Orthogonal frequency division multiple access resource allocation in mobile multihop relay networks using an adaptive frame structure

Transcription

1 WIRELESS COMMUNICATIONS AND MOBILE COMPUTING Wirel. Commun. Mob. Comput. 2013; 13: Published online 13 July 2011 in Wiley Online Library (wileyonlinelibrary.com) RESEARCH ARTICLE Orthogonal frequency division multiple access resource allocation in mobile multihop relay networs using an adaptive frame structure Bongyoung Kwon 1, Raheem A. Beyah 2 *, Myunghwan Lee 1 and John A. Copeland 1 1 CSC Lab, School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, U.S.A. 2 Communications Assurance and Performance Group, School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, U.S.A. ABSTRACT For wireless mobile multihop relay (MMR) networs, we have chosen orthogonal frequency division multiple access (OFDMA) and time division duplex as a multiple access scheme and a duplex communication technique, respectively. We have also selected nontransparent relay stations (nt-rss) as relay nodes to extend the MMR networ coverage. Through the nt-rss, far-off subscriber stations (SSs) or hidden SSs can communicate with a base station (BS) that is connected to bachaul networs. In these MMR networs, the way in which a BS and nt-rss use OFDMA resources (e.g., OFDMA symbols and subcarriers) and share them might reduce system capacity and networ throughput. Therefore, we proposed a new adaptive OFDMA frame structure for both the BS and the nt-rss. The proposed scheme is the first approach that incorporates the adaptive technique for wireless MMR networs. Based on the proposed adaptive OFDMA frame structure, an adaptive OFDMA resource allocation for SSs within a BS as well as nt-rss was proposed. To derive the maximum OFDMA resource that nt-rss can be assigned and to synchronize access zones and relay zones between a superior station and its subordinate nt-rss, three properties are introduced: a data relay property, a maximum balance property, and a relay zone limitation property. In addition, we propose max-min and proportional fairness schemes of the proposed adaptive frame structure. Our numerical analysis and simulations show that the proposed OFDMA allocation scheme performs better than the nonadaptive allocation scheme in terms of networ throughput and fairness especially in the asymmetric distribution of subscriber stations between access zones and relay zones in the MMR networs. Copyright 2011 John Wiley & Sons, Ltd. KEYWORDS adaptive frame structure; OFDMA allocation; MMR networs *Correspondence Raheem A. Beyah, Communications Assurance and Performance Group, School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, U.S.A. rbeyah@ece.gatech.edu 1. INTRODUCTION Providing ubiquitous coverage with wireless metropolitan area networs can be costly especially in sparsely populated areas. In this scenario, cheaper relay stations (RSs) can be used to provide coverage instead of expensive base stations (BSs). The RS extends the coverage area of traditional BSs. This sort of networ is nown as a wireless mobile multihop relay (MMR) networ. These wireless MMR networs have been the focus of considerable interest because they enhance networ coverage, throughput, and system capacity at a reduced cost by deploying RSs rather than expensive BSs. The newly formed IEEE j woring group, which introduced MMR networs, is actively standardizing relay schemes for worldwide interoperability for microwave access (WiMAX). In addition to the benefits provided by the classical pointto-multipoint (PMP) networ, MMR networs can provide other benefits including flexible cell site placement, decreased subscriber station (SS) power, and load sharing. At the same time, however, it has several drawbacs such as increased latency, overhead caused by multihop communication, and a complex infrastructure. MMR networs consist of a BS, RSs, and SSs. RSs play an important role Copyright 2011 John Wiley & Sons, Ltd. 967

2 OFDMA resource allocation in mobile multihop relay networs B. Kwon et al. because they not only supply networ access to far-off SSs or hidden SSs but also relay lins to a BS or other RSs. MMR networs consist of two types of communication lins: a relay lin, which is a lin between a BS and an RS or between a pair of RSs, and an access lin, which is a lin between a BS and an SS or between an RS and an SS. The access lin always originates from, or terminates at, an SS. The MMR networ with IEEE j-2009 [1] is one example of a wireless MMR networ. The IEEE j-2009 further classifies MMR networs according to their multihop relay functionality, channel information announcement, and mobility. A BS that has MMR capabilities is called an MMR-BS, and an RS that broadcasts channel information and an RS that does not broadcast channel information are called a nontransparent RS (nt- RS) and a transparent RS (t-rs), respectively. This detailed classification is shown in Figure 1. In this paper, we have chosen the MMR-BS and the nt-rs to increase the coverage of the MMR-BS, but any type of SS can be deployed as long as it can communicate with either the MMR-BS or the nt-rs. In MMR networs, the way in which a BS and nt- RSs use orthogonal frequency division multiple access (OFDMA) resources (e.g., OFDMA symbols and subcarriers) and share them might reduce system capacity and networ throughput. For example, a data frame might be shared with an nt-rs that does not have any SSs. Therefore, we propose a new adaptive OFDMA frame structure and OFDMA resource allocation for both the BS and the nt-rss. In the proposed OFDMA resource allocation, we have created three properties: a data relay property, a maximum balance property, and a relay zone limitation property. Using these three properties, we can derive the maximum OFDMA resources that nt-rss can be assigned given the system parameters. We also propose max-min and proportional fairness schemes in the proposed OFDMA allocation scheme. We evaluate our scheme using simulations and numerical analysis. Results show that our technique improves resource allocation in wireless MMR networs. Furthermore, in asymmetric distributions of SSs between access zones and relay zones, the proposed OFDMA allocation scheme performs significantly better than the nonadaptive allocation scheme in terms of average max-min fairness and average throughput. This paper proceeds as follows. Bacground information is provided in Section 2, and related wor is presented in Section 3. A detailed description of our proposed protocol and the proposed fairness schemes are presented in Sections 4 and 5, respectively. The simulation of the proposed allocation algorithms is given in Section 6. We state our conclusions in Section BACKGROUND 2.1. Orthogonal frequency division multiple access frame structure in point-to-multipoint networs The OFDMA frame in the PMP topology is built at the BS and transmitted to all SSs associated with the BS. The frame in the downlin (DL) transmission (from a BS to SSs) begins with a preamble followed by a DL transmission period and an uplin (UL) transmission period. In each frame, the transmit/receive transition gap (TTG) and receive/transmission transition gap (RTG) are inserted between the DL and the UL and at the end of each frame, to allow the BS to turn around [2]. Figure 2 shows this frame structure. The fixed size of the DL/UL subframe has a disadvantage with bandwidth utilization because the load of the DL and the UP traffic is very hard to match to the predetermined DL/UL subframe size. Because of this problem, the concept of the adaptive OFDMA frame structure in the PMP networs (Figure 3) has been proposed. In this adaptive frame structure, the duration of the DL and the UL subframes is flexible. The main advantage of the adaptive frame structure is that the DL and UL allocation ratio is not fixed. Thus, it can provide maximum flexibility and system throughput according to the variance in the traffic Orthogonal frequency division multiple access frame structure in mobile multihop relay networs When considering MMR networs, the frame structure varies from that used in PMP networs. This is because some OFDMA resources should be assigned to RSs to relay data from/to their superior stations and SSs. These are referred to as relay zones in the OFDMA frame structure. A DL subframe of the nt-rs should have at least one Figure 1. Classification of mobile multihop relay (MMR) networs. 968 Wirel. Commun. Mob. Comput. 2013; 13: John Wiley & Sons, Ltd.

3 B. Kwon et al. OFDMA resource allocation in mobile multihop relay networs Figure 2. Frame structure in point-to-multipoint networs. BS, base station; DL, downlin; UL, uplin; RTG, receive/transmission transition gap; TTL, transmit/receive transition gap. Figure 3. The concept of the adaptive frame structure. DL, downlin; UL, uplin; RTG, receive/transmission transition gap; TTL, transmit/receive transition gap. access zone and one or more relay zones to enable the nt- RS to operate in either the transmit or receive mode. The main reason why the frame structure is designed differently for each RS is that the t-rs is located within the BS coverage and the nt-rs is deployed around the edge of the BS coverage. Using the relay zone of the DL subframe, the nt- RS can relay data to its SS from a BS. In general, there are two types of frame structures that support more than two hop relays for nt-rss: a multiframe structure and a single frame structure. In the multiframe structure, a BS and RSs are assigned to transmit, receive, or be idle during each of the relay zones within the multiframe. For example, odd hop RSs transmit in the DL relay zone during the odd number of frames, and the BS and even hop RSs transmit in the DL relay zone during the even number of frames in the multiframe consisting of two frames. In the single frame structure, the DL subframe consists of more than one relay zone. The BS and RSs are assigned to transmit, receive, or be idle in each relay zone within the frame. Figure 4 shows an example of the frame structure used in the MMR networs. 3. RELATED WORK 3.1. Frame structure with time division duplex In [3], Chian et al. proposed an adaptive split ratio (ASR) algorithm for time division duplex (TDD)-based WiMAX PMP networs. In the algorithm, a BS determines the DL and the UL split ratios in a frame according to transmission control protocol (TCP)-based traffic from SSs. The main motivation of this algorithm is that improper DL and UL allocation can cause TCP acnowledgement pacets that accumulate in a UL queue to be sent, which eventually degrades the system performance. However, they consider only the best-effort service class to determine the split ratio. Pries et al. [4] compared different TDD split ratios with different traffic loads and proposed an adaptive TDD split algorithm based on the current traffic load within one cell coverage. Because it considers all DL and UL traffic, this approach differs from that in [3]. The algorithm first starts with a 50:50 ratio and then measures Figure 4. Fixed frame structure in the mobile multihop relay (MMR) networs. BS, base station; DL, downlin; UL, uplin; RTG, receive/transmission transition gap; TTL, transmit/receive transition gap; R-RTG, relay RTG; R-TTG, relay TTG. Wirel. Commun. Mob. Comput. 2013; 13: John Wiley & Sons, Ltd. 969

4 OFDMA resource allocation in mobile multihop relay networs B. Kwon et al. each DL and UL load during the last n frames duration. Based on the measurement, the algorithm decides whether to increase the DL or UL subframe. Even though both [3] and [4] used an adaptive frame, their design is only for the PMP networ topology. Deb and Ramayian [5] proposed heuristic scheduling algorithms (heuristic argmax, proportional fairness, and tree-traversal scheduling algorithms) in WiMAX relay networs. They segmented time slots in a frame according to lins between a BS and stations and assigned subchannels based on the stations priority. However, they did not clearly demonstrate the frame structure in terms of relay zones and access zones. This fact is important because a BS and the RSs need to synchronize so that they do not interfere with each other. Narliar et al. [6] proposed an even odd frame structure for delay-constrained wireless relay networs. Nodes are labeled even or odd and alternately transmit data based on their label with regard to the frame structure in wireless MMR networs. Hoymann et al. [7] proposed two types of media access control (MAC) frame concepts to support multihop communication in IEEE j MMR networs. In the first concept, referred to as the centralized approach, a BS has full control over one MMR cell, whereas in the second concept, referred to as the semidistributed approach, an RS can control its associated SSs. The proposed method places a multihop subframe within either a UL subframe or both DL and UL subframes based on which concept has been chosen. Through this approach, any legacy SSs can interpret new MAC frames with a multihop subframe. Tao et al. [8] designed a new OFDMA frame structure, in which DL and UL subframes are divided into multiple zones in a time domain. The first zone in both the DL and UL subframes is dedicated for access lins and followed by one or multiple relay lins. In addition, when multiple relay lins exist, frequency reuse is also considered in the design. Although [7] and [8] considered MMR networs, they used a fixed frame structure, which is not optimized for various types of traffic Orthogonal frequency division multiple access resource allocation Kularni et al. [9] proposed the adaptive subcarrier allocation scheme to minimize the total transmission power in the networs while satisfying the data rate requirement of each lin. Ermolova et al. [10] proposed a low complexity suboptimal power and subcarrier allocation for the OFDMA system. They designed a heuristic noniterative method as an extension of the ordered subcarrier selection algorithm for a single-user case. Biagioni et al. [11] proposed adaptive subcarrier allocation schemes for a wireless OFDMA system in a WiMAX networ. They defined the size of a slot consisting of a set of OFDMA symbols and subcarriers and then allocated slots to users based on multiuser diversity. They also considered both fair and proportional allocation, the latter of which will increase bandwidth efficiency. However, the proposed adaptive subcarrier allocation is only for the PMP networ topology. Erwu et al. [12] theoretically analyzed bandwidth allocation in an n-hop MMR networ consisting of n access lins and n 1 bachaul lins (relay lins). The spectrum efficiency-based adaptive resource allocation method was also proposed to fully utilize a given overall bandwidth spectrum in an MMR networ Fairness General fairness is simple but not practical because it gives the same amount of resources to all associated nodes. All other fairness techniques are based on general fairness. The main drawbac of general fairness is that it does not consider the difference among the nodes, which ends up with less utilization of radio resources. Min-max fairness shares resources equally based on different resource demands [13 15]. Resource capacity (C)isfirstdivided by the number of stations (n), and C/n is given to the station with the smallest demand. If the demand is smaller than C/n, the extra resources from the station is added to the remaining resources and divided by n 1 stations again. This process ends when each station has no more than its demand or when no resource to be assigned remains. That is, stations with small demands will be assigned resources that they request, and the remaining resources are distributed to stations with larger demand. The main drawbac of max-min fairness is that users with the best channel conditions obtain a lower number of resources than users with the worst channel conditions. Proportional fairness tries to maximize total wireless networ throughput and, at the same time, allows all users to have at least a minimal level of service. The basic procedure of proportional fairness in wireless networs is that it assigns different weights to different stations based on the channel condition and then gives resources to each station with respect to an assigned weight. Biagioni et al. [11] considered both fair and proportional allocation, but they proposed an adaptive subcarrier allocation scheme with fairness only for the PMP networ topology. In terms of fairness, proportional fairness usually achieves the best trade-off between system throughput and user fairness in the PMP networs. However, this type of proportional fairness cannot be applied directly in wireless MMR networs because the direct lin and the relay lin are present simultaneously. Lei et al. [16] proposed a partial proportional fairness (PPF) algorithm based on two-dimensional proportional fairness, which taes advantage of channel variations in the time domain as well as in the frequency domain. However, Xiao and Cuthbert [17] pointed out that the PPF algorithm gives an absolute priority to RSs when assigning the two-dimensional resources consisting of time subslots and frequency subchannels. Therefore, they proposed the two-hop proportional fairness (THPF) to compensate for the unfairness between RSs and SSs. In THPF, subchannels in the first time subslot are fairly allocated to RSs and direct lin users, and subchannels in the second time 970 Wirel. Commun. Mob. Comput. 2013; 13: John Wiley & Sons, Ltd.

5 B. Kwon et al. OFDMA resource allocation in mobile multihop relay networs subslot are allocated only to relay lin users. Liu and Leung [18] proposed an analytic model for the proportional fair scheduling (PFS) in the PMP networ topology where Rayleigh fading model is applied. Through their analytic solution, the throughput of PFS in the PMP networ can be estimated Other issues in wireless mobile multihop relay networs A number of researchers have used other approaches in wireless MMR networs. Yu et al. [19] proposed a way to determine optimal node locations for BSs and RSs in IEEE j MMR networs. Among a set of candidate BS and RS locations within a given area, the proposed function finds the best-located set of BSs and RSs to accommodate user traffic demand. In terms of the MAC protocol, Tao et al. [20] proposed new MAC protocol data unit concatenation and MAC service data unit aggregation schemes by modifying the pacet construction mechanism used in the current IEEE /16e standard. A new resource scheduling method with directional antennas, especially for Manhattan style environments where many hidden SSs reside between buildings, was proposed in [20]. 4. PROPOSED ADAPTIVE FRAME STRUCTURE 4.1. Adaptive frame structure with one relay direction The IEEE shows the concept of an adaptive OFDMA frame for UL and DL, and the IEEE j 2009 introduces the concept of the relay zones and the access zones. However, neither these standards nor previous research have addressed challenges with the combination of an adaptive frame structure in networs with relay and access zones (i.e., MMR networs). In this paper, we introduce how the frame structure is adaptively changed based on the distribution of nt-rss and SSs. The basic idea is that after the DL and UL ratio is fixed, a BS or an nt-rs starts to assign OFDMA slots from the lowest slot index and from the largest slot index for the access zone and the relay zone, respectively. Constraints are applied to assign the OFDMA slots assignment process based on three properties presented in Section 4.3. Figure 5 shows how the coverage of a BS is extended into one relay direction. Figure 6 illustrates the proposed adaptive frame structure. In the first stage of Figure 6, the BS splits a frame into a DL and a UL subframe, the ratio of which is changeable according to the DL and UL traffic variation. Then, using each subframe, the BS assigns OFDMA resources (shadow regions in DL/UL relay zones of the BS) to an nt- RS (nt-rs 1 1 ). Using the data rate given by the BS (shadow regions in the DL/UL access zones of the nt-rs), the nt-rs serves its associated SSs. The data rate is determined by a combination of OFDMA resources, the modulation scheme, and the coding rate. The ratio of the relay zone to the access zone between the BS and the nt-rs is also changeable, and only the nt-rs requires extra time to switch from receiving mode to transmit mode (or vice versa). The relay transmit/receive transition gap (R-TTG) and the relay receive/transmit transition gap (R-RTG) show these time durations. In the second stage of Figure 6, the second-hop nt-rs (nt-rs 2 1 )isplacedtoextendthecoverage. After the nt-rs 1 1 is assigned more OFDMA resources from the BS, the ratio of the DL/UL access to the DL/UL relay zone between the BS and the nt-rs 1 1 changes. Finally, the nt-rs 1 1 can support its nt-rs2 1 by using the data rate of its relay zone, and the nt-rs 2 1 can serve its SSs by using the assigned access zone. Figure 5. Mobile multihop relay networ with one relay direction. BS, base station; nt-rs, nontransparent relay station. Wirel. Commun. Mob. Comput. 2013; 13: John Wiley & Sons, Ltd. 971

6 OFDMA resource allocation in mobile multihop relay networs B. Kwon et al. Figure 6. Frame structure with one relay direction. AZ, access zone; RZ, relay zone; BS, base station; DL, downlin; UL, uplin; nt-rs, nontransparent relay station; RTG, receive/transmission transition gap; R-RTG, relay RTG; R-TTG, relay transmit/receive transition gap Adaptive frame structure with multiple relay directions Figure 5 shows one relay direction and Figure 7 shows the MMR cell extending in multiple directions. In the first stage of Figure 8, the first-hop three nt-rss share the OFDMA resources of the relay zone in the BS. That is, the sum of the data rate that each nt-rs uses as its access zone should be equal to the data rate of the relay zone in the BS. Through the assigned access zone, each nt-rs supports its own SSs. In the second stage of Figure 8, a new nt-rs (nt-rs 2 1 ) associated with the nt-rs1 3 is added to extend coverage in a specific direction. Only the nt-rs 1 3 splits its access zone into an access zone and a relay zone to support its nt-rs (nt-rs 2 1 ). Finally, the nt-rs2 1 can serve its SSs by using the assigned data rate of its access zone Numerical analysis In this section, we present how to numerically calculate a basic OFDMA resource unit in the time and frequency domains. The basic unit is the smallest resource unit used in our proposed OFDMA resource allocation fairness scheme (Section 5). In addition, we introduce three relationship properties between a superior station and its nt-rss. Table I shows the notations used for this numerical analysis. First, we need to calculate the time duration of an OFDMA symbol in an OFDMA frame, given system parameters, including the number of subcarriers that determine the fast Fourier Transform (FFT) size used Ts fr N FFT D.1 C G/ b. BW 8000/c8000 (1) 972 Wirel. Commun. Mob. Comput. 2013; 13: John Wiley & Sons, Ltd.

7 B. Kwon et al. OFDMA resource allocation in mobile multihop relay networs Figure 7. Mobile multihop relay networs with multiple relay direction. BS, base station; nt-rs, nontransparent relay station. where BW is the channel bandwidth used by a BS, G is the ratio of T g (cyclic prefix time) to T b (useful symbol time), and is the sampling factor determined by the channel bandwidth. Using the Ns fr obtained by dividing the frame time duration by Ts fr, the capacity of a subcarrier in an OFDMA frame is calculated by the following equation: Csc fr D BW Nsc fr log 2 1 C E s (2) N 0 where Nsc fr is the number of subcarriers in an OFDMA frame, E s is the mean symbol energy, and N 0 is the power spectral density of the additive white Gaussian noise (AWGN). Equation (2) explains the maximum capacity of a subcarrier. To calculate the maximum capacity of an OFDMA resource unit that consists of an OFDMA subcarrier and an OFDMA symbol, Equation (2) needs to be divided by the Ns fr, the number of OFDMA symbols. Csc,sym fr D C sc fr Ns fr D BW Nsc fr N s fr log 2 1 C E s (3) N 0 From Equation (3), we can define a slot, the smallest allocation unit that a BS or an nt-rs can assign to its subordinate nt-rs. We assume that a slot is formed by a group of adjacent subcarriers and symbols. Then, the capacity of the slot is obtained by Equation (4): C slot sc,sym D BW Nsc frn s fr N slot sc Nsc slot log 2 1 C E s (4) N 0 where Nsc fr is the number of subcarriers in a slot, and N slot s is the number of OFDMA symbols in a slot. Now that we have the minimum resource allocation unit called an OFDMA slot, an OFDMA frame can be indexed with this slot: i (1, 2,..., x): the slot index along the frequency domain in a frame, where x = Nsc fr =N slot sc j (1, 2,..., y): the slot index along the time domain in a frame, where y = Ns fr =N slot sc As a practical allocation scheme, we can calculate the capacity of a slot that was assigned to SS associated with a BS or an nt-rs, based on Equation (4) and the modulation scheme and the coding rate. C BS SS.slot.i; j // D BW NscNs N sc slot N s slot M BS SS CR BS SS (5) where MSS BS and CR BS SS are the modulation scheme and the coding rate between a BS and the SS, respectively. They are determined by the SNR value of the SS.We assume that MSS BS and CR BS SS are the same in all slots to which the SS is assigned. Therefore, the total capacity of the SS can be expressed as follows: C BS SS D acn SS X f slot ida bcn SS X t slot j Db C SS SS.slot.i; j // (6) where N SS is the number of the OFDMA slots in the frequency domain to which the SS is assigned and N SS f slot t slot is the number of the OFDMA slot in the time domain. To derive the maximum OFDMA resources that nt-rss can be assigned and to synchronize access zones and relay zones Wirel. Commun. Mob. Comput. 2013; 13: John Wiley & Sons, Ltd. 973

8 OFDMA resource allocation in mobile multihop relay networs B. Kwon et al. Figure 8. Frame structure with multiple relay directions. AZ, access zone; RZ, relay zone; BS, base station; DL, downlin; UL, uplin; nt-rs, nontransparent relay station; RTG, receive/transmission transition gap; R-RTG, relay RTG; R-TTG, relay transmit/receive transition gap. between a superior station and its subordinate nt-rss, we create three properties for the BS and the nt-rss: a data relay property, amaximum balance property, andarelay zone limitation property. These properties will be also used in the proposed fairness allocation explained in Section Data relay property To relay data from a superior station (a BS or a superior nt-rs), the total data rate used for the access zones of the DL in the subordinate nt-rss should not exceed the total data rate used for a relay zone of the DL in a superior station. nx R.DL_AZ nt-rs 1 / R.DL_RZ BS / D1 nx D1 R.DL_AZ nt-rs i / R.DL_RZ nt-rs i 1/ To relay data from the SSs of the nt-rss, the total data rate used for the access zones of the UL in the subordinate nt-rss should not exceed the total data rate used for a relay zone of the UL in a superior station. nx R.UL_AZ nt-rs 1 / R.UL_RZ BS / D1 nx R.UL_AZ nt-rs i / R.UL_RZ nt-rs i 1/ D Relay zone limitation property The maximum number of slots of the relay zone in the time domain that a BS or a superior nt-rs can assign depends on the maximum number of slots of the access zone in the time domain among all the subordinate stations. 974 Wirel. Commun. Mob. Comput. 2013; 13: John Wiley & Sons, Ltd.

9 B. Kwon et al. OFDMA resource allocation in mobile multihop relay networs Notation Table I. DL BS DL_AZ BS UL_RZ BS DL_AZ i hop nt-rs DL_RZ i hop nt-rs R.DL_AZ BS / Notations for numerical analysis. Description DL of a BS DL_AZ of a BS UL_RZ of a BS DL_AZ of the ith-hop nt-rs DL_RZ of the ith-hop nt-rs Data rate assigned to the DL_RZ of the BS R.DL_AZ i hop / Data rate assigned to the DL_AZ nt-rs of the ith-hop nt-rs N BS.nt-RS i / The number of the ith-hop nt- RSs associated with a BS N i 1 nt-rs.nt-rs i / N DL_RZ.t_slot/ BS N DL_AZ.t_slot/ nt-rs 1 GfN DL_AZ g.t_slot/ nt-rs i GfR.DL_AZ nt-rs 1 /g The number of the ith-hop nt- RSs associated the i 1 nt-rs in which 2 < i < max hop The number of slots of the BS s relay zone in the time domain The number of slots of the firsthop th nt-rs s access zone in thetimedomain The group of the number of slots of the access zone from all the ith-hop nt-rss in the time domain The group of the data rate that each first-hop nt-rs is assigned AZ, access zone; RZ, relay zone; BS, base station; DL, downlin; UL, uplin; nt-rs, nontransparent relay station. maxfn DL_RZ BS.t_sl/gDNBS DL DL_AZ.t_sl/ maxfn nt-rs 1.t_sl/g maxfn UL_RZ BS.t_sl/gDNBS UL UL_AZ.t_sl/ maxfn nt-rs 1.t_sl/g maxfn DL_RZ.t_sl/gDN DL nt-rs i 1 nt-rs i 1.t_sl/ maxfag maxfn UL_RZ.t_sl/gDN UL.t_sl/ maxfbg nt-rs i 1 nt-rs i 1 where A is GfN DL_AZ nt-rs i.t_slot/g and B is GfN UL_AZ.t_slot/g. nt-rs i Maximum balance property Based on the data relay property, the relay zone limitation property, and the adaptive modulation and coding rate between the superior station and its subordinate nt-rss, the maximum data rate of the DL/UL relay zone in a superior station should be acceptable enough for the nt-rss to use the same data rate for their DL/UL access zone. N BS.nt-RS X 1 / max C DL_RZBS max C DL_AZnt-RS 1 D1 AX AX C DL_RZnt-RS max C i 1 DL_AZnt-RS i D1 D1 max C UL_RZBS max max AX D1 C UL_RZnt-RS i 1 N BS.nt-RS 1 / X D1 max C UL_AZnt-RS 1 AX D1 C UL_AZnt-RS i where 2<i<max hop, A D N nt-rs i 1.nt-RS i /. 5. ORTHOGONAL FREQUENCY DIVISION MULTIPLE ACCESS RESOURCE ALLOCATION WITH FAIRNESS Based on the three properties aforementioned, OFDMA resource allocation algorithms with two popular fairness schemes are proposed: a max-min fairness scheme and a proportional fairness scheme. The basic unit of OFDMA allocation is based on the numerical analysis in Section 4. The existing max-min and proportional fairness schemes cannot be directly applied to wireless MMR networs because all stations in the networs cannot share the same resources due to the access zone and the relay zone. That is, some stations are restricted to only some portion of the resources. Even in the MMR networs, we try to allocate the same amount of resources to all SSs regardless of what superior station they are associated with. Table II shows the notations used in this section Max-min fairness The main purpose of the proposed max-min fairness scheme is to allocate OFDMA slots to SSs to maximize the minimum number of all SSs assigned data rates regardless of what superior station they are associated with. In other words, some SSs are allocated OFDMA slots in the relay zone of the superior station, and some are allocated slots in the access zone of the superior station. Thus, the proposed max-min fairness scheme in the MMR networ can be formulated as follows: arg max x arg max y fmin R.SS DL /g (7) fmin R.SS UL /g (8) where x 2 N.SS DL / and y 2 N.SS UL /. R.SS DL / and R.SS DL / are DL and UL capacity of the th SS, respectively. Algorithms I and II show the proposed max-min fairness scheme in the wireless MMR networ. In this section, we show the proposed scheme using a DL subframe. Algorithm I shows a BS s initialization phase. The BS first initializes available slot indices in the time and frequency domains. Then, it obtains the number of its directly Wirel. Commun. Mob. Comput. 2013; 13: John Wiley & Sons, Ltd. 975

10 OFDMA resource allocation in mobile multihop relay networs B. Kwon et al. Notation SS BS x SS nt-rsi x Table II. Notations for fairness allocation. Description The xth SS associated with a BS The xth SS associated with the nt-rs i N.t_slot DL SS BS x / The number of slot of the DL in the time domain assigned to SS BS x N.f _slot DL SS BS x / The number of slot of the DL in N.SS/ N.SS BS DL_AZ / N.SS BS DL_RZ / N.SS nt-rsi DL_AZ / R.DL BS R.DL BS total / avail / R.DL_RZ BS max / R.Unit DL / R.Unit DL_RZ / maxfn DL_AZ nt-rs 1.t_slot/g the frequency domain assigned to SS BS x The total number of SSs in an MMR networ The total number of SSs within the DL_AZ of a BS The total number of SSs within the DL_RZ of a BS The total number of SSs within the DL_AZ of the nt-rs i Total DL capacity of a BS The current available DL capacity of a BS The maximum RZ capacity of a BS A common minimum allocation unit in a DL A common minimum allocation unit only in the RZ of the DL The maximum slot number of the DL_AZ in the time domain among the first-hop nt-rss curfn DL_AZ BS.t_slot/g The current slot number of the DL_AZ of a BS in the time domain AZ, access zone; RZ, relay zone; BS, base station; DL, downlin; nt- RS, nontransparent relay station; SS, subscriber station; MMR, mobile multihop relay. Algorithm II. Max-min fair allocation of the base station. 1: while N.SS/ 0 do 2: find the SS with the smallest rate 3: if the SS 2 SS BS DL_AZ then 4: res D det_rate.r.ss DL_AZ 5: N.SS BS DL_AZ / D N.SSBS / req ; R.Unit DL /; ss/ DL_AZ / 1 6: N.SS/ D N.SS BS DL_AZ / C N.SSBS 7: update curfn DL_AZ BS g 8: if res > 0 then 9: R.DL BS avail / D R.DLBS avail 10: R.Unit DL / D R.DL BS 11: R.Unit DL_RZ / D R.Unit DL / 12: end if 13: else 14: if maxfn DL_AZ DL_RZ / / R.SSDL_AZ avail /=N.SS/ / req.t_sl/g > curfn DL_AZ nt-rs 1 BS.t_sl/g then 15: R.Unit DL_RZ / D R.DL_RZ BS max /=NS.SSBS 16: R.Unit DL / D R.DL BS avail /=N.SS/ DL_RZ / 17: R.Unit DL_RZ / D minfr.unit DL_RZ /; R.Unit DL /g 18: end if 19: r D det_rate.r.ss DL_RZ / req ; R.Unit DL_RZ /; ss/ 20: N.SS BS DL_RZ / D N.SSBS DL_RZ / 1 21: N.SS/ D N.SS BS DL_AZ / C N.SSBS 22: update maxfn DL_AZ nt-rs 1.t_slot/g 23: if r > 0 then 24: R.DL BS avail / D R.DLBS avail 25: R.Unit DL / D R.DL BS 26: R.Unit DL_RZ / D R.Unit DL / 27: end if 28: end if 29: end while 30: det_rate (req_rate, unit_rate, ss) 31: if req_rate > unit_rate then 32: assign unit_rate to the ss 33: return 0 34: else 35: assign req_rate to the ss 36: return.unit_rate req_rate/ 37: end if DL_RZ / / R.SSDL_RZ avail /=N.SS/ / req Algorithm I. Initialization phase of a base station. 1: obtain N.SS BS DL_AZ /; N.SSBS DL_RZ / 2: calculate N.SS/ D N.SS BS DL_AZ / C N.SSBS DL_RZ / 3: R.DL BS avail / D R.DLBS total / 4: R.Unit DL / D R.DL avail BS / N.SS/ 5: R.Unit DL_RZ / D R.Unit DL / 6: curfn DL_AZ BS gd0; maxfn DL_AZ.t_slot/gD0 nt-rs 1 associated SSs (N.SS BS DL_AZ /) and the number of SSs that belongs to its first-hop nt-rss (N.SS BS DL_RZ /). Using the total number of SSs, the BS can calculate the minimum slot unit that can be equally assigned to its directly associated SSs and first-hop nt-rss. Finally, it calculates the minimum slot unit for the SSs associated with the first nt-rss. Algorithm II shows how the BS allocates slots according to max-min fairness. The BS continuously assigns slots until all SSs in the MMR networ are assigned their minimum data rate. The difference between our max-min algorithm and general max-min fairness algorithms is that the proposed algorithm always checs the relay zone limitation property. That is, the SSs that belong to relay zone in the BS are restricted to the maximum relay zone capacity even though OFDMA slots in the access zone are available. In this case, the BS maintains two minimum allocation slots: one is for SSs in the access zone, and the other is for SSs in the relay zone. The proposed max-min algorithm first finds an SS with the least data rate and allocates slots to that SS. If the requested data rate is smaller than the minimum data rate to be assigned, the BS recalculates the minimum data rate based on the current data rate and the remaining number of SSs after it allocates slots to the SS. When the BS allocates a data rate to an SS in the access zone or the relay n zone, it updates cur N DL_AZ BS o or max n N DL_AZ nt-rs 1.t_slot/ o, 976 Wirel. Commun. Mob. Comput. 2013; 13: John Wiley & Sons, Ltd.

11 B. Kwon et al. OFDMA resource allocation in mobile multihop relay networs respectively. These two values are used to chec the relay zone limitation property Proportional fairness The main drawbac of the proposed max-min fairness scheme is that the SS associated with a subordinate nt-rs taes more OFDMA resources because the channel condition between a superior station and its subordinate nt-rss is poor because of the distance of their locations. Therefore, the networ capacity is not fully exploited. To avoid this drawbac, we propose a proportional fairness scheme. We also propose a two-layer proportional weight concept for the proposed scheme. In the first layer, a weight value is given to the access zone and the relay zone of the superior station. The sum of the assigned weight is one. However, how to assign the weight value in the first layer is outside the scope of this paper. In the second layer, every SS is assigned a weight based on its channel condition with its associated station. Based on these two weight values, OFDMA resources are proportionally assigned to every SS. Therefore, the proposed proportional fairness scheme in the MMR networ can be formulated as follows: arg maxfmin.wz 1 w2 i R.SSDL i //g (9) i2 arg maxfmin.wz 1 w2 i R.SSUL i //g (10) i2 where z is the access zone or the relay zone, is the total number of SS in the MMR networ, w 1 is the first weight value, and w 2 is the second weight value. Algorithms III and IV show the proposed proportional fairness scheme in the wireless MMR networ. First, Algorithm III shows the initialization phase of a BS. The BS assigns the first weight value to its access zone and relay zone and the second weight value to SSs associated with its access zone or relay zone. Using the first and the second weight values, the BS initializes a weight array consisting of every weight value of SSs and another weight array with only SSs associated with its subordinate nt-rss. Finally, the BS obtains Algorithm III. Initialization phase of a base station. 1: assign waz 1 and w RZ 1.w AZ 1 C w RZ 1 D 1/ 2: obtain w 2 x.1 < x < N.SSBS DL_AZ //; w 2 y.1 < x < N.SSBS DL_RZ // 3: calculate N.SS/ D SS BS DL_AZ C SSBS DL_RZ 4: for all x in the access zone do 5: w x D waz 1 w 2 x 6: end for 7: for all y in the relay zone do 8: w y D waz 1 w 2 y 9: end for 10: Array.w / D w 1 ; w 2 ;:::;w. D N.SS BS DL // 11: RZ_Array.w y / D w 1 ; w 2 ;:::;w y.y D N.SS BS DL_RZ // 12: maxfn DL_AZ.t_slot/gD0; curfn DL_AZ nt-rs 1 BS.t_slot/gD0 Algorithm IV. Proportional fairness allocation of the base station. 1: while N.SS/ 0 do 2: nor_array.w nor / D nor_weight.arrary.w // 3: w_sum D w1 nor C w2 nor C :::Cw nor 4: find the SS with the smallest rate 5: if the SS 2 SS BS DL_AZ then 6: R.Unit SS DL / D R.DLBS avail /. wnor w_sum / 7: res D det_rate.r.ss DL_AZ / req ; R.Unit SS DL /; ss/ 8: N.SS BS DL_AZ / D N.SSBS DL_AZ / 1 9: N.SS/ D N.SS BS DL_AZ / C N.SSBS DL_RZ / 10: update curfn DL_AZ BS.t_slot/g 11: if res > 0 then 12: R.DL BS avail / D R.DLBS avail / R.SSDL_AZ / req 13: end if 14: else 15: if maxfn DL_AZ.t_sl/g > curfn DL_AZ nt-rs 1 BS.t_sl/g then 16: nor_rz_array.w nor y / D nor_weight.arrary.w y // 17: w_rz_sum D w1 nor C w2 nor C :::Cw nor y 18: R.Unit SSy DL_RZ / D R.DL_RZBS max /. 19: end if w nor y w_rz_sum / 20: R.Unit DL_RZ / D minfr.unit DL_RZ /; R.Unit DL /g 21: r D det_rate.r.ss DL_RZ y / req ; R.Unit DL_RZ /; ss/ 22: update maxfn DL_AZ.t_slot/g nt-rs 1 23: if r > 0 then 24: R.DL BS avail / D R.DLBS avail / R.SSDL_RZ y / req 25: end if 26: end if 27: end while 28: det_rate (req_rate, unit_rate, ss) 29: if req_rate > unit_rate then 30: assign unit_rate to the ss 31: return 0 32: else 33: assign req_rate to the ss 34: return.unit_rate req_rate/ 35: end if the total data rate that it can support and initializes the current number of slots in its access zone and the maximum number of slots in its relay zone in the time domain. Algorithm IV shows how the BS allocates slots according to proportional fairness. The BS continuously assigns slots until all SSs in the MMR networ are assigned their minimum data rate based on their weights. Lie the MMR- BS-2 algorithm, the proposed algorithm checs the relay zone limitation property when it assigns slots to the SS associated with its relay zone. Another different point from general proportional fairness is that the proposed algorithm gives two weight values to all SSs and allocates slots based on the mixed weight from the two. Every time the proposed proportional algorithm allocates OFDMA slots to an SS, it first normalizes every SS s weight value. Then, the proposed algorithm finds the SS with the least data rate and allocates slots to the SS. Based on the normalized weight, the minimum data rate of SS(R.Unit SS DL /) can be calculated by the algorithm. If the requested data rate of the SS is Wirel. Commun. Mob. Comput. 2013; 13: John Wiley & Sons, Ltd. 977

12 OFDMA resource allocation in mobile multihop relay networs B. Kwon et al. smaller than the minimum data rate to be assigned, the BS recalculates the normalized weight value from the remaining SSs and their weights after it allocates slots to the SS. When the BS allocates a data rate to an SS in the access zone or the relay zone, it updates curfn DL_AZ BS.t_slot/g or maxfn DL_AZ nt-rs1.t_slot/g, respectively. When an SS associated with the subordinate nt-rs is assigned slots, if the maxfn DL_AZ DL_AZ nt-rs1.t_slot/g is larger than curfnbs.t_slot/g, which means the relay zone cannot be more extended within a subframe, the algorithm calculates the normalized weight from only the SSs associated with the subordinate nt-rss. Then, the minimum data rate is determined by selecting the minimum between the data rate calculated by all the SSs and the data rate calculated by only the SS associated with the subordinate nt-rs. 6. PERFORMANCE ANALYSIS Based on the proposed equations and properties, numerical simulations were conducted to determine the maximum capacity of the access zone of each nt-rs and the maximum hop count a BS can have, given the system parameters in an MMR networ. We used the PYTHON (Python Software Foundation, Wilmington, DE, USA) script language and MATLAB (MathWors, Natic, MA, USA) for the simulations. To determine the accuracy of the simulation results, we used a 95% confidence level with 50 simulation runs for each scenario of the simulations. From the 95% confidence level, we constructed 95% confidence interval for the average value as follows: Zc p n (11) where Z c is the z-score associated with the 95% confidence level (Z c D 1:91), is the average standard deviation obtained from simulations, and n is the number of simulation (n = 50). In other words, the 95% confidence intervals for the obtained mean is expressed as follows: Z c p n C Z c p n (12) In the simulations, the free space path loss model is used. It is also assumed that the signal does not suffer from any shadowing or fading effects and varies only by AWGN over time. The MMR networ parameters used in our simulation and the relationship between transmission ranges and SNR values are described in Tables III and IV, respectively Data rate The main purpose of these simulations shown in Figure 9 is to estimate how many nt-rss can be theoretically deployed based on the system parameters and the three properties that we have proposed for the wireless MMR networs. In this simulation, we used the constant bitrate of the data Radio parameters Table III. System parameters. Value Base frequency 5 GHz Bandwidth 20 MHz Duplex method TDD Frame duration 20 ms Symbol duration s Number of subcarriers 1790 Number of data 1440 subcarriers Aslotunit f2 symbols, 24 data subcarriersg (TTG, RTG) (100 s, 60 s) (R-TTG, R-RTG) (50 s, 50 s) RTG, receive/transmission transition gap; TDD, transmit/receive transition gap; R-RTG, relay RTG; R-TTG, relay TTG. Table IV. Transmission range and signal-to-noise ratio (SNR). Modulation SNR Range (m), fbs, RSg QPSK 1/2 6.0 f11.4, 5.7g QPSK 3/4 9.0 f8.0, 4.0g 16 QAM 1/ f6.0, 3.0g 16 QAM 3/ f4.0, 2.0g 64 QAM 1/ f3.2, 1.6g 64 QAM 2/ f2.6, 1.3g 64 QAM 3/ f2.0, 1.0g BS, base station; RS, relay station; QAM, quadrature amplitude modulation; QPSK, quadrature phase shift eying. rate from each SS and did not apply our adaptive allocation algorithm. When an SS is created, we randomly assign its data rate range from 100 to 400 b/s. First, we create SSs and add them to the first-hop nt-rs until it reaches the relay zone limitation property. For the creation of each SS, we assume that an OFDMA slot in this simulation (6 bytes) is used for a control message. After the first-hop nt-rs reaches the threshold of the proposed relay zone limitation property, we create the second-hop nt-rs and SSs. Then, we set the maximum capacity of the first nt-rs available and associate the newly created SSs with the nt-rs. We repeat until no more nt-rss can be created. Figure 10 shows the maximum data rate of each nt- RS with one relay direction as shown in Figure 9(a). In the simulation, the ratio of a DL subframe to a UL subframe is 8:2. In addition, quadrature phase shift eying, quadrature amplitude modulation (QAM) 16, and QAM 64 modulation schemes were used with 1/2, 2/3, and 3/4 coding rates depending on the signal strength between SSs and their superior station. This simulation indicates that the first-hop nt-rs can theoretically serve around 7 Mb/s, and the MMR networ can have a third-hop nt- RS. In a new simulation scenario, we limit the maximum data rate that the first-hop nt-rs can provide with its SSs and add more first-hop nt-rss until each nt-rs reaches the relay zone limitation property. Figure 9(b) shows that the MMR networ can have three first-hop nt-rss, and 978 Wirel. Commun. Mob. Comput. 2013; 13: John Wiley & Sons, Ltd.

13 B. Kwon et al. OFDMA resource allocation in mobile multihop relay networs Figure 9. A simulation configuration. BS, base station; nt-rs, nontransparent relay station. Figure 10. Data rate of each nontransparent relay station (nt-rs) with one relay direction. SS, subscriber station. Figure 11. Data rate of each nontransparent relay station (nt-rs) with three relay directions. SS, subscriber station. Figure 11 illustrates that each first-hop nt-rs can have a data rate of around 2.7 Mb/s. This is because three nt-rss are deployed exclusively and they can serve their associated SSs simultaneously based on the OFDMA allocation scheme. The system model of the new simulation is shown in Figure 12. In this simulation, we also fixed the ratio of a DL subframe to a UL subframe at 8:2. To compare with the nonadaptive scheme, we set the ratio of a relay zone to an access zone at 5:5 and 6:4 in each subframe. We compared the networ throughput and the number of OFDMA slots allocated between the proposed adaptive allocation algorithm and a nonadaptive allocation scheme as the number of SSs increases. In this simulation, we can see how many SSs and OFDMA slots each scheme can serve and allocate. Fairness is not considered in this simulation (it will be considered in the next section). When an SS is created within the boundary of a BS, we randomly assign its data rate, the range of which is from 100 to 400 b/s. In addition, we assign a different channel condition on each time slot of each SS. Depending on the channel condition, the BS and SSs use a different modulation scheme and coding rate. Figure 13 shows the throughput of the proposed adaptive allocation scheme and the nonadaptive allocation scheme as the number of SSs associated with the BS increases. For the nonadaptive allocation scheme, we set the ratio of a relay zone to an access zone at 5:5 and 6:4. As we expected, the BS with the nonadaptive allocation scheme cannot allocate OFDMA slots after it has allocated all the OFDMA resources of its access zone. However, our proposed allocation algorithm can continue to give OFDMA slots because it can use the remaining OFDMA slots in a DL/UL subframe. Figure 14 shows the number of OFDMA slots allocated to SSs in the access lin of the BS as the Wirel. Commun. Mob. Comput. 2013; 13: John Wiley & Sons, Ltd. 979

14 OFDMA resource allocation in mobile multihop relay networs B. Kwon et al. Figure 12. A new simulation configuration. AZ, access zone; RZ, relay zone; SS, subscriber station; nt-rs, nontransparent relay station. Figure 13. Throughput comparison. SS, subscriber station. Figure 14. Comparison of the number of slots. AZ, access zone; BS, base station; SS, subscriber station. number of the SSs increases. The results indicate that if the BS has enough OFDMA slots to be allocated to the SSs, the nonadaptive allocation scheme uses fewer OFDMA slots than the proposed allocation algorithm. This is because the proposed algorithm has to allocate slots from the minimum number of slot index from the available slot indices in the time domain, whereas the nonadaptive allocation scheme can find the slot index with the best channel condition within its fixed size of the access zone. However, as the number of SSs in the access zone increases, the proposed algorithm can select a user that has the best channel condition for the minimum slot index of the available slot indices in the time domain Fairness In this section, we focus on max-min and proportional fairness between the proposed adaptive allocation algorithm and a nonadaptive allocation scheme. For the maxmin fairness scheme, we use the existing max-min fairness index [21] to measure fairness of the proposed algorithm and the nonadaptive allocation algorithm. For the proportional scheme, we assign different weight values to a relay zone and an access zone and compare the throughput between proportional and max-min fairness. The maxmin fairness index used in our simulations is expressed as follows: 980 Wirel. Commun. Mob. Comput. 2013; 13: John Wiley & Sons, Ltd.

15 B. Kwon et al. OFDMA resource allocation in mobile multihop relay networs I.max_min/ D R asgn.ss x /.x y/ (13) R asgn.ss y / In this scenario, the SSs use the same data rates used in the previous section (the max-min fairness simulations). First, we set the total number of SSs in the simulation to 100 and start to assign one node to the access zone and all the other 99 nodes to the relay zone. The simulation ends when the access zone has 99 nodes and the relay zone has one node. Figure 15 shows the result of the proposed adaptive allocation algorithm and a nonadaptive allocation scheme with respect to max-min fairness as we increase the proportion of SSs in the access zone. The result illustrates that the max-min fairness index of the proposed scheme is on average 2.4 times better than the fixed scheme. However, our scheme performs similarly to the fixed scheme when nodes are distributed symmetrically. In general, the proposed algorithm shows better max-min fairness because it can use all of the subframes to allocate slots to SSs regardless of what superior station (i.e., BS or an nt-rs) they are associated with. As the number of SSs in the access zone increases (more SSs than in the relay zone), the fairness index of the proposed scheme decreases. This is because the throughput increases as the number of SSs in the access zone increases, which means that the SSs in the access zone can obtain the OFDMA slots that they request. Therefore, the fairness index is determined by the data rate of each SS when it is created. Figure 16 shows the throughput of the proposed adaptive allocation algorithm and a nonadaptive allocation scheme with max-min fairness. The graph indicates that the proposed scheme performs on average 26% better than the nonadaptive scheme even though the latter is a little better than the former only in the area where SSs are almost symmetrically distributed between the access zone and the relay zone. This is somewhat expected because the bps 1.5 x Throughput with MM Fairness(confidence level=95%) Number of SS in the AZ of the BS (total=100) Figure 16. Throughput comparison with 100 subscriber stations (SSs). AZ, access zone; BS, base station; MM, max-min. nonadaptive allocation scheme selects the best time slot among a fixed access or relay zone and the proposed scheme selects the smallest or the largest indexed time slot that is best to an SS. In any asymmetric distribution of SSs, the proposed scheme is always much better than the nonadaptive scheme because the proposed scheme always uses all the OFDMA slots regardless of the distribution of SSs between access zones and relay zones. Figures 17 and 18 show the throughput of the proposed allocation algorithm with proportional and max-min fairness. In these simulations, we vary the data rate of each SS based on the distance between an SS and its superior station. In other words, the shorter the distance is between an SS and its superior stations, the greater the data rate the SS has. This shows how the proposed proportional fairness algorithm performs. The results indicate that the proposed algorithm with proportional fairness is better than the 0.9 Max Min Fairness Index(confidence level=95%) Index(min/max) Number of SS in the AZ of the BS (total=100) Figure 15. Max-min fairness index with 100 subscriber stations (SSs). AZ, access zone; BS, base station. Figure 17. Throughput of the proposed proportional and maxmin fairness (50 SSs). AZ, acccess zone; BS, base station; SS, subscriber station. Wirel. Commun. Mob. Comput. 2013; 13: John Wiley & Sons, Ltd. 981

16 OFDMA resource allocation in mobile multihop relay networs B. Kwon et al. Figure 18. Throughput of the proposed proportional and maxmin fairness (100 SSs). AZ, acccess zone; BS, base station; SS, subscriber station. one with max-min fairness regardless of the weight value assigned to the access zone of the BS. Also, the throughput increases with the higher weight on the access zone as the number of SSs associated with the BS increases. The proposed max-min fairness scheme shows the same throughput regardless of the distribution of SSs. This is because the proposed max-min fairness scheme does not care about the signal strength between SSs and their superior station. 7. CONCLUSION We proposed a new adaptive OFDMA frame structure and OFDMA resource allocation scheme for both the BS and the nt-rss. To enable the proposed OFDMA resource allocation, we have created three properties: a data relay property, a maximum balance property, and a relay zone limitation property. We have also proposed a max-min fairness scheme and a proportional fairness scheme for the proposed adaptive frame structure in wireless MMR networs. Through simulations, we show that the proposed OFDMA allocation scheme performs better than the nonadaptive allocation scheme in terms of max-min fairness and throughput, especially in an asymmetric distribution of SSs between access zones and relay zones. The largest benefit of our schemes occurs during asymmetric distribution of SSs between access zones and relay zones in the MMR networs. REFERENCES 1. IEEE j IEEE Standard for Local and Metropolitan Area Networs Part 16: Air Interface for Broadband Wireless Access Systems Amendment 1: Multihop Relay Specification. IEEE Press, IEEE IEEE Standard for Local and Metropolitan Area Networs Part 16: Air Interface for Broadband Wireless Access Systems. IEEE Press, Chiang CH, Liao W, Liu T, Chan IK, Chao HK. Adaptive downlin and uplin channel split ratio determination for TCP-based best effort traffic in TDD-based WiMAX networs. IEEE Journal on Selected Areas in Communications 2009; 27(2): Pries R, Staehle D, Marsiso D. IEEE capacity enhancement using an adaptive TDD split. In Proceedings of the 67th IEEE Vehicular Technology Conference (VTC 08), Marina Bay, Singapore, May 2008; Deb S, Mhatre V, Ramayian V. WiMAX relay networs: opportunistic scheduling to exploit multiuser diversity and frequency selectivity. In Proceedings of the 14th ACM international conference on Mobile computing and networing (MOBICOM 08), San Francisco, CA, September 2008; Narliar G, Wilfong G, Zhang L. Designing multihop wireless bachaul networs with delay guarantees. In Proceedings of the 25th IEEE International Conference on Computer Communications (Infocom 06), Barcelona, April 2006; Hoymann C, Klagges K, Schinnenburg M. Multihop communication in relay enhanced IEEE networs. In Proceedings of the 17th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC 06), Helsini, September 2006; TaoZ,LiA,TeoKH,ZhangJ.Framestructuredesign for IEEE j mobile multihop relay (MMR) networs. In Proceedings of IEEE Global Telecommunications Conference (GLOBECOM 07), Washington, DC, November 2007; Kularni G, Adlaha S, Srivastava M. Subcarrier allocation and bit loading algorithms for OFDMA-based wireless networ. IEEE Journal on Mobile Computing 2005; 4(6): Ermolova NY, Maarevitch B. Low complexity adaptive power and subcarrier allocation for OFDMA. IEEE Journal on Wireless Communications 2007; 6(2): Biagioni A, Frantacci R, Marabissi D. Adaptive subcarrier allocation schemes for wireless OFDMA systems in WiMAX networs. IEEE Journal on Selected Areas in Communications 2009; 27(2): Erwu L, Dongyao W, Jimin L, Gang S, Shan J. Performance evaluation of bandwidth allocation in j mobile multi-hop relay networs. In Proceedings of the 65th IEEE Vehicular Technology Conference (VTC 07), Dublin, April 2007; Wirel. Commun. Mob. Comput. 2013; 13: John Wiley & Sons, Ltd.

17 B. Kwon et al. OFDMA resource allocation in mobile multihop relay networs 13. Jun J, Sichitiu ML. Fairness and QoS in multihop wireless networs. In Proceedings of the 58th IEEE Vehicular Technology Conference (VTC 03), Orlando, FL, Vol. 5, October 2003; Aoun B, Boutaba R. Max-min fair capacity of wireless mesh networs. In Proceedings of IEEE International Conference on Mobile Ad Hoc and Sensor Systems (MASS 06), Vancouver, October 2006; Boche H, Wiczanowsi M, Stancza S. Unifying view on min-max fairness, max-min fairness, and utility optimization in cellular networs. EURASIP Journal on Wireless Communications and Networing 2007: Lei H, Mengtian R, Lan W, Xue Y, Schulz E. Resource scheduling for OFDMA/TDD based relay enhanced cellular networs. In Proceedings of IEEE Wireless Communications and Networing Conference (WCNC 07), Kowloon, March 2007; Xiao L, Cuthbert L. Improving fairness in relay-based access networs. In Proceedings of the 11th international symposium on Modeling, analysis and simulation of wireless and mobile systems (MSWiM 08), Vancouver, October 2008; Liu E, Leung KK. Throughput analysis of opportunistic scheduling under Rayleigh fading environment. In Proceedings of the 68th IEEE Vehicular Technology Conference (VTC 08), Calgary, Alberta, September 2008; Yu Y, Murphy S, Mirphy L. Planning base station and relay station locations in IEEE j multi-hop relay networs. In Proceedings of the 5th IEEE Consumer Communications and Networing Conference (CCNC 08), Las Vegas, NV, 2008; Tao Z, Teo KH, Zhang J. Aggregation and concatenation in IEEE j mobile multihop relay (NMR) networs. In IEEE Mobile WiMAX Symposium,March 2007; Dianati M, Shen X, Nai S. A new fairness index for radio resource allocation in wireless networs. Proceedings of IEEE Wireless Communications and Networing Conference 2005; 2: AUTHORS BIOGRAPHIES Bongyoung Kwon is a software engineer in the section of Service and Developer Experience at Noia. He received his Bachelor s and Master s degrees in Electrical and Communications Engineering from Kwangwoon University in 1995 and 1997, respectively. He also received his Master s and PhD degrees in Electrical and Computer Engineering from the Georgia Institute of Technology in 2008 and 2009, respectively. Prior to joining the PhD program at Georgia Tech in 2005, He also wored as a software engineer in LG Electronics and Daewoo Telecommunication from 2003 to 2005 and from 1997 to 2003, respectively. His research interests include networ security, integration of wireless networs, and future mobile solution. Raheem Beyah is an associate professor in the School of Electrical and Computer Engineering at Georgia Tech where he leads the Georgia Tech Communications Assurance and Performance Group (CAP) and is a member of the Georgia Tech Communications Systems Center (CSC). Prior to returning to Georgia Tech, Dr. Beyah was an assistant professor in the Department of Computer Science at Georgia State University, a research faculty member with the Georgia Tech CSC, and a consultant in Andersen Consulting s (now Accenture) Networ Solutions Group. He received his Bachelor of Science in Electrical Engineering from North Carolina A&T State University in He received his Master s and PhD in Electrical and Computer Engineering from Georgia Tech in 1999 and 2003, respectively. Dr. Beyah served as a Guest Editor for MONET. He is an Associate Editor of several journals including the (Wiley) Wireless Communications and Mobile Computing Journal. His research interests include networ security, wireless networs, networ traffic characterization and performance, and security visualization. He received the National Science Foundation CAREER award in 2009 and was selected for DARPA s Computer Science Study Panel in He is a member of ACM, NSBE, ASEE, and a senior member of IEEE. Myounghwan Lee, who received his Bachelor s degree in Electrical Engineering from Seoul National University in 2005, his master s degree in electrical engineering from Columbia University in 2006, and his PhD in Electrical and Computer Engineering from Georgia Institute of Technology in 2010, is a senior engineer woring on WiFi SoC at the Connectivity Lab in the Samsung Digital Media & Communication R&D Center. His main research interests are networ architecture modeling and performance optimization for quality of service in wireless multihop networs for multimedia communications. Wirel. Commun. Mob. Comput. 2013; 13: John Wiley & Sons, Ltd. 983

18 OFDMA resource allocation in mobile multihop relay networs B. Kwon et al. John A. Copeland holds the John H. Weitnauer Jr. Chair in the School of Electrical and Computer Engineering at the Georgia Institute of Technology and is a Georgia Research Alliance Eminent Scholar. He is the Director of the Communications Systems Center (CSC). This center is doing research on digital communication networs, including wireless sensor networs and WiFi and WiMAX networs, with emphasis on providing security and Quality of Service. Prior to joining Georgia Tech in 1993, Dr. Copeland was the vice president of technology at Hayes Microcomputer Products ( ) and the vice president of engineering technology at Sangamo Weston, Inc. ( ) and served at Bell Labs ( ). He began his career at Bell Labs conducting research on semiconductor microwave and millimeter-wave devices. Later, he supervised a group that developed magnetic bubble computer memories. In 1974, he led a team that designed CMOS integrated circuits, including Bell Labs first microprocessor, the BELLMAC-8. His last contributions at Bell Labs were in the area of lightwave communications and optical logic. At Sangamo Weston, he was responsible for research and development groups at 10 divisions. At Hayes, he was responsible for the development of modems with data compression and error control and for Hayes representation on CCITT and ANSI standards committees. In 2000, he invented the StealthWatch system for networ security monitoring and founded LANcope Inc., which today has deployed StealthWatch on over 100 corporate, government, and defense networs. Dr. Copeland received BS, MS, and PhD degrees in physics from the Georgia Institute of Technology. He has been awarded 49 patents and has published over 50 technical articles. In 1970, he was awarded IEEE s Morris N. Liebmann Award for his wor on gallium arsenide microwave devices. He is a fellow of the IEEE and has served that organization as the editor of the IEEE Transactions on Electron Devices. He served on the board of trustees for the Georgia Tech Research Corporation ( ) and was director of the Georgia Center for Advanced Telecommunications Technology ( ). 984 Wirel. Commun. Mob. Comput. 2013; 13: John Wiley & Sons, Ltd.