IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 2, FEBRUARY Cooperative Relaying in Multi-Antenna Fixed Relay Networks

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1 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 2, FEBRUARY Cooperative Reaying in Muti-Antenna Fixed Reay Networks Abdukareem Adinoyi and Haim Yanikomerogu Abstract Space, cost, and signa processing constraints, among others, often precude the use of mutipe antennas at wireess terminas. This paper investigates distributed decodeand-forward fixed reays infrastructure-based reaying which are engaged in cooperation in a two-hop wireess network as a means of removing the burden of mutipe antennas on wireess terminas. In contrast to mobie terminas, the depoyment of a sma number of antennas on infrastructure-based fixed reays is feasibe, thus, the paper examines the impact of mutipe antennas on the performance of the distributed cooperative fixed reays. Threshod-based maxima ratio combining MRC and threshodbased seection combining SC of these mutipe antenna signas are studied and anayzed. It is found that the end-to-end E2E error performance of a network which has few reays with many antennas is not significanty worse than that which has many reays each with a fewer antennas. Obviousy, the former network has a tremendous depoyment cost advantage over the atter. It is aso observed that the E2E error performance of a network in which the mutipe antennas at reays are configured in SC fashion is not significanty worse than that in which MRC is used. For impementation, SC presents a significanty ower compexity and cost than a fu-bown MRC. The anaysis in this paper uses the versatie Nakagami fading channes in contrast to the Rayeigh mode used in most previous works. Index Terms Cooperative diversity, fading channes, fixed wireess reays, mutipe antennas, seection combining, threshod maxima ratio combining. I. INTRODUCTION THE future wireess systems are envisaged to offer ubiquitous high data-rate coverage in arge areas. To meet such ambitious demands, fundamenta changes in system design and depoyment as we as incorporation of advanced signa processing techniques are required to enabe nove and effective ways of coection, distribution and utiization of wireess terminas signas [1], [2]. Muti-antenna techniques are we studied; a number of promises in these schemes are documented in [3]-[5]. Their appication to wireess systems often encounters numerous impementation probems. For exampe, an eement spacing of Manuscript received Apri 8, 25; revised December 23, 25, Apri 21, 26, and June 3, 26; accepted August 8, 26. The associate editor coordinating the review of this paper and approving it for pubication was T. Duman. This work was supported in part by the Natura Sciences & Engineering Research Counci of Canada NSERC under participation in project WINNER Wireess Word Initiative New Radio - This paper was presented in part at the IEEE Wireess Communications and Networking Conference WCNC, Las Vegas, Nevada, USA, Apri 3-6, 26. The authors are with the Broadband Communications and Wireess Systems BCWS Centre, Dept. of Systems and Computer Engineering, Careton University, 1125 Coone By Drive, Ottawa, Ontario, K1S 5B6 Canada, emai: {adinoyi, haim}@sce.careton.ca. Digita Object Identifier 1.119/TWC /7$2. c 27 IEEE haf the carrier waveength is required to ensure uncorreated signas. The future wireess terminas are expected to be sma and ight. The sma size feature imits the spatia separation needed by mutipe antenna systems for their optima performance. The ightweight feature imits the power capabiity and signa processing that the terminas can support. Hence, the depoyment of a arge number of antennas on wireess terminas is not feasibe, at east in some networks. In addition, efficient power utiization continue to be of great priority in wireess terminas. Therefore, nove techniques for expoiting network resources through the cooperation of nodes, known as cooperative diversity or antenna sharing, are being considered. The interest in this area is steadiy growing, thus spawning a surge of pubications on reaying and cooperative reaying networks in [1], [2], [6]-[15]. The idea behind cooperative communication dates back to the cassica and motivating work of Meuen [16] and Cover and E-Gama [17] on reay channes. Their theoretica exposition assumes fu-dupex, and therefore expensive reays. However, upon reaxing this condition, their work provides the important basis for the cooperative schemes and protocos for inexpensive wireess reay networks that have gained prominence recenty [1], [2]. In [1], Laneman and Worne discuss a cooperative protoco for combating mutipath fading. This protoco expoits the spatia diversity avaiabe among a coection of distributed terminas that assist one another. The work in [2] presents a simiar treatment referred to as user cooperation diversity. It aso highights a practica impementation of the cooperation scheme in the framework of CDMA systems. In the IEEE 82 wireess word framework, a number of working groups are focusing on deveoping mesh-enabed standards such as IEEE 82.11s - WLAN Wireess Loca Area Network, IEEE WPAN Wireess Persona Area Network, Mesh Networking, IEEE 82.16j - WMAN Wireess Metropoitan Area Network, and IEEE MBWA Mobie Broadband Wireess Access. In addition to these on-going standardization efforts, various proprietary mesh/reay network soutions in the unicensed bands are aso being deveoped by the industria payers. The emergence of the reay-enabed standards in the IEEE 82 famiy is ikey to resut in much higher interest and activity for reay-based communications. Aready, the WINNER project is deveoping a reay-enabed depoyment concept for the next generation broadband mobie radio access. Their reay depoyment strategy is expected to integrate wide area and short range scenarios cosing the gap between WLAN-type and ceuar systems [18]. It is important to note that the

2 534 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 2, FEBRUARY 27 First Hop 1 2 L Reay # 1 Second Hop S R D S D a S : Source R: Reay D: Destination Reay # j Reay # b Fig. 1. Reay networks a DF fixed protoco conventiona reaying, b TDF protoco with muti-antenna cooperative reays. WINNER project focuses mainy on infrastructure-based reay depoyments. This paper presents how infrastructure-based fixed reays with/without mutipe antennas can be used for providing diversity gains for a wireess termina which, otherwise, has imitations in the number of antennas that it can bear. Singe antenna reaying is a specia case of this set-up. Threshodbased maxima ratio combining MRC and threshod-based seection combining SC of these mutipe antenna signas at the reays are examined and anayzed. Threshod decoding is empoyed as an additiona measure towards combating error propagation. Finay, the paper uses the versatie Nakagami channe mode in the anayses in contrast to the Rayeigh fading mode which is commony anayzed. By adopting the Nakagami mode the anayses is thus appicabe to reaying under a wide variety of channe scenarios, with the Rayeigh channe mode serving as a specia case. A muti-antenna reay scheme is discussed in [9] but with a number of differences between the present work. Firsty, the reays in [9] do not cooperate but the antennas at each reay do the cooperation. Secondy, the network capacity has been used as their performance criterion. The foowing main resuts are derived. The cooperative diversity strategy empoyed as an add-on to infrastructurebased reays which might be depoyed primariy for high data rate coverage extension can provide a sma wireess terminas with the advantages of spatia diversity without the need for the physica antennas at these wireess terminas. For a given performance requirement, the mutipe antennas at reays can tremendousy reduce the number of reays required in a network area, thereby, reducing system depoyment cost. Threshod SC at the reays represents an exceent compromise between performance and compexity. It is found that a minimum of two antennas are required at the reay to yied an E2E diversity order equa to the number of reays pus one. Furthermore, it is observed that with a arge number of antennas at the reays, threshod decoding is not necessary. However, for a sma number of antennas, the choice of threshod becomes crucia. In the next section the system mode, the reaying protoco and the channe mode are presented. Section III motivates possibe modifications at the reay eve that coud address the bandwidth inefficiency of repetition-based protoco for mutireay schemes. Foowing the E2E error performance formuation, some numerica resuts on decode-and-forward probabiity of reays are discussed in Section IV. The error probabiity cacuations at the reays are presented in Section V. This is foowed by numerica exampes and discussions on E2E system performance in Section VI. Finay, concusions are drawninsectionvii. II. THE SYSTEM OF MULTI-ANTENNA MULTIPLE RELAYS The conventiona fixed protoco decode-and-forward DF reay network is shown in Fig. 1a where the destination reies ony on the signa from the reay. The two-hop system architecture consists of threshod decode-and-forward TDF-based fixed reays each carrying L diversity antennas Fig. 1b. The scenario referred to as symmetric network, as opposed to the asymmetric one, is considered. The symmetric networks assume that a inks source-reay, reay-destination, and source-destination experience independent but statisticay identica channes with the same mean pathoss. The empoyed protoco operates as foows. In the first time sot, the source broadcasts a signa that is received by both destination and reays. The destination stores this signa for future processing. The received L signas at each reay are processed using either SC or MRC diversity technique, depending on the processing compexity that the reays possess. Whether SC or MRC is used, the reay checks the SNR of the received signa against a preset threshod. The reay decodes and forwards ony when this SNR is greater than this threshod.

3 ADINOYI AND YANIKOMEROGLU: COOPERATIVE RELAYING IN MULTI-ANTENNA FIXED RELAY NETWORKS 535 In the second time sot, the reay either does or does not forward a new regenerated signa to destination. If at east one reay forwards, the destination MRC combines the deayed buffered signa received in the first time sot with the new versions from the reays. It is assumed that ony one antenna is utiized at each reay for forwarding. The SC detection-based reay requires one receiver chain in contrast to MRC detectionbased reay which requires a separate receiver chain for each antenna [19, pp. 262]. A singe transmitting antenna is adopted to keep the cost comparabe to a conventiona singe antenna reay network where one receiver chain is required. Using one transmit antenna provides a basis for fair comparison between a singe antenna reaying which uses one transmit antenna. The reays, however, coud empoy the mutipe antennas in an inteigent" transmit beamforming. Shoud this be the case, the system performance coud be improved which wi further increase the attractiveness of muti-antenna reays. III. SYSTEM COMPLEXITY AND BANDWIDTH PRESERVATION A muti-reay scheme empoying repetition-based protoco coud require enormous bandwidth since each reay requires its own sub-channe in the form of orthogona time sots for time division mutipe access TDMA or different frequency sots for frequency division mutipe access FDMA appications. For a arge number of reays, the bandwidth efficiency of such schemes might be so ow to the extent that the bandwidth penaty coud outweigh the advantages of the muti-reay scheme. To avoid such an inefficient use of the bandwidth, possibe modifications on the conventiona reays are necessary. The muti-reay system coud use simucast techniques, where in the second hop the reay set those with SNR greater than the threshod simutaneousy transmits their signas after being appropriatey processed. For instance, the reay coud use a finite impuse response FIR to fiter the input symbos prior to performing a inear-type digita moduation scheme such as MPSK, MQAM, and others. The impuse responses of these reay-embedded fiters are different from one reay station to another. However, they are designed to meet the necessary conditions to expoit the maximum diversity gain of MRC. In this case a form of orthogonaity is achieved, in terms of fiter responses, not in terms of time or frequency sots which are bandwidth-intensive. This transmit moduation diversity strategy is shown to be a fraction of 1 db inferior to the cassica MRC receive diversity [21]. More detais on the fiter design can be found in [21], [22]. Another possibe strategy is the coherent cooperative transmissions from mutipe adjacent nodes proposed in [23], where prior to transmission of the signas, these mutipe nodes adjust their transmission characteristics, for exampe, phases and symbo timings, so that their signas add up coherenty at the destination. In fading channes, however, this adjustment is based on the a priori knowedge of the forward channe which can be obtained through feedback from the BS in TDD-based systems. The modifications compexities discussed above may be considered in the depoyment of the muti-antenna muti-reay schemes in order to avoid bandwidth expansion invoved in the repetition or round-robin transmission protocos. The amount of compexity of reays woud depend on how much bandwidth the system designer is prepared to exchange for ower system compexity. IV. FORMULATION OF SYSTEM END-TO-END ERROR PERFORMANCE We define a genera ink in the network as a node i communicating with another node j. A node coud correspond to the source, a reay or the destination. The received signa at node j transmitted from node i can then be written as r ij r i j h ij x i + n j,wherex i is the signa emanating from node i, h ij is the channe gain between node i and node j and n j is the additive white Gaussian noise AWGN. For a reay in a muti-antenna reay network, the input-output reation of the first hop, i.e., source node S to reays, can be expressed as r j h Sj x S + n j, j 1, 2,,, 1 where is the tota number of reays, r j is the L1 received vector at the jth reay, h Sj [h 1 Sj,,hL Sj ]T is the random channe vector with independent components which are aso independent of the components in the L 1 AWGN noise vector n j. For a coherent detection scheme, perfect recovery of phase and carrier is possibe, therefore, each entry h ij represents the magnitude of the fade sampe which is assumed foows the Nakagami distribution. It is aso assumed that the channe state information for the reay-destination R- D inks is avaiabe to the destination whereas, those of the source-reay S-R inks are known to the respective reays. The destination does not require any knowedge of the S-R channes. In the second hop time-sot, a reay j forwards the preprocessed signa ˆx j to the destination node D provided that the received SNR is greater than a threshod γ th. This signa is received at the destination as r jd h jdˆx j + w j, j 1,,, 2 where h jd is the fade sampe of the ink between reay j and destination, and w j is the receiver noise. The mode 2 assumes that the signas received at the destination satisfy the orthogonaity condition that is the reay signas do not constitute interference. We have assumed the mode in 2 in exposing the diversity benefit of the cooperative networks thereby estabishing a ower bound on the performance of the system modifications motivated in Section III. We compete the discussion of this section with the channe mode. The anaysis assumes that the fading sampe has the Nakagami-m distribution, a versatie statistica mode that can mode a wide range of wireess environments [2]. For instance, the Ricean mode which represents the ine-of-sight LOS communication is captured through the Ricean K parameter to Nakagami-m parameter transformation, K m 2 m m ; moreover, m 1 gives the Rayeigh fading m 2 m mode. The SNR per symbo γ at a reay antenna foows a

4 536 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 2, FEBRUARY 27 gamma distribution described by 1 pγ,m mm γ m1 m Γ[m] where γ h 2 exp mγ,γ, m 1/2, 3 ij E s /N and E[h 2 ij E s /N ]ΩE s /N is the average SNR per symbo, E s is the energy per symbo and ΩE[h 2 ij ]. The AWGN is characterized by one-sided power spectra density N W/Hz and Γ[ ] is the gamma function. A. Error Rate Anaysis The overa end-to-end E2E error rate P TDF e,e2e of mutiantenna muti-reay and protoco can be approximated, using an approach simiar to that presented in [24] as P TDF e,e2e P dec P e,rp e,p + P dec 1 P e,rp e,coop + 1 P dec P e,dir, 4 The first and second terms represent the component due to cooperation whie the third demonstrates the case when cooperation fais. The first term is needed to account for possibe error propagation. P e,r is the error probabiity at the reay given that the received SNR is greater than the threshod, P e,coop is the destination error rate when cooperation is in effect i.e., more than one reay paths are combined at destination. P dec is the probabiity that at east one reay performs decoding and forwarding, 2 P e,dir is the destination probabiity of error when no reay forwards. The impact of the number of reays have been captured by averaging over the possibe cooperative scenarios P e,coop and P dec, and therefore, the error probabiity due to error propagation P e,p can be bounded with the worst scenario, P e,p 1/2 [24]. The expression in 4 is an approximation for the foowing reasons: The cumuative impact of the error propagation by the reays athough sma in the muti-antenna scheme is ony represented with a bound. The probabiity of having diversity combining at the destination is modeed with the assumption that at east one reay forwards. To get the exact vaue we need to consider a possibe combinations of forwarding reays, which wi ony bring computationa compexity with no significant impact on the resuts. This is deduced from the fact that E2E system simuation resuts match cosey with those obtained using this formuation. P dec is obtained as foows. Let P reay r does not forward 1 P reay r does forward 1 P DFP,r. Then, can be expressed as P dec P dec 1 1 P DFP,r r1 r1 NR r 1 r+1 P DFP r, 5 where P DFP,r P DFP,forar and P DFP is the decodeand-forward probabiity DFP. 1 The is dropped from the PDF since the SNR at antennas have identica distributions. 2 This impies there is diversity combining at destination. In symmetric network scenarios assuming that a the reays have the same error performance, then P e,coop can be evauated for equa-ampitude moduation as foows: First, it is shown beow that the probabiity of error for a T - branch MRC-receiver in Nakagami-m channe is given as h Γ[T m+1/2] π Γ[T m] B μ [Tm,1/2]. The probabiity that i reays forward which gives rise to i +1 diversity branches at the destination is given as NR C i 1 P DFP NRi PDFP i where N C i R! i!n. Therefore, P Ri! e,coop can be expressed by weighted average over the possibe cooperation scenarios as P e,coop h π i1 C i 1 P DFP NRi P i DFP Γ[i +1m +1/2] B μ [i +1m, 1/2], Γ[i +1m] where B μ [, ] and Γ[ ] are the incompete beta and gamma functions [29], respectivey. The parameter λ g sin 2 π/m, M is the moduation consteation size. The parameters g and h are defined according to the moduation scheme and the nature of signa detection. Finay, μ m/m + λ. By examining 4 and 6 it can be shown that how we the reay performs has a significant impact on the cooperation benefit. For instance, if P e,r is ow and P dec is high, one obtains the most desirabe benefit from the cooperation: 6 P TDF e,e2e P e,coop. 7 The resut given in 7 provides considerabe information. First, reays aways have good and reiabe signa to transmit. Then, combining these signas at the destination provides the fu diversity benefit. This impies that a diversity order equa to +1 can be achieved for terminas with one antenna. Furthermore, since the reay perfecty decodes the source information, the source appears to the destination as if it were at the position of the reay, hence, path-oss saving advantage can be expoited. This is visibe ony in the asymmetric channe scenario that incorporates the distancedependent received power variations. B. Decode-and-Forward Probabiity Cacuation The aim in threshod decoding is to ensure that signa forwarded by the reay is reiabe since the number of times, reiaby detected signa is reayed to the destination has an impact on the cooperation benefit. Therefore, the decodeand-forward probabiity of reays is an important system performance criterion. Let us now examine the DFP of the muti-antenna reay with threshod DF strategy. We begin with SC where the reay first seects the branch with the argest instantaneous SNR, i.e., γ max[γ 1,,γ L ] and then compares it with the set decoding threshod γ th. The joint probabiity density function PDF of seecting n argest from L independenty and identicay distributed random variabes is given in a genera form in [25] as p γ1,,γ n γ 1,,γ n n!cn L [F γ] Ln n 1 pγ, wheref γ γ pξdξ is the cumuative distribution function CDF. Therefore, for the SC-based reaying protoco and the underying Nakagamim distribution, the required PDF reduces to pγ,m

5 ADINOYI AND YANIKOMEROGLU: COOPERATIVE RELAYING IN MULTI-ANTENNA FIXED RELAY NETWORKS 537 L[F γ,m] p γ γ,m as pγ,m Lm m γ m1 exp mγ m Γ[m] L k+m a k, 8 γm where a k 1k k!m+k. We empoy the functiona series representation to rewrite the series in 8 with the hep of [29, pp. 19,.314] as k+m a k γm m γm p c p, 9 γm p eading to the foowing PDF pγ,m mγ Le Γ[m] L γ p p+ml mγ c p, 1 where c m 1L, c p m p p k1 kl pa kc pk, γ Ω sr E s /N and Ω sr is the average power of source-reay channe. The derivation of DFP of the seection-based DF reay P DFP,SC can be accompished by using [29, pp. 356, ] as P DFP,SC γ th,m p γ ξ,mdξ γ th L exp mγ th Γ[m] L p + ml 1! k! p+m p mγth c p k. 11 The infinite summation in the PDF in 8 can be eiminated if integer vaues of m are stricty considered. Hence, further simpification can be performed eading to an aternative PDF [26]: pγ,m L 1 L 1 m 1! m m1 m+k γ m+k1 exp +1 mγ b k, 12 where b 1, b 1, b 1 m1, and b m1! k 1 min[k,m1] j+1k k j1 j! b kj are recursivey computed with k 2, 3,,m1 1. With this PDF, a more convenient DFP expression for the seection-based DF reay can be obtained as P DFP,SC γ th,m p γ ξ,mdξ γ th L 1 L 1 m 1! m1 m+k1 t b k exp γ th +1m m + k 1! t! mγ th / t +1 m+kt. 13 The DFP for the MRC reception at the reay can simiary be derived. In this case, assuming that the branch fading ampitudes are statisticay independent and distributed with the Nakagami distribution, then γ aso foows the Nakagami distribution with a parameter Lm [27]. Thus, the foowing PDF is obtained Lm m γ Lm1 pγ,m Γ[Lm] exp mγ. 14 Consequenty, the DFP of MRC-based reay detection can be obtained as exp mγ th P DFP,MRC γ th,m Γ[Lm] Lm1 k Lm 1! mγth. k! 15 Fig. 2 shows the improvement in DFP of a reay that is equipped with two antennas L 2 and SC or MRC detection is utiized. The figure gives curves for different Nakagami parameter m 1, 2, 4, and 6. The singe antenna case is aso shown for comparison purposes. Thus, a significant increase in the number of times the reay decodes and forwards is observed for the dua-antenna. This impies that there is an increase in the number of times the destination reies on diversity combining using signas received via the reays. This, however, has to be compemented by the improved error performance at the reays as shown beow. These reay performance indicators reay error rate and probabiity of decode and forward are shown to characterize the system E2E performance. V. RELAY ERROR PERFORMANCE ANALYSIS In threshod decoding, error performance at the reay impies conditiona error. That is, the error performance residua given that receiver decodes ony when the received SNR is greater than the set threshod. In a cear abuse of notation, to be compact and simpe, this conditiona dependence wi be dropped but shoud be understood in this context. We proceed with the derivation of the probabiity of error at a reay when a threshod is imposed. For a given received SNR γ, the probabiity of symbo error for equa ampitude moduation MPSK can be expressed as P mpsk e γ h erfc γλ, 16

6 538 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 2, FEBRUARY 27 Reay Decodeandforward Probabiity: P DFP SC/ L 2 L 1 MRC/L 2 m1 m2 m4 m Reay detection threshod SNR db: γ th Fig. 2. Probabiity of decode in threshod decode-and-forward muti-antenna reaying. where λ g sin 2 π/m. For BPSK M 2,h1/2, g 1, and equaity is satisfied. For higher MPSK consteations h 1 and for other coherent binary transmission ike orthogona BFSK, M 2,g1/2, h1/2 [28]. In this paper, MPSK moduation schemes are used to iustrate the derivations, other coherent moduation schemes that have error rate defined by Q-function in AWGN can be accommodated as we. Let us express the combined received SNR in this genera form L c γ γ i, 17 i1 where L c L 1impies no diversity, L c 1,L>1 impies SC diversity, L c L, L > 1 impies MRC diversity, and finay, 1 < L c L, L > 1 represents the generaized seection combining GSC diversity. Traditionay, is computed by averaging the conditiona i.e., 16 over the underying PDF. Foowing this trend, the error rate for a reay that bindy decodes and forwards i.e., does not perform threshod detection is P e m6 m1 P mpsk e γ p γ γ dγ. 18 In the threshod decoding the receiver refrains from detection if the received SNR fas beow the threshod γ th. The probabiity of error at the reay is thus the probabiity of error in the γ γ th regimes. Let us ca this error performance P e,r,γ th. Proceeding with the integration in 18 we have P mpsk e γ p γ γ dγ + γ γ P mpsk e γ p γ γ dγ γ th P mpsk e γ p γ γ dγ P mpsk e γ p γ γdγ + υp e,r,γ th, 19 upon which P e,r,γ th is expressed as P e,r,γ th 1 P υ mpsk e γ p γ γ dγ }{{} γt I 1 P mpsk e γ p γ γ dγ. 2 γ } {{ } I 2 Next, we evauate I 1 and I 2 for the MRC-based detection at the muti-antenna reay. The factor υ has been evauated in Appendix I and the derivation of I 1 and I 2 for SC-based detection is contained in Appendix II. A. MRC-Based Muti-Antenna Reay and Threshod Decodeand-Forward Strategy First, we provide the performance expressions for the scenario where MRC-based TDF reaying technique. In this case, using the PDF in 14, I 1 in 2 is obtained thus, I MRC 1 h exp m mγ Lm γ Lm1 erfc ΓLm γλ dγ, 21 where this integra can be expressed in terms of generaized hypergeometric function as I MRC 1 h Γ[Lm +1/2] π Γ[Lm +1] mλ Lm 2 F 1 [Lm, Lm +1/2; Lm +1; m ]. 22 λ Further simpification can be performed by using [29, pp ] to express 2 F 1 [Lm, Lm+1/2; Lm+1; m λ ] as λ λ+m Lm m 2F 1 [Lm, 1/2,Lm+1, λ+m ]. Finay, using [29, pp ] 22 can be simpified to I MRC h Γ[Lm +1/2] 1 B μ [Lm, 1/2]. 23 π Γ[Lm] This expression is more compact than the one shown in [31]. To evauate I 2 we foow the same steps as performed above Lm I MRC m γ Lm1 2 h exp mγ erfc Γ[Lm] γλ dγ. 24 It is difficut to obtain a cose form expression for the exact integra of 24. Therefore, two things can be done. The first is to empoy numerica integration techniques to evauate it. The second option is to invoke some approximations that are known to be tight. For exampe 1/2 erfcx/ 2 has been shown to be we approximated by expx 2 /2/ 2πx, x> [3]. Therefore, 24 can be expressed as I MRC 2 exp h πλγ mγ Lm m γ Lm1 Γ[Lm] + λγ dγ, 25

7 ADINOYI AND YANIKOMEROGLU: COOPERATIVE RELAYING IN MULTI-ANTENNA FIXED RELAY NETWORKS 539 where a convenient expression can then be obtained as Lm m h I MRC 2 Γ[Lm 1/2] πλ Γ[Lm]λ + m Lm1/2 Γ[Lm 1/2,λγ th + mγ th ], 26 where Γ[a, z] z t a1 e t dt represents the upper incompete gamma function. Though, this approximation is tight at high SNR, it is oose at ow SNR. In certain scenarios, the ow SNR regime may be of interest. Therefore, the foowing exact expression for ow SNR regime is pursued which can be combined with the high SNR regime anaysis above for evauating the system performance. It is noted that erfcx Γ[1/2,x 2 ]/ π. Therefore, erfc γλ Γ[1/2,γλ]/ π and by using [29] I MRC 2 can be written as Lm I MRC m γ Lm1 ΓLm exp mγ 2 h 1 2 π n 1 n n+1/2 λγ dγ, n!2n +1 with further manipuations, it can be shown that I MRC 2 mγth h Γ[Lm] Γ[Lm, ] Γ[Lm] 4h 1 p π p!2p +1 p Γ[Lm + p +1/2] Γ[Lm] λ p+1/2 p+1/2 m 27 Γ[Lm + p +1/2,mγ th /]. 28 Simiary, error performance expressions for the SC-based reaying can be derived. The steps are given in Appendix II. B. On the Seection of Threshod Vaue Fig. 3 shows the variation of the with the threshod for different network configurations and various vaues of average SNR ASNR. The figure demonstrates that mutipe antennas at reays can reieve the cooperation s dependence on the threshod decoding protoco, especiay when there are few reays and many antennas at these reays. It is found that for arge L and sma, E2E performance is insensitive to the choice of threshod over a wide range of threshod vaues Fig. 3. In this scenario, it is preferred that a threshod is not appied at a. For sma L and arge the choice of threshod is critica. The resuts aso indicate that a good choice for the threshod is γ th 2 γ [db]whichisusedin[24] for a simpe singe antenna reay network. This setting does not generaize for the muti-antenna muti-reay. However, any reasonabe threshod setting can be used to compare the system architectures as it provides some indications of their reative performance. Athough, such a setting may not produce the best possibe E2E performance. E2E , L1, ASNR2 db 1, L1, ASNR25 db 1 5 1, L2, ASNR15 db 1, L4, ASNR15 db N 2, L1, ASNR1 db R N 2, L2, ASNR1 db R N 2, L4, ASNR15 db R Reay threshod SNR db Fig. 3. E2E vs. reay decoding threshod for different network configurations and average SNR. 1, 2, andl 2, 4. The issue of optimum threshod remains an open probem as it has not received sufficient attention. For instance, recenty, it has been shown that in asymmetric reay networks the choice of threshod depends on S-D and R-D channes [32] in contrast to the S-R channes usuay used in symmetric reay networks. Therefore, more investigations of this issue is required for any comprehensive concusion. VI. NUMERICAL ILLUSTRATIONS Fig. 4 shows the performance of the muti-antenna reay in symmetrica networks for different number of antennas L at the reay. The reay utiizes MRC and BPSK moduation is used in a the inks. Resuts are shown for m 1,2,6andL 1, 2, 4. It is assumed that the fading distributions between the tripartite source to reay, source to destination and reay to source are identica. The performance of conventiona reaying see network reay depoyment, Fig. 1 a is shown as we. The evauation of system performance for non-identica fading conditions is straightforward. For instance, suppose a fixed reay is positioned in such a way that it sees NLOS to the source and LOS to the destination. Assuming that the source have NLOS to destination, the reay-destination channe can be modeed with a suitabe m using the Nakagami-m to Ricean K-factor transformation and the source-reay and sourcedestination channes modeed using the Rayeigh distribution m 1. From Fig. 4, it is observed that the threshod-based mutiantenna reay systems yied significant gains over the referenced singe antenna fixed protoco reaying. Let us compare the SNR requirements at an error rate of 1 2. The foowing approximate gains are obtained over the conventiona reaying, 1.5 db L 1, 13 db L 2, and 14.5 db L 4forthe Rayeigh channes m 1. These gains represent a significant improvement. Furthermore, at 1 3,theTDFprotoco with dua antenna exhibits about 4 db superiority over that using a singe antenna. When four antennas are depoyed, this gain is about 5 db. For m 2, however, the gain of dua antennas over the singe antenna is about 1.5 db whie that of four antennas is 2.5 db. From these cases, it can be

8 54 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 2, FEBRUARY L 1, m 1, DF fixed protoco L1, m1 L1, m2 L1, m6 L2, m1 L2, m2 L2, m6 L4, m1 L4, m2 L4, m L4, m1 L4, m2 L4, m6 L2, m1 1 5 L2, m2 L2, m6 L1, m1 L1, m2 L1, m E /N db b Fig. 4. performance of MRC-based muti-antenna TDF reay in Nakagami fading, 1. TABLE I MRC-BASED AND SC-BASED RELAY DETECTION:REQUIRED SNR FOR A 1 4 FOR DIFFERENT NETWORK SCENARIOS MRC-based 2 4 # of antennas L m 1 m 2 m 1 m db 11.5 db 12.8 db 9.2 db db 8. db 8.2 db 6.4 db db 6.8 db 5.8 db 3.8 db SC-based 2 4 # of antennas L m 1 m 2 m 1 m db 11.5 db 13. db 9.2 db db 9.2 db 9.2 db 7.6 db db 7.8 db 7.6 db 6.1 db E /N db b Fig. 5. performance of MRC-based muti-antenna TDF reay in Nakagami fading, L1, m1 L1, m2 L1, m6 L2, m1 L2, m2 L2, m6 L4, m1 L4, m2 L4, m6 deduced that the diversity gain is better for the muti-antenna system in Rayeigh m 1 than in ess scattering channes m >1 which again confirms the notion of the benefit of the rich scattering environment. Furthermore, with dua antennas, the necessary diversity is aready acquired, and ony margina gains are observed for an increasing number of antennas. Fig. 5 shows the performance of the network with 2. We compare this reay network for different number of antennas at a 1 4. In Rayeigh fading, it is observed that a gain of 6 db is achieved for the network [ 2,L 2] over that of [ 2,L 1]. The gain of the network [ 2,L 4] over that of [ 2,L 1] increases ony marginay to 7.5 db which buttresses the point that with dua antenna, the necessary gain is amost derived. For the ess severe fading cases m >1, we observe that the gains are reduced. For exampe, for m 2, a gain of 3.5 db is obtained for configuration [ 2,L 2] and 4.7 db for [ 2,L 4]overthatof[ 2,L 1]. The trends observed in Figs. 4 and 5 are generay seen for the mutiantenna 4-reay network. The performance of this network is shown in Fig. 6. Let us now compare some of the system architectures Tabe I and Fig. 7. In the tabe the SNR required for an error rate 1 4 for different L and m is considered. It is observed that [ 2,L2] network performs comparaby to that [ 4,L 1], athough, the number of detection chains required in both configurations is the same. However, E /N db b Fig. 6. performance of MRC-based muti-antenna TDF reay in Nakagami fading, 4. E2E , L 4 4, L 1 2, L 2 2, L 4 4, L E b /N db Fig. 7. Comparison of network architectures demonstrating the impact of mutipe antennas on reays in Rayeigh fading.

9 ADINOYI AND YANIKOMEROGLU: COOPERATIVE RELAYING IN MULTI-ANTENNA FIXED RELAY NETWORKS 541 the network [ 2,L 2] has an additiona advantage over that of [ 4,L 1]; it is consideraby cheaper to insta additiona antennas at reays than depoying more reays. When two antennas are depoyed with 4,itis observed that [ 4,L 2] provides a SNR gain over [ 2,L 4] of about 2.2 db for m 1and about.4 db for m 2. The gain of the network [ 4,L 2] over that of [ 2,L 4] has to be carefuy viewed. If the cost of these two systems is considered depoying two reay stations as opposed to instaing two antennas on reay stations this gain as inconsequentia can be quicky dismissed, i.e., it is too sma in comparison to the concomitant cost and compexity over the network [ 2,L 4]. In fact, as observed, this gain disappears at a ess severe fading. In concusion, the network [ 2,L 4] maybe preferred to that of [ 4,L2] for depoyment purposes considering the capita invovement on and acquisition, abor, maintenance, signaing overhead, radio resources, etc. This concusion is based on the fact that cooperative diversity is the main interest. In addition, the impact of depoying four antennas on a singe reay node as opposed to four reays nodes each with singe antenna shoud be noted Fig. 7. Note aso that without these resuts, intuition woud have ed to the beief that the diversity order for the 4network is five 4+1. The fact is that it ony has the potentia of providing this much diversity order. Ceary, Fig. 7 shows that this is not the case. The configuration [ 2,L 4] indicates that adding more antennas from L 2to L 4 does not provide more diversity order; however, it wi ony increase antenna gains. Hence, an important concusion that can be derived is that two antennas are enough to provide the maximum diversity order, but any additiona antenna provides ony antenna gains. This aso heps expain why [ 2,L 2] shows performance advantage over the setup [ 4,L 1]. Moreover, increasing the number of antennas, the 2network can significanty outperform [ 4,L1]. At 1 5,[ 2,L4] provides more that 2 db SNR gain over [ 4,L1]. Fig. 8 serves to compare the threshod-based MRC and SC reaying. First, et us compare these techniques for the Rayeigh fading. Fig.s 8 a, b, c, and d show that MRCbased reay detection coud yied no more than 2 db gain over the SC-based. The maximum gain is recorded for a arge system configuration, specificay with [ 4,L4]. For a smaer number of reays say 2, the gain consideraby shrinks. Furthermore, it is observed that though MRC-based reaying is about 2 db superior to the SC-based counterpart the former is at expense of a huge system compexity and cost in the network [ 4,L 4]. For instance, the MRC requires sixteen separate receiver chains four at each reay station whie the SC-based requires ony four. The ow SNR gain cannot offset the cost disadvantage incurred by using MRC. Therefore, SC-based reaying offers an exceent tradeoff between cost and performance. Finay, for higher vaues of Nakagami parameter m >1, MRC sti records gains over the SC-based detection but these gains are too sma to justify for the cost invoved. This, further, tits the baance in favor of SC-based detection at reays. We wi now compare the SC-based detection for different system configurations Tabe I. We consider the SNR required for an error rate of 1 4 for different L and m. We compare network configurations [ 4,L 1], [ 4,L 2], and [ 2,L 4]. In the case of the networks [ 4,L 1]and[ 4,L 2], four detection chains are required but the network [ 4,L 2] requires extra four inexpensive antennas and switching mechanisms. It is observed that in Rayeigh fading environments, a gain as high as 3.8 db is obtained with the network [ 4,L 2] over that of [ 4,L 1] and this gain drops to 1.6 db for m 2.When[ 2,L 4] network configuration is empoyed in pace of [ 4,L 2], a degradation of 1.6 and.2 db, for m 1and m 2, respectivey, is observed. However, two detection chains are used in [ 2,L 4] network as compared to four in [ 4,L 2]network. Furthermore, as Fig. 8 and Tabe I indicate, depoying two reays each with two antennas [ 2,L 2] with SC at the reay yieds amost the same performance as depoying four reays each with one antenna [ 4,L1] Fig. 6. It is worth mentioning that two detection resources are required in the [ 2,L 2] case whereas the [ 4,L 1] case necessitates the use of four detection resources. Besides, the resource required for depoying extra reays is not comparabe to microdiversity antenna eements. Therefore, depoying microdiversity at reays may resut in considerabe savings in the number of reays to be depoyed in a given area. VII. CONCLUSION This paper investigates the cooperative diversity achieved when mutipe reays and source are engaged in a cooperation in two-hop wireess networks. Since space, cost, and signa processing constraints prohibit the use of a arge number of antennas at wireess terminas, the promises associated with muti-antenna techniques can be expoited through such a cooperation by mimicking the performance of a arge array of antennas. Infrastructure-based fixed reays may have the capabiity to carry mutipe antennas in contrast to terminas. Therefore, muti-antenna reay networks are examined. Threshod-based maxima ratio combining and threshod-based seection combining techniques to diversity process the reay signas are anayzed. From the perspective of end-to-end error performance, it is derived that for a given performance requirement, the mutipe antennas at reays can significanty reduce the number of reays required in a network area, with a considerabe impact on the system depoyment investment. The threshod seection combining reaying emerges as an exceent candidate in terms of performance-compexity tradeoff. Furthermore, it is observed that two antennas at the reays are enough to provide the diversity order equa to the number of reays in the network pus one. It is aso found that threshod decoding is not required when there are few reays and these reays have arge number antennas. APPENDIX I NORMALIZING FACTOR For MRC-based reaying, the normaizing factor is Lm m γ Lm1 υ MRC Γ[Lm] exp mγ dγ. 29 γ th

10 542 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 2, FEBRUARY MRC, m 6 MRC, m 2 MRC, m 1 SC, m 6 SC, m 2 SC, m MRC, m 6 MRC, m 2 MRC, m 1 SC, m 6 SC, m 2 SC, m E /N db b a 2,L E /N db b b 2,L MRC, m 6 MRC, m 2 MRC, m 1 SC, m 6 SC, m 2 SC, m MRC, m 6 MRC, m 2 MRC, m 1 SC, m 6 SC, m 2 SC, m Fig E b /N db c 4,L2 Performance comparison of MRC-based vs. SC-based muti-antenna TDF reay in Nakagami fading E b /N db d 4,L4 With the definition of the incompete gamma function the expression in 29 can be expressed as [ ] Γ Lm, mγ th υ MRC. 3 Γ[Lm] For Rayeigh fading m 1 and no diversity antennas at reay i.e., L 1, [ υ Γ Lm, mγ ] th Γ[1,γ th /] expγ th /. 31 For Nakagami SC-based reaying, the normaizing factor is υ SC γ th m m1 L L 1 1 m 1! m+k γ m+k1 exp +1 mγ L L 1 1 m 1! m1 b k dγ, b k k+m 1 Γ[ k + m, 1 + mγ ] th APPENDIX II SC-BASED MULTI-ANTENNA RELAY AND THRESHOLD DECODE-AND-FORWARD STRATEGY The derivation of error expressions for SC-based reay is considered here. In this scenario, the PDF in 12 is empoyed in computing I SC 1, thus I SC 1 h m1 exp L m 1! b k m +1 mγ 1 L 1 m+k γ m+k1 erfc γλ dγ, hl L 1 1 m 1! m1 b k

11 ADINOYI AND YANIKOMEROGLU: COOPERATIVE RELAYING IN MULTI-ANTENNA FIXED RELAY NETWORKS 543 m+k m γ m+k1 exp +1 mγ erfc γλ dγ. 33 Using the same approach as empoyed for MRC, I SC 1 can be expressed as I SC 1 hl m1 1 L 1 b m 1! k m+k Γ[1/2+k + m] 2F 1 [k + m, k + m πk + m m λ + 1/2; k + m +1; m1 + λ ]. 34 With the hep of [ [29], the hypergeometric function can] be expressed as 2 F 1 k + m, k + m+1/2; k + m+1; m1+ λ [ ] k+m m1+ 2F 1 k+m, 1/2,k+m+1,, λ+m1+ λ m1++λ thus, empoying [29, pp. 96, 8.391] a simpified expression is obtained I SC 1 hl 1 L 1 πm 1! m1 Γ[k + m +1/2] 1 + k+m B y [k + m, 1/2], 35 where y m 1+ λ +m 1+. Finay, the derivation of I SC 2 is performed as I SC 2 h m1 exp L m 1! b k m +1 mγ m+k γ m+k1 1 L 1 erfc γλ dγ, hl L 1 1 m 1! m+k m 1 m1 πλ λ + m+1 m+k1/2 Γ[m + k 1/2] [ Γ m + k 1/2,λγ th + m +1γ th b k ]. b k 36 As with 26 for MRC, this approximation is ony tight at high SNR. Therefore, it is necessary to find an expression for the ow SNR regimes. The steps to the fina soution are amost the same as in the MRC derivation. Without repeating those steps, the fina expression is given as I SC 2 h m1 exp L 1 L 1 m 1! b k m +1 mγ m+k γ m+k1 erfc γλ dγ, hl 1 L 1 m 1! k+m 1 Γ[k + m] 1+ [ Γ k + m, m1 + γ ] th 4h 1 p π p p+1/2 p!2p +1 m1 p+1/2 m λ Γ[k + m + p +1/2] Γ[k + m + p +1/2,m1 + γ th /]. b k 37 REFERENCES [1] J. Laneman, D. Tse, and G. Worne, Cooperative diversity in wireess networks: Efficient protocos and outage behavior, IEEE Trans. Inform. Theory, vo. 5, no. 11, pp , Dec. 24. [2] A. Sendonaris, E. Erkip, and B. Aazhang, User cooperation diversity - Part I: System description, IEEE Trans. Commun., vo. 51, no. 11, pp , Nov. 23. [3] G. J. Foschini and M. J. Gans, On imits of wireess communications in fading environment when using mutipe antennas, IEEE Wireess Pers. Commun., vo. 6, pp , Mar [4] L. Zheng and D. N. C. Tse, Diversity and mutipexing: A fundamenta tradeoff in mutipe antenna channes, IEEE Trans. Inform. Theory, vo. 49, no. 5, pp , May 23. [5] E. Teatar, Capacity of muti-antenna Gaussian channes, European Trans. Teecommun., vo. 6, pp , Nov [6] J. Laneman and G. Worne, Distributed space-time-coded protocos for expoiting cooperative diversity in wireess networks, IEEE Trans. Inform. Theory, vo. 49, no. 1, pp , Oct. 23. [7] R. Pabst, B. Wake, D. Schutz, P. Herhod, H. Yanikomerogu, S. Mukherjee, H. Viswanathan, M. Lott, W. Zirwas, M. Doher, H. Aghvami, D. Faconer, and G. Fettweis, Reay-based depoyment concepts for wireess and mobie broadband radio, IEEE Commun. Mag., pp. 8-89, Sep. 24. [8] H. Hu, H. Yanikomerogu, D. Faconer, and S. Periyawar, Range extension without capacity penaty in ceuar networks with digita fixed reays, in Proc. IEEE Gobecom, Nov. 24, vo. 5, pp [9] V. Morgenshtern and H. Böcskei, On the vaue of cooperation in interference reay networks, in CD Record Aerton Conference, Dec. 25. [1] J. Boyer, H. Yanikomerogu, and D. Faconer, Mutihop diversity in wireess reaying channes, IEEE Trans. Commun., vo. 52, no. 1, pp , Oct. 24. [11] M. Hasna and M. Aouini, End-to-end performance of transmission systems with reays over Rayeigh fading channes, IEEE Trans. Wireess Commun., vo. 2, no. 6, pp , Nov. 23. [12] M. Yukse and E. Erkip, Diversity in reaying protocos with ampify and forward, in Proc. IEEE Gobecom, Dec. 23, vo. 4, pp [13] A. Stefanov and E. Erkip, Cooperative space-time coding for wireess networks, IEEE Inform. Theory Workshop, Apr. 23, pp [14] Y. Hua, Y. Mei, and Y. Chang, Parae wireess mobie reays with space-time moduations, in Proc. IEEE Workshop Statistica Signa Processing, Oct. 23, pp

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Proakis, Digita Communications, New York: McGraw Hi, [29] I. Gradshteyn and I. Ryzhik, Tabe of Integras, Series, and Products. San Diego: Academic Press, [3] S. Verdu, Mutiuser Detection. Cambridge, UK: Cambridge University Press, [31] M. Aouini and M. Simon, Performance of coherent recievers with hybrid SC/MRC over Nakagami-m fading channes, IEEE Trans. Veh. Techno., vo. 48, no. 4, pp , Juy [32] F. Atay, A. Adinoyi, Fan Yijia, H. Yanikomerogu, and J. Thompson, On the optimum threshod of digita cooperative reaying schemes, submitted to IEEE Wireess Commun. and Networking Conf., Mar. 27. Abdukareem Adinoyi received a B.Eng degree from the University of Iorin, Nigeria, in 1992, M.S degree from the King Fahd University of Petroeum and Mineras KFUPM, Dhahran, Saudi Arabia, in 1998 and Ph.D degree from Careton University, Ottawa, Canada, in 26, a in eectrica engineering. He was with Dubi Oi Limited, Port Harcourt, Nigeria as an Instrument/Eectrica Engineer from Apri 1993 to August He was with KFUPM between September 1995 and October 1998 as a Research Assistant. Between January 1999 and August 22 he hed the position of a ecturer at the Department of Eectrica Engineering, KFUPM. He is currenty a senior research associate at the Department of Systems and Computer Engineering at Careton University where he participates in the European Union 6th Framework integrated project - the WINNER, dedicated to researching, deveoping and demonstrating a seamess muti-scenario next generation wireess air interface. His research interest is in wireess communication networks with a specia emphasis on infrastructure-based mutihop and reay networks, cooperative diversity schemes and protocos. Haim Yanikomerogu received a B.S. degree in eectrica and eectronics engineering from the Midde East Technica University, Ankara, Turkey, in 199, and an M.A.S. degree in eectrica engineering now ECE, and a Ph.D. degree in eectrica and computer engineering from the University of Toronto, Canada, in 1992 and 1998, respectivey. He was with the Research and Deveopment Group of Marconi Kominikasyon A.S., Ankara, Turkey, from January 1993 to Juy Since 1998, he has been with the Department of Systems and Computer Engineering at Careton University, Ottawa, where he is now an Associate Professor and Associate Chair for Graduate Studies. His research interests incude amost a aspects of wireess communications with a specia emphasis on infrastructure-based mutihop/mesh/reay networks. He has been invoved in the steering committees and technica program committees of numerous internationa conferences in communications; he has aso given severa tutorias in such conferences. He was the Technica Program Cochair of the IEEE Wireess Communications and Networking Conference 24 WCNC 4. He was an Editor for IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS during 22-25, and a Guest Editor for Wiey Journa on Wireess Communications & Mobie Computing; he was an Editor for IEEE COMMUNICATIONS SURVEYS &TUTORIALS for Currenty he is serving as the Chair of the IEEE Communications Society s Technica Committee on Persona Communications TCPC, he is aso a Member of IEEE ComSoc s Technica Activities Counse TAC.