Capacity Evaluation of DF Protocols for OFDMA Infrastructure Relay Links Taneli Riihonen, Risto Wichman, and Stefan Werner SMARAD Centre of Excellence and Department of Signal Processing and Acoustics Helsinki University of Technology P.O. Box 3000, FI-02015 TKK, Finland Email: {taneli.riihonen, risto.wichman, stefan.werner}@tkk.fi Abstract—We consider a downlink OFDMA transmission system in which an infrastructure-based relay node is deployed for extending the coverage of a base station. Focusing on decode-andforward (DF) operation, we study how different relay functionalities affect the system performance. The functionalities include fixed or adaptive subcarrier pairing, information redistribution, buffering, and adjustment of the time shares allocated for the two hops. In particular, it is of great interest for system design to be able to evaluate the performance gains due to each functionality, because they come at the expense of increased complexity and cost of the relay architecture. The main contribution of the paper is to analyze the performance of the proposed protocols by deriving new closed-form expressions for the average end-to-end capacity. The calculated expressions facilitate the performance comparison between the different functionalities.

I. I NTRODUCTION In future cellular systems operating on high carrier frequencies, high data rates require dense network infrastructure while cell sites contribute substantially to the system cost. To limit the costs it is foreseen that two-hop communication via a relay node (RN) will be a key technology to extend coverage areas or enhance hotspot capacity [1]. Especially, RNs are expected to be cheaper to deploy and easier to operate than full-blown base stations (BSs), because relays do not require a wired backhaul connection. Recently, relaying has been adopted as an essential transmission technique in IEEE 802.16j and in the on-going air interface specification process of 3GPP LTE-Advanced [2]. When introducing relaying to a cellular system it is necessary to specify which functionalities and protocols should be included in the RN, and whether RNs should operate at the physical, link, or network layer. Signal processing in relays is often categorized into amplify-and-forward (AF) and decodeand-forward (DF) operation. An AF relay inherently operates on the physical layer, while functionalities in a DF relay fall into data link or higher layers. Thereby, the variety of functionalities to design DF relaying protocols is wide. The functionality portfolio of the RN impacts evidently several aspects in system design, like adaptive modulation and coding, scheduling, packet segmentation, signaling, handovers, etc. When extending conventional one-hop technology to support multiple hops, like with LTE-Advanced, it is beneficial to This work was partially funded by The Finnish Foundation for Economic and Technology Sciences — KAUTE.

resort to as few changes as possible in the system specification. On the other hand, the more functionalities are included in the RN, the better improvement in system performance is expected. So far, an analytical comparison of different OFDMA relay architectures and corresponding impact to system design is not available in literature. In particular, it is of great interest for system design to be able to evaluate and compare the performance gains due to each functionality, because they increase the complexity and cost of the system. In this paper, we focus on DF operation and investigate the performance of relaying protocols that are implemented by using different combinations of the following functionalities in the RN: subcarrier pairing [3], [4] (which can be fixed or adaptive), information redistribution [5], buffering [6], and adjustment of time sharing between the two hops [7]. These functionalities have previously been studied only separately and by means of simulations. In this paper, we setup an analytical framework to evaluate the performance benefits of different protocols and to conduct a discerning comparison. The main contribution of the paper is to study the performance of the proposed protocols by deriving new closed-form expressions for average end-to-end capacities. These results facilitate then comparison between the different functionalities. Especially, we see that some functionalities, that have high implementation complexity such as information redistribution, do not offer substantially better capacity than some of the simpler functionalities such as optimization of the subcarrier pairing. Altogether, the presented analysis provides valuable information for specifying the relaying protocols of the future OFDMA systems. The rest of the paper is organized as follows. In the next section, we present the system model of the infrastructurebased OFDMA relay link and explain the different relay functionalities and protocols. Closed-form expressions of the average end-to-end capacity are derived in Section III, and the performance of the relaying protocols is numerically compared in Section IV. Finally, Section V concludes the paper. II. S YSTEM M ODEL We analyze a two-hop OFDMA relay link that consists of a base station (BS), a fixed infrastructure-based relay node (RN) and N mobile user equipments (UEs). The system is illustrated in Fig. 1. At both hops, data designated for the UEs

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is multiplexed into OFDM symbols that contain K subcarriers (K ≥ N ). For simplicity, we assume that multicast data is not transmitted, and all subcarriers are occupied. Furthermore, we assume that the RN is employed for coverage extension such that the direct BS–UE links are too weak to be useful. γSR [1]

γRD [1]

γSR [2] γSR [3]

γRD [2] γRD [3]

UE2

RN

BS γSR [K − 1] γSR [K]

UE1

γRD [K − 1] γRD [K]

UEN

Fig. 1. Two-hop OFDMA relay link. The γ variables denote the subcarrier signal-to-noise ratios.

We invoke the standard assumptions to facilitate analytical performance evaluation. The OFDM cyclic prefix is assumed to be sufficiently long, and all nodes have perfect frequency and time synchronization. Likewise, the channel coherence times are required to be longer than several OFDM symbols. Thus, all subcarriers are orthogonal and transmitted over flat channels. Additive noise is assumed to be white and Gaussian. For brevity, we consider then in the rest of the paper only the parallel frequency-domain subcarriers without presenting the actual time-domain signals. A. Signal and Channel Models The relay link operates in a time-division half-duplex mode, which guarantees that the two hops are orthogonal. Hence, the BS and the RN transmit alternately on the same frequency so that first the BS sends NSR OFDM symbols to the RN and then the RN sends NRD OFDM symbols to the UEs. The resulting SR represents the relative time time sharing factor τ = NSRN+N RD share used for BS–RN transmission. The channels on the two hops are modeled as follows. 1) The first (BS–RN) hop: The instantaneous signal-tonoise ratio (SNR) of the kth BS–RN subcarrier is denoted by γSR [k]. For convenience, the SNRs are sorted in descending order, i.e., γSR [1] ≥ γSR [2] ≥ . . . ≥ γSR [K]. The BS and the RN are both fixed nodes in the considered system. Thereby, the BS–RN channel varies only slightly (if at all) due to movement of surrounding objects. However, it is not necessarily a lineof-sight link, but a multipath channel depending on the radio propagation environment and network planning. Thus, it is reasonable to assume that the BS–RN channel is frequencyselective and static, i.e., γSR [k] = γ¯SR [k] = E {γSR [k]} for all k, where E {·} is the expectation  operator. The mean of K 1 BS–RN subcarrier SNRs is γ¯SR = K ¯SR [k]. k=1 γ The instantaneous and average capacities [bit/s/Hz] of the kth BS–RN subcarrier are equal to each other and they are expressed as CSR [k] = C¯SR [k] = E {CSR [k]} = τ log2 (1 + γ¯SR [k]) , (1) which is scaled by the time share τ given for the first hop.

2) The second (RN–UE) hop: The relay processes the OFDM symbols received from the BS according to the selected relaying protocol, and the obtained data is then multiplexed again into OFDM symbols. The UEs share the second hop OFDMA transmission based on centralized round robin scheduling that assigns one or more subcarriers for each UE’s data. Different quality of service requirements may be satisfied by varying the number of subcarriers allocated for each UE. The UEs are mobile, and we assume flat block-fading Rayleigh channels for all RN–UE subcarriers. In particular, we assume that slow power control is employed for balancing the average RN–UE subcarrier SNRs to the same level for every subcarrier and UE. Furthermore, we assume that instantaneous subcarrier SNRs are mutually independent. The assumption is reasonable, because correlation between subcarriers allocated for different UEs is very small, and a good scheduling policy minimizes the correlation between multiple subcarriers allocated for a single UE to fully benefit from frequency diversity. The instantaneous SNRs γRD [l], l = 1, 2, . . . , K, of the RN–UE subcarriers are modeled as independent and identically distributed exponential random variables with average subcarrier SNR γ¯RD = E {γRD [l]}. Thus, the distribution of every γRD [l] is defined by the probability density function γRD )e−x/¯γRD for x ≥ 0. Similarly, (PDF) fγRD [l] (x) = (1/¯ the cumulative distribution function (CDF) is FγRD [l] (x) = 1 − e−x/¯γRD for x ≥ 0. The instantaneous capacity [bit/s/Hz] of the kth RN–UE subcarrier is given by CRD [k] = (1 − τ ) log2 (1 + γRD [k]) ,

(2)

which reflects the time share 1 − τ used for the second hop. B. Relay Functionalities and Relaying Protocols We aim at comparing the performance of various relaying protocols where each protocol requires different functionalities to be implemented in the RN. Common to all studied protocols, the RN demodulates the OFDM signal and processes the individual subcarriers in the frequency domain. This study omits the simplest analog physical-layer repeaters that merely amplify signals in the time-domain. The first functionality choice in the design of relaying protocols is between amplify-and-forward (AF) and decode-andforward (DF) operation. The RN can either amplify the BS– RN subcarriers and forward them to the RN–UE subcarriers, or it can decode the BS–RN symbols and encode the data again for the RN–UE hop. In this paper, we concentrate on DF protocols, whereas reference results considering AF protocols are available in [8]. The major functionality choice affecting the complexity of the relaying protocol is between parallel and joint processing of the subcarriers. Both with AF and DF, the RN may be implemented to process all subcarriers separately so that processed data of one BS–RN subcarrier is forwarded to exactly one RN–UE subcarrier. This is referred to as subcarrier pairing. By allowing more complex operation, which is only possible with DF, the RN can decode the information of

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all BS–RN subcarriers and redistribute it for the RN–UE subcarriers. This is referred to as information redistribution. When the BS–RN and RN–UE subcarriers are pairwiseconnected (with subcarrier pairing), the relaying protocol can either apply a fixed pairing between the subcarriers, or adaptively optimize the pairing for each channel state. Additional functionalities that are possible for relaying protocols operating above the physical layer include buffering of the BS– RN data in the RN to compensate for the effect of fading on the RN–UE hop, and adaptive optimization of the time sharing factor τ based on the average channel SNRs. Two-hop networks can operate under centralized or distributed control. In a centralized network, the BS decides on the resource allocation between UEs and the RN maps the subcarriers in the two-hop link to optimize the system performance. In case of distributed control, the RN allocates the resources in the second hop. The distributed scheduler can operate faster than the centralized one and reduce the control channel overhead. On the other hand, distributed resource allocation requires significant changes to radio resource management algorithms of the legacy single-hop network. Without functionality to use buffering, RNs may operate in the centralized or the distributed mode as long as the necessary channel quality information is made available to the appropriate nodes. On the other hand, when the relaying protocol is allowed to buffer received data before retransmission it is feasible to let the RN to allocate resources for the served UEs to avoid excessive control signaling. In both cases, with or without buffering, system capacity can be further improved when the time sharing between BS–RN and RN–UEs links is optimized. However, this additional degree of freedom increases again the complexity of radio resource management. III. C APACITY A NALYSIS We next derive new closed-form expressions for the average end-to-end capacity in the OFDMA relay link with the DF relaying protocols that are implemented by exploiting different combinations of the aforementioned functionalities. A. Subcarrier Pairing In this subsection, we concentrate on relaying protocols that process all subcarriers separately, and the BS–RN subcarriers are pairwise-connected with the RN–UE subcarriers. Thereby, we denote that the data of the kth BS–RN subcarrier is transmitted after decoding, buffering (if used), and re-encoding on the lth RN–UE subcarrier. The subcarrier mapping is denoted by bijection l = v[k]. 1) Fixed Pairing (No Buffering): In the simplest case, the relaying protocol does not optimize the subcarrier mapping v[k] according to the channel states. Any fixed or randomized subcarrier permutation in the relay results in the same average performance. We may, therefore, assume that the fixed pairing is v[k] = k without loss of generality. We first consider the case when the relaying protocol does not buffer information. That is, all data from the NSR OFDM symbols of the BS–RN time slot is directly forwarded to the

NRD OFDM symbols of the RN–UE time slot. In this case, the instantaneous end-to-end capacity of the kth subcarrier can be expressed as C[k] = min {CSR [k], CRD [k]} .

(3)

Here we consider standard repetition-based DF relaying in which the modulation and coding scheme is selected according to the weakest hop to guarantee reliable detection both in the RN and in the UE. The average capacity of all subcarriers is then calculated as C¯ = =

K   1   E min C¯SR [k], CRD [k] K k=1 K   1  ∞ min τ log2 (1 + γ¯SR [k]), K k=1 0  (1 − τ ) log2 (1 + s) fγRD [k] (s)ds K

=

(4)

1

1  (1 − τ )e γ¯RD K loge (2)

 k=1

 τ 1 (1 + γ¯SR [k]) 1−τ − E1 . × E1 γ¯RD γ¯RD

The integral is solved by first applying partial integration, and the final form is obtained by using the exponential integral ∞ −t E1 (z) = z e t dt [9, Eq. 5.1.1]. 2) Optimized Pairing (No Buffering): By implementing more complex relay functionalities and increasing the channel estimation and signaling overhead, the average capacity can be improved by optimizing the subcarrier mapping v[k] based on instantaneous channel state information. With a priori fixed RN–UE subcarriers, the optimal mapping connects the BS–RN subcarrier having the kth largest SNR with the RN-UE subcarrier having the kth largest SNR for all k = 1, 2, . . . , K. Optimality of this pairing scheme is proven for the AF protocol in [3], and similar proof is expected to hold also for the DF protocol. We denote the optimal subcarrier mapping with bijection l = v ∗ [k] which is the index of the kth largest instantaneous RN–UE subcarrier SNR. With the notation used in this paper, a relay employing the optimal subcarrier pairing forwards the data of kth BS–RN subcarrier on the v ∗ [k]th RN–UE subcarrier. For capacity derivation, we can use the following result from order statistics [10]. Let us have K independent and identically distributed random variables γRD [l], l = 1, 2, . . . , K. Then the PDF of the kth largest variable γRD [v ∗ [k]] is expressed as  K−k K! FγRD [l] (x) fγRD [v∗ [k]] (x) = (K − k)!(k − 1)!  k−1 × 1 − FγRD [l] (x) fγRD [l] (x). (5)



 K l−k (−1) K K − k − γ¯ x l = k e RD , γ¯RD k K −l l=k

in which the last expression is obtained by substitution of the exponential PDF and CDF and using the binomial expansion.

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The instantaneous capacity of the kth BS–RN subcarrier using the optimal subcarrier mapping without buffering is given by (6) C[k] = min {CSR [k], CRD [v ∗ [k]]} . By exploiting (5), we can then calculate the average capacity of all subcarriers as K   1   E min C¯SR [k], CRD [v ∗ [k]] C¯ = K k=1 K   1  ∞ = min τ log2 (1 + γ¯SR [k]), K k=1 0  (7) (1 − τ ) log2 (1 + s) fγRD [v∗ [k]] (s)ds l  

K K K − k (1 − τ )e γ¯RD 1  k K (−1)l−k = K −l K l k loge (2) l=k

 k=1

 τ l (1 + γ¯SR [k]) 1−τ , − E1 × E1 γ¯RD γ¯RD /l where the integration inside the double sum is similar to that of (4). 3) With Buffering: The effect of fading on the RN–UE channel may be reduced by buffering in the RN. The buffer is filled when the quality of the second hop is poor compared to that of the first hop. More data (extra data is taken from the buffer) is then transmitted at those time instants when the second hop is better than the first hop. Thus, the average endto-end capacity is improved, if the buffer is long enough to store data over reasonably many independent fading states. To facilitate the derivation of closed-form capacity expressions we assume that the buffers are infinite (or very long). This means in practice that the buffer never overflows or underflows. As observed in [6] by simulations, the capacity of relaying with a quite small finite buffer is already close to the capacity of relaying with an infinite buffer. Thus, the theoretical infinite buffer model offers a reasonable approximation and an upper bound for the average capacity. As we now constrain the relaying protocol to process all subcarriers separately, every RN–UE subcarrier needs to have its own buffer. Ideal buffering then guarantees that each end-to-end subcarrier pair achieves average capacity that is limited by the of the weakest hop, i.e.,   average capacity ¯ = min C¯SR [k], C¯RD [k] . Thus, the average capacity of C[k] all subcarriers is calculated as K   1  min C¯SR [k], C¯RD [k] , (8) C¯ = K k=1

where C¯RD [k]

 =

∞

(1 − τ ) log2 (1 + s)fγRD [k] (s)ds   1 1 (1 − τ )e γ¯RD E1 γ¯RD . (9) = loge (2) The above result, which is the well-known average capacity of a Rayleigh-fading channel, is obtained using [11, Eq. 4.337.2]. 0

B. Information Redistribution In this subsection, we concentrate on relaying protocols that jointly process the subcarriers. The RN has functionality to extract all information from the decoded BS–RN subcarriers and then redistribute it after buffering (if used) to the RN–UE subcarriers. Hence, there does not exist any physical one-toone mapping between the BS–RN and the RN–UE subcarriers, because all BS–RN subcarriers are shared between all UEs. Due to information redistribution, the end-to-end capacity is determined by the per-hop mean capacities of all subcarriers instead of the individual subcarrier capacities as with subcarrier pairing. The mean instantaneous and average capacities of all BS–RN subcarriers are given by CSR = C¯SR =

K K 1  1 ¯ CSR [k] = CSR [k]. K K k=1

(10)

k=1

Likewise, the mean instantaneous and average capacities of all RN–UE subcarriers are given by CRD

=

K 1  CRD [k], K k=1

C¯RD

=

E {CRD } =

K 1 ¯ CRD [k] = C¯RD [k], K

(11)

k=1

respectively. The expression for C¯RD [k] is solved in (9). 1) No Buffering: Without buffering in information redistribution, the instantaneous end-to-end capacity is given by the minimum of the mean BS–RN and RN–UE subcarrier capacities: (12) C = min {CSR , CRD } . For calculating the average capacity, we next exploit the well-known central limit theorem. As CRD [k], k = 1, 2, . . . , K are independent and identically Kdistributed random variables, 1 the distribution of CRD = K k=1 CRD [k] converges towards the normal distribution according the central limit theorem when K → ∞, i.e., C − C¯RD D RD −→ N (0, 1). (13) Var {CRD } Thus, when K is sufficiently large, the CDF of CRD can be closely approximated as

x − C¯RD , (14) FCRD (x) ≈ Φ  Var {CRD } z 2 in which Φ (z) = √12π −∞ e−t /2 dt is the CDF of the standard normal distribution N (0, 1) having zero mean and unit The variance in (14) is given by Var {CRD } =   variance. 2 2 − C¯RD , where the second raw moment of CRD is E CRD calculated with the Meijer G-function [11, Eq. 9.301] as  ∞  2  = ((1 − τ ) log2 (1 + s))2 fγRD (s)ds E CRD 0    1 3,0 1  1,1 e γ¯RD G2,3  γ ¯ 0,0,0 RD = 2(1 − τ )2 . (15) (loge (2))2

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TABLE I P OWER - DELAY PROFILE FOR THE BS–RN LINK

Finally, the average end-to-end capacity without buffering can be calculated by using integration by parts as    C¯ = E min C¯SR , CRD  ∞   = min C¯SR , s fCRD (s)ds (16)

B5f-NLOS rooftop-to-below rooftop Delay [ns] 0 10 20 50 Power [dB] -0.1 -5.3 -11.5 -8.9 Delay [ns] 95 100 180 205 Power [dB] -5.2 -12.7 -3.5 -6.3

0

 C¯SR   min C¯SR , s FCRD (s) − FCRD (s)ds 0 0

 C¯SR s − C¯RD ≈ C¯SR − ds, Φ  Var {CRD } −∞ ∞

where fCRD (s) is the PDF of CRD , and the approximation is accurate when the number of subcarriers K is large enough. 2) With Buffering: If the information redistribution-based relaying protocol is extended with functionality to buffer information, the average end-to-end capacity becomes simply   (17) C¯ = min C¯SR , C¯RD , because buffering compensates the effect of fading on the RN– UE hop. Expressions for C¯SR and C¯RD are given in (10) and (11), respectively.

20

γ ¯SR [k] [dB]

=

90 0.0 260 -4.6

15 10 5 0

Average over 106 snapshots 10 example snapshots 2

4

6

8

10

12

k

14

16

18

20

22

24

Fig. 2. The sorted BS–RN subcarrier SNRs from WINNER B5f-NLOS rooftop-to-below rooftop channel model when K = 24 and γ ¯SR = 15dB. The average channel is used in numerical performance evaluation.

IV. N UMERICAL E VALUATION

C. Optimization of Time Allocation We see that all of the derived capacity expressions depend on the time shares τ and 1 − τ of the BS–RN and RN–UE hops. Thus, the end-to-end capacity can be further boosted if τ is properly adjusted for balancing the per-hop capacities. Analytically, the optimization problem is expressed as τ ∗ = arg max C¯ subject to 0 ≤ τ ≤ 1. τ

(18)

In practice, τ would assume discrete values, because the alternating transmissions of the BS and the RN are segmented into radio frames which further divide into time slots given for the two orthogonal hops. Thus, the resolution of τ is dictated by NSR and NRD . Nevertheless, we let τ to take continuous values for illustrative purposes. Finally, we remark that in case of AF relaying, NSR = NRD and τ = 12 always, because AF relays cannot change the modulation and coding scheme. In the following, we determine the optimal time sharing factor τ ∗ by using numerical optimization tools, because the optimization problem does not in general have a closedform solution. However, one of the relaying protocols, namely information redistribution with buffering (considered in Section III-B2), admits an analytical expression for the optimal time sharing factor:   1 1 e γ¯RD E1 γ¯RD   . (19) τ∗ = 1 K 1 1 γ ¯RD log (1 + γ ¯ [k]) + e E SR 1 e k=1 K γ ¯RD By substitution of τ ∗ , the corresponding optimal average endto-end capacity becomes ⎡ ⎤−1 loge (2) K  ⎦ . + 1 C¯∗ = ⎣ K γ ¯ ¯SR [k]) e RD E1 1 k=1 log2 (1 + γ γ ¯RD

(20)

In this section, we first describe OFDMA parameters and a BS–RN channel model for an example system setup. Then we compare the capacities of the relaying protocols with different functionalities by applying the parameters to the formulas derived in the previous section. The system setup is similar to that of [8] and the performance results for the AF protocol are taken directly from there as an additional reference. In practice, it is not feasible to implement OFDMA on a subcarrier basis due to signaling and channel estimation overhead. Instead, subcarriers are grouped into chunks of consecutive subcarriers that are assigned as single entities. In our evaluation, these subcarrier chunks are the physical resource blocks (RBs) of 3GPP Release 7 baseline proposal [12] in which each 375kHz physical RB consists of 25 consecutive subcarriers for the 6 or 7 consecutive OFDM symbols in a subframe when the system bandwidth is 10MHz and 600 subcarriers are occupied. Thus, the number of RBs is K = 24. To model the BS–RN channel, we assume that the RN observes a single fixed snapshot of the B5f non-line-of-sight (NLOS) rooftop-to-below rooftop channel, which is adopted from the WINNER project [13]. Thus, the impulse response consists of 10 Rayleigh fading taps with the power-delay profile shown in Table I. The SNR value γ¯SR [k] is measured at the center of the kth RB, and SNRs are sorted in descending order to comply with the notation used for mathematical analysis. To generalize evaluation for all different relay locations and to avoid choosing a very optimistic or pessimistic snapshot, we exploit the average sorted channel illustrated in Fig. 2. The performance of some snapshots was also evaluated and the results were similar to that of the average channel, but the performance plots are omitted in this paper. The adjustment of the time sharing factor τ is illustrated in Fig. 3. The optimal value of τ is quite the same for all

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2.8

2.2 2

Average capacity [bit/s/Hz]

Average capacity [bit/s/Hz]

2.6

2.4

2.2

2

1.8 DF: Redistribution, with buffering DF: Redistribution, no buffering DF: Pairwise, no buffering, optimal pairing DF: Pairwise, with buffering DF: Pairwise, no buffering, fixed pairing

1.6

1.4 0.35

0.4

0.45

0.5

0.55

τ

0.6

0.65

0.7

1.8 1.6 1.4 1.2 1 DF: Redistribution, with buffering DF: Redistribution, no buffering DF: Pairwise, no buffering, optimal pairing DF: Pairwise, with buffering DF: Pairwise, no buffering, fixed pairing AF: Pairwise, no buffering, optimal pairing AF: Pairwise, no buffering, fixed pairing

0.8 0.6 0.4 0.2

0.75

0.8

0

5

10

15

γ¯RD

20

(a) With equal time sharing (τ =

Fig. 3. Optimization of time sharing when γ ¯SR = 15dB and γ ¯RD = 25dB.

25

30

1 ) 2

3

V. C ONCLUSION

2.5

Average capacity [bit/s/Hz]

considered protocols. The average end-to-end capacities are then compared with equal time sharing in Fig. 4(a) and with optimized time sharing in Fig. 4(b). We see that optimal time sharing is beneficial only when the hops are unbalanced. As expected, allowing more complex functionalities in the relay protocol improves the capacity, but the differences are not large. In particular, DF protocol with optimized subcarrier pairing seems to offer a good trade-off between complexity and capacity. On the contrary, the benefit of buffering is small compared to the other functionalities. The AF protocols are simple to implement, but they result in the lowest capacity.

2

1.5

0.5

We analyzed the performance of OFDMA decode-andforward relay links by deriving new closed-form expressions for average end-to-end capacities. Various relaying protocols were proposed by considering different sets of functionalities to be implemented in the relay. The presented analysis provides useful information for specifying new systems, because it allows us to evaluate and compare the performance gains due to the functionalities that can be employed only at the expense of increased complexity and cost of the network architecture. R EFERENCES [1] R. Pabst et al., “Relay-based deployment concepts for wireless and mobile broadband radio,” IEEE Communications Magazine, vol. 42, no. 9, pp. 80–89, September 2004. [2] S. Parkvall, E. Dahlman, A. Furusk¨ar, Y. Jading, M. Olsson, S. W¨anstedt, and K. Zangi, “LTE-Advanced - evolving LTE towards IMT-Advanced,” in IEEE 68th Vehicular Technology Conference, September 2008. [3] A. Hottinen and T. Heikkinen, “Optimal subchannel assignment in a twohop OFDM relay,” in Proc. IEEE 8th Workshop on Signal Processing Advances in Wireless Communications, June 2007. [4] Y. Wang, X. Qu, T. Wu, and B. Liu, “Power allocation and subcarrier pairing algorithm for regenerative OFDM relay system,” in Proc. IEEE 65th Vehicular Technology Conference, April 2007, pp. 2727–2731. [5] L. Xiao and L. Cuthbert, “Adaptive power allocation scheme for energy efficient OFDMA relay networks,” in Proc. 11th IEEE Singapore International Conference on Communication Systems, November 2008, pp. 637–641.

DF: Redistribution, with buffering DF: Redistribution, no buffering DF: Pairwise, no buffering, optimal pairing DF: Pairwise, with buffering DF: Pairwise, no buffering, fixed pairing

1

0

5

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γ¯RD

20

25

30

(b) With optimized time sharing (τ = τ ∗ ) Fig. 4. The average end-to-end capacities of the proposed protocols in terms of the average second hop SNR when γ ¯SR = 15dB.

[6] B. Xia, Y. Fan, J. Thompson, and H. V. Poor, “Buffering in a three-node relay network,” IEEE Transactions on Wireless Communications, vol. 7, no. 11, pp. 4492–4496, November 2008. [7] Y. Kim and H. Liu, “Infrastructure relay transmission with cooperative MIMO,” IEEE Transactions on Vehicular Technology, vol. 57, no. 4, pp. 2180–2188, July 2008. [8] T. Riihonen, R. Wichman, J. H¨am¨al¨ainen, and A. Hottinen, “Analysis of subcarrier pairing in a cellular OFDMA relay link,” in Proc. International ITG Workshop on Smart Antennas, February 2008, pp. 104–111. [9] M. Abramowitz and I. A. Stegun, Eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover Publications, 1972. [10] B. C. Arnold, N. Balakrishnan, and H. N. Nagaraja, A First Course in Order Statistics. Wiley-Interscience, 1992. [11] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. Academic Press, 2007. [12] 3GPP TR 25.814 V7.1.0: Physical layer aspects for evolved Universal Terrestrial Radio Access (UTRA) (Release 7), September 2006. [13] IST-4-027756 WINNER II D1.1.2 V1.1: WINNER II Channel Models, November 2007.

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