregate throughput is expressedas T (N) = NLd=Tf where N = n m is the number of nodesin a network and m is the number of clusters. Fig. 2 showsthe aggregate throughput and the optimal number of nodesin a cluster, n, according to the length of data frame, Ld,when the number of nodes in a network, N , is set to 1,000.In n-throughput, as Ld increases, n increases. However, ink-throughput, as Ld increases, n is close to the number offixed cooperative nodes and it is determined by achievable

TABLE ISYSTEM PARAMETERS

Bandwidth (B) 20 [MHz]Total sub-carriers (Nc) 128The length of cyclic perfix (Lcp) 16The number of data bit per sub-carrier (bm) 1 [bit]

(QPSK, 1/2 coding rate)Pilot subcarrier in block (Np) 4The frequency interval of pilot SCs (Mf ) 4The time interval of pilot SCs (Mt) 64

102

103

104

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5

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40

Length of a data frame (Ld) [bit]

Ag

greg

ate

d t

hro

ug

hp

ut[

Mb

ps]

n-Th

k-Th (k=3)

k-Th (k=5)

102

103

104

2

4

6

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12

14

Th

e o

pti

ma

l n

um

ber o

f n

od

es

in a

clu

ster (

n*

)

n-Th

k-Th (k=3)

k-Th (k=5)

Fig. 2. Aggregate throughput and optimal number of nodes in a cluster forvarying the length of a data frame when N is 1,000

capacity from fixed cooperative nodes. Depending on Ld, theperformance of the V-MIMO transmissions is opposite. The n-throughput has higher throughput in the regime of long frame-length, while the k-throughput has higher throughput in theregime of short frame-length.

IV. CONCLUSIONSWe model and evaluate the n-throughput and k-throughput

considering control overhead from the viewpoint of the ag-gregate throughput performance. From our numerical results,the n-throughput with n cooperative nodes shows that anincrement of throughput due to spatial multiplexing gain ishigher than a reduction in throughput due to pilot overheadand data overhead in the long frame-length. In contrast, thek-throughput with k fixed cooperative nodes achieves higheraggregate throughput due to small overhead in the short frame-length.

REFERENCES[1] A. Ozgur, O. Leveque, and D. Tse, Hierchical cooperation achieves optimal

capacity scaling in ad hoc networks, IEEE Trans. Inform. Theory, vol. 53, no.10, pp. 3549-3572, Oct. 2007.

[2] A. Ozgur and O. Leveque, Throughput delay tradeoff for hierarchical coopera-tion, IEEE Trans. Inform. Theory, vol. 56, no. 3, pp. 1369-1377, Mar. 2010.

[3] J. Ghaderi, L. Xie, and X. Shen, Hierarchical cooperation in ad hoc networks:Optimal clustering and achievable throughput, IEEE Trans. Inform. Theory, vol.55, no. 8, pp. 3425-3436, Aug. 2009.

[4] U. Niesen, P. Gupta, and D. Shah, On capacity scaling in arbitary wirelessnetwork, IEEE Trans. Inform. Theory, vol. 55, no. 9, pp. 3959-3982, Sep. 2009.

[5] T. Kim, E. Chu, I. Bang, S. H. Kim, and D. K. Sung, Effect of control and dataframe overheads on the capacity scaling of a hierarchical cooperation scheme,IEEE WCNC, 2014 (accepted)

[6] D. Shen, Z. Pan, K. Wong, and V. Li, Effective throughput: A unified benchmarkfor pilot-aided OFDM/SDMA wireless communication systems, IEEE Infocom,2003, v. 3, p. 1603-1613.