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Communications and Network, 2009, 42-45 doi:10.4236/cn.2009.11006 Published Online August 2009 (http://www.scirp.org/journal/cn) Copyright © 2009 SciRes CN A Study of Multi-Node and Dual-Hop Collaborative Communi- cation Performance Based on Harmonic Mean Method Tingting YANG1, Shufang ZHANG2 College of Information Engineering, Dalian Maritime University, Dalian, China Email: 1xinxi2004jiuye@163.com; 2sfzhang@dlmu.edu.cn Abstract: Closed form expressions for the PDF and MGF of the harmonic mean of two independent expo- nential variates are cited and derived, and then applied to study the performance of cellular multi-node and dual-hop cooperative communication systems with non-regenerative relays over flat Rayleigh fading channels. We derive the probability density function (PDF) and asymptotic symbol error rate (SER) expression with MRC scheme. Then we use Matlab to simulate the performance. Keywords: harmonic mean, cooperative communication, multi-node, dual-hop, MGF 1. Introduction MIMO technique has been regarded as the essential technique for beyond 3G mobile cellular networks. The Benefits of MIMO system have been extensively studied by researchers in both academic and industry. It success- fully meets the rapidly growing demand for high rate, voice and especially for multimedia services [1]. In wireless cellular networks, base station can be equipped with multiple antennas and keeps them spa- tially separated. Unfortunately, it is hardly to fix multiple antennas in portable mobile terminals (also called as mo- bile terminals or users) due to insufficient antenna space, energy, and price, etc. So, the bottleneck of capacity is limited and the diversity technique of mobile terminals could not be realized from the traditional end-to-end transmission systems. In order to break this embarrassing situation, a novel concept, namely cooperative commu- nication (or user cooperative diversity) was introduced by Sendonaris et al. [2]. Mazen O Hasna et al. in [3,4] firstly applied the har- monic mean to the cellular multi-node and dual-hop co- operative communication systems. They respectively derived the probability density function (PDF), the cu- mulative distribution function (CDF) and the moment generating function (MGF) of the expression. It’s a new train of thought of cooperative diversity scheme. This paper applied the method of the harmonic mean to derive PDF and MGF of two independent exponential variates are cited and derived to study the performance of cellular multi-node and dual-hop cooperative communication systems with non-regenerative relays over flat Rayleigh fading channels. 2. Harmonic Mean of Exponential Variates 2.1 Definitions 1) Harmonic Mean Given two numbers X1 and X2, the harmonic mean of X1 and X2, 12 , H X X is defined as the reciprocal of the arithmetic mean of the reciprocals of X1 and X2 [3] that is: 12 12 12 12 2 2 ,11 H X X XX X X XX (1) 2) Exponential RV X follows an exponential distribution with parameterβ > 0 if the PDF of X is given by x X px eUx, where U is the unit step function. 2.2 Derive the Moment Generating Function MGF of the Harmonic Mean of Two Exponential RVs Given a RV X ∼ E(β), the PDF of Y = 1/X can be evalu- ated with the help of [9]. Then, ),()( 2yUe y yp y Y s y YY MsEe , v K (X)= v K (X) According to [5], we can get: 2 1 0 22[0, 0] v x vx vee xe dxKRR 2 00 sy sysy y Y Y M sEepy edyeedy y =1 () 2(2) y M ssKs When X= 12 , H X X, we can get: A STUDY OF MULTI-NODE AND DUAL-HOP COLLABORATIVE COMMUNICATION 43 PERFORMANCE BASED ON HARMONIC MEAN METHOD 12 12 12 12 11 2 012 12 12 2 121 12012 012 2 1212 112 0 12 0 2 2 12 2 1 2 sx sx XX x sx x sx sx MsEe ee KxKx Uxdx eeKx Kxdx exe Kxdx exe 12 2 1 x 12 2 012 x Kx (2) where K0(·) is the zero-order modified Bessel function of the second kind defined in11]. Where K(x) is the first order modified Bessel func n be constituted with [ 1 of the second kind defined in [11]. Here, we find the Formula (2) ca tion ① + ②, according to [5]. 1 0 vx v xeK xdx 211 ,, , 122 2 v v vv Fv v Then, we can get: ①2 , 12 1 2 ;1vs,12 ②2 , 12 1 2 s, 0v,12 12 2 12 12 1212 12 21 12 12 12 12 12 12 2 12 12 16 32 42 35 *3,;; 22 2 2 2 15 2, ; ; 22 2 X Ms s s F s s s Fs 3. Scheme of Cellular Multi-Node and Dual- erative Communication Systems erative communication ource, one destination and arbi- mobile terminals to base station). ase station. This paper research the M e, where Ps=Pr=1. In the lay and the MRC receiv- re respectively: Hop Coop with Non-Regenerative Relays over Flat Rayleigh Fading Channels 3.1 System Model Consider an uplink wireless coop system with only one s trary N relays (from The source terminal transmits Mary phase-shift keying (M-PSK) modulation signals to destination terminal through a direct path along with N dual-hop paths. The channel is assumed to be quasi-static with flat fading. Furthermore, perfect channel state information is as- sumed available at the receivers, but the channels are unknown at the transmitters. There are two transmission phases. Firstly, the source broadcasts signals to destina- tion and relays. Secondly, the relays which can success- fully decode the signals will retransmit them to destina- tion. Otherwise, they remain idle and do not participate in the cooperation. Figure 1 is the system model of multi-node and dual- hop cooperative communication system. S is the moving terminal, D is the b PSK modulation of non-regenerative relay over flat Rayleigh fading channels, and the noise is the additive white Gaussian noise (AWGN). We suppose there are m relays on the uplink, and the gains are Gi. Assume that terminal S is transmitting a signal S(t) which has an av- erage power normalized to 1. 3.2 Performance Analysis Assume that in the EPA mod situation of non-regenerative re ing mode, the receiving signal a 111 R Sthst nt StgGhst ntnt 11 11 12d 1/ ii Gh When can according with the harmonic mean format, as 22 11 2 hg 00 22 11 00 NN hg NN which can use the method of harmonic mean to calculate. Figure 1. System model C opyright © 2009 SciRes CN 44 A STUDY OF MULTI-NODE AND DUAL-HOP COLLABORATIVE COMMUNICATION PERFORMANCE BASE ON HARMONIC MEAN METHOD We define i and i g are respectively instantane- ous SNR of the ith channels. The total SNR is: 1 m fi i rr r According to [4], we can achieve the cumulative dis- tribution function (CDF) of the instantaneous SNR i of the Multi-node and dual-hop Collaborative Commu- nication channels: 1i g i ()1() () ii m rh F rprrpr r i g The probabilitydensity function (PDF) of the instanta- neous SNR __ 11 __ __ /2[()() ]1/ 2 1 1 () 1()[( hg ii iii mrr r rhgh i Frrrr eKrrr 1/2) ] i i of the Multi-node and dual-hop Col- laborative Communication channels: 11 1 2 2 1 0 2 2 hg ii ii ii ii ii rr hg hg ihg hg rr rr U rr K rr The Outage Probability ii hg m rr K e 0 th th P utPPd o On the assumption that the average SNR i when i h = i g = i (MGF) of th , can obtain the moment generating functione instantaneous SNR i of the Multi-node and dual-hop Collaborative Communicatio channels[4][8]: n 1 21 1 3 ()11,2; ; 24 M i f i M ss F s 0 1 1!! 12 12 sin 1 22 0 1357 21! 2 sin 2 2 0 1 1!! sin 22 () 11sin !2 1! 2 K iK N K KM Ms K M The upper limit of average SER of the Multi-node and dual-hop channels is: 1 1 11 m s fp i Es sk g 2 22 1sin sin sin 12 24 1 1!2! 1!2! sin sin 33 44 !1!! 2 ! K N K K xpression expressed as: MM kK K d M This formula can’t get it’s closed-form, but we can get the asymptotic e 22 m ii i S f E 2 2 22 1 1sin sin sin sin 1!2! 1!2! 33 4!1!! 2 ! 22 m f m i i When 1 4 i ,as (1, ) im 2 22 2 0 1 1sin () sin sin 12 sin( )3 4! 2 S f mN miKK k i K PE K 4. Numerical Results and Performance Analysis In thper, we will respectively simulate and analysis the PDF of insSNR is pa tantaneous i of about different situation the Multi-node and dual-hop Collaborative Communication channels. We research the M-ary phase- shift keying (M-PSK) modulation, M=4,8; the number of relays m=4,10. We respectively simulate the situation of high SNR and low SNR with 20 sampling nodes. Figure 2 is the compare of PDF about different sam- pling ranks and different relay numbers. From this figure, C opyright © 2009 SciRes CN A STUDY OF MULTI-NODE AND DUAL-HOP COLLABORATIVE COMMUNICATION 45 PERFORMANCE BASED ON HARMONIC MEAN METHOD Copyright © 2009 SciRes CN Figure 2. The compare of PDF about different sampling ranks and different relay numbers Figure 3. The compare of error symbol rate (SER) abou e different sampling ranks and different relay numbers e performance is bette hen the relay number is more. On the same relay no the performance is almost the same when the high sam pling ranks and low sampling ranks. Figure 3 is the compare of error symbol rate (SER) about the different sampling ranks and different rela numbers. We respectively simulate the situation of m=4,10, M=4,8, with 20 sampling nodes. Because little SER, we adopt the logarithmic scale coord method. We can find on the same SNR, the performance better when the relay number is more. When the same e erformance of Multi-node and dual-hop Collaborative C, Canada, RYZHIK I M. Table of integrals, series, and is sampling nodes, the performance is better which is adopt with the high rank modulation. It’s also approved that th p Communication can be improved when adopt the high rank modulation while the user’s number is definite. 5. Conclusions This paper applies the method of the harmonic mean to derive PDF and MGF of two independent exponential variates which are cited and derived to study the per- formance of cellular multi-node and dual-hop coopera- tive communication systems with non-regenerative relays over flat Rayleigh fading channels. We derive the probability density function (PDF) and asymptotic symbol error rate (SER) expression. These numerical results indicate that the number of relay is more, the performance is better. It also indicates the as- cendance performance of cooperative diversity. REFERENCES [1] YIN Q Y, ZHANG Y, DING L. A new space diversity technology. Transactions of Xi’an Jiaotong University. 2005, 39(6): 551-557. [2] SENDONARIS A, ERKIP E, AAZHANG B. Increasing uplink capacity via user cooperation diversity. IEEE Int. Symp. on Information Theory, Cambridge, MA, Aug. 1998, 156-156. [3] HASNA M O, ALOUINI M-S. Harmonic mean and end-to-end performance of transmission systems with relays. IEEE Transactions on Communications, 52(1): Jan. 2004. [4] HASNA M O, ALOUINI M-S. Performance analysis of two-hop relayed transmission over Rayleigh fading channels. Proc. IEEE Vehicular Technology Conf. (VTC’02), Vancouver, B t th r pr Sept. 2002, 1992-1996. [5] GRADSHTEYN I S, oducts. San Diego, CA: Academic Press, 5th Ed., 1994. [6] ABRAMOWITZ M, STEGUN I A. Handbook of mathematical we can find on the same SNR, th des, - functions with formulas, graphs, and mathematical tables. New York, NY: Dover Publications, 9th Ed., 1970. [7] IKKI S, AHMED M H. Performance analysis of cooperative w y diversity wireless networks over nakagami-m fading channel. IEEE Communications Letters, Apr. 2007, 11(4). [8] SIMON M K, ALOUINI M-S. Digital communication over fading of the inate channels: A unified approach to performance analysis. New York: Wiley, 2000. |