A Load Balancing Relay Selection Algorithm for Relay Based Cellular Networks Fan Jiang
Benchao Wang
School of Communications and Information Engineering Xian University of Posts and Telecommunications, Xian 710121 E-mail:
[email protected] Abstract—A load balancing relay selection algorithm (LB-RS) is presented for relay based cellular networks. According to current user channel conditions as well as the user numbers that relay serves, LB-RS chooses the optimal relay node for each user in a distributed way. Simulation results demonstrate that compared with other relay selection schemes, LB-RS can achieve load balancing through effective relay selection method. This is realized by jointly consider physical layer parameters as well as MAC layer parameters, so as to obtain a tradeoff between the system throughput and the user equity. Keywords-Relay selection, relay based cellular network, load balancing,cooperative relay
I.
INTRODUCTION
In the cooperative relay network, by adopting reasonable relay selection scheme [1-6], multiple relays forms a virtual antenna array to realize spectral diversity, so as to improve system throughput. Some more recent work on relay selection criteria includes (but is not limited to) shortest distance, minimum path-loss, maximum receiving power, maximum signal-to-interference-ratio(SIR), based on which to choose one or multiple optimal relay nodes to fulfill cooperative diversity. In order to deal with relay selection problem concerned with different scenarios, various relay selection algorithms are proposed accordingly. In [2], Cai discusses the relay selection and power allocation problem under Amplify-and-Forward (AF) signaling method, which proposes a semi-distributed method to choose the optimal relay node among multiple candidates. Bletsas[3] presents a distributed relay selection method based on wireless channel interoperability and instant channel condition. Li [4] investigates the way of choosing the optimal forwarding manner as well as relay node with instant channel information under hybrid relay protocol. Sreng[5] considers relay selection schemes in cooperative relay networks, and discusses the potential impacts of relay selection criteria on the overall performance improvement. In [6], Madan proposes a relay selection scheme for wireless fading channel environment, where the relay nodes are chosen based on physical distance, and the cost of getting the channel state information (CSI) is also analyzed. Basically, by adopting different physical layer parameters (such as SIR, transmitted power, distance, path-loss), most of the aforementioned relay selection criteria aimed at to obtain the maximum achievable rate for each cooperative user. Actually, in the relay based cellular networks, the throughput of each mobile station (MS) not only depends purely on current physical channel state, but also relates to the total user
Huawei Technologies Co., Ltd. Bantian, Longgang District shenzhen 518129
[email protected] numbers that are served by the base station (BS) as well as the relay node (RN), the resource allocation algorithm and the scheduling schemes. Assume a RN is serving with amount of users, even if this RN is chosen as the optimal RN by a certain MS, the optimal throughput performances can not be anticipated since there might be not enough resource left for cooperative transmission. Consequently, even though the above relay selection approaches are adopted according to certain criteria, MS still can not adapts to its channel dynamics and the load fluctuations within cells simultaneously, hence the optimal performance can not be guaranteed. In this work, and to overcome the aforementioned problem, we first propose a utility based system level loadaware relay selection algorithm, and analyze its feasibility and the inherent problem. In light of above, we derive a distributed load balancing based relay selection (LB-RS) algorithm. When adopting two hop transmissions, in order to leverage the asymmetric traffic loading across RNs, the proposed LB-RS will distributed select the optimal RN for each MS, according to the current CSI as well as the user numbers that RN serves. Our ultimate goal is to proactively avoid congested RNs for individual MSs and locate a good service sites. Extensive experiments show the advantages of our schemes over the legacy schemes: our schemes enable the relay based cellular system to accommodate more satisfied users, to reduce regional congestions, and to leverage asymmetric load dynamics among RNs. The remainder of this paper is organized as follows. Section II presents the description of the centralized approach and the proposed LB-RS algorithm, and the performance evaluated in section III. Section IV concludes this paper. II.
A LOAD BALANCING RELAY SELECTION ALGORITHM
A. System model Consider a two-hop fixed relay based cellular network employing orthogonal frequency-division multiple access (OFDMA) physical-layer with L sub-carriers as illustrated in Fig.1, where all the OFDM frames are time-synchronized. The assumption is that the network operates in a slow fading environment, and that channel estimation is possible. Furthermore, full channel state information (CSI) is available for both MSs and RNs. Each cell focuses solely on uplink transmissions from the MT to the BS, either directly or via the RNs. The transmission in the time domain is on a frame-byframe basis. More specifically, for the direct transmission, the
This work is supported by New Century Supporting Project, Ministry of Education under project number: NCET-08-0891, Natural Science Research Project of Education Department of Shaanxi Provincial Government (project number: 11JK1009)
978-1-4244-6252-0/11/$26.00 ©2011 IEEE
MS accesses the BS in each frame. While for relay transmission, each frame consists of two consecutive time slots, where the MS transmits to the RN (MS-RN) in the first timeslot, and the RN forwards in the second timeslot(RN-BS). Decode-and-Forward (DF) forwarding is adopted by RNs.
In this formulation, (4) as an intra-cell constraint says that at any time t, each RN m , if associated with a non-empty user set, can pick one and only one associated user k for data transmission due to TDM-based channel access within each cell. Constraints (5) and (6) as inter-cell constraints say that at any time t, each user k can be associated with at most one BS i and RN m. For k-th user, assume all MSs have the same transmission power and consider both inter-cell and intra-cell interference in the system. We can obtain the instantaneous signal-tointerference-and noise ratio (SINR) of the BS-RN link, RN-MS link as well as the BS-MS link as follows
MSe
S k ,i (t ) = hk ,i (t )
K
∑
B. A centralized utility based load balancing relay selection algorithm Now let us describe the multi-cell system from the point of view of network economy. The optimal system utility should represent the maximized long-term revenue, which is set up as[7]
R(t ) = ∑ U k (Tk (t ))
(1)
k =1
where R(t) represents the sum of K MSs’ utility, Uk(·) is a concave non-decreasing utility function of the mean throughput Tk(t) of MS k up to time t. Given N BSs, 6 RNs in each cell and K MSs, ideally when two-hop transmission is adopted, our goal is to find optimal MS-RN-BS matching pair that maximize R(t) at current time t. Define a RN assignment indicator variable ⎧1, k-th MS selectes m-th RN within cell i at time slot t Ii,m,k (t) = ⎨ ⎩0,otherwise
(2)
At any time slot t, I i ,m ,k (t ) represents k-th MS will select the optimal m-th RN to realize two-hop transmission. Thus, the non-zero decision set is a vector of indicator I(t ) = { Ii,m,k (t ), i ∈1,2,...N , m ∈1,2,...6, k ∈1,2,...K} ,which
denotes the one-to one matching among BS i, RN m and MS k. Note I(t) is only one of the whole solution set 6N I = {1, 2,..., K } . At the beginning of t-th time slot, the optimization problem is thus formulated as K
max R(t ) = ∑ U k (Tk (I (t ))) I (t )
s.t.:
K
∑I
∑I
(4)
(t ) ≤ 1, ∀k ∈1,2,...K, ∀m ∈1,2,...6,
(5)
(t ) ≤ 1, ∀i ∈1,2,...N,∀k ∈1,2,...K
(6)
i ,m ,k
i =1 6
∑I m =1
i ,m , k
(3)
k =1
(t ) ≤ 1, ∀i ∈1,2,...N,∀m ∈1,2,...6
i ,m,k
k =1 N
2
h j ,i (t ) p j l j ,i (t ) + σ (n) 2
j =1, j ≠ k
Figure 1. System Model
K
(7)
pk lk ,i (t )
2
Sk ,m (t ) = hk ,m (t )
(8)
pk lk ,m (t )
2 K
∑
2
h j ,m (t ) p j l j ,m (t ) + σ (n) 2
j =1, j ≠ k
S m ,i (t ) = hm ,i (t )
(9)
pmlm,i (t )
2 N
∑
2
hm , j (t ) p j lm , j (t ) + σ (n) 2
j =1, j ≠ m
Where pk, pm is the transmit power of MS and RN, li , k (t ) , lk , m (t ) , lm , i (t ) correspond to propagation loss of the transmission power and the large time-scale log-normal fading form MS to BS, MS to RN and RN to BS, respectively. hk ,i , hk , m , hm ,i represent the fast Raleigh fading, characterizing the multi-path scattering and shadowing effect. The K K 2 2 denominator ∑ hj ,i (t) p jl j ,i (t) + σ (n)2 , ∑ hj,m (t) p jl j,m (t) + σ (n)2 , j =1, j ≠ k
N
∑
j =1, j ≠ k
hm, j (t) pjlm, j (t) + σ (n) denote the interfering signal from non2
2
j =1, j ≠m
serving cells together with complex additive Gaussian white noise (AGWN). Assume MS k chooses to access BS i directly at time t, then the upper bond rkd, i of the average achievable rate of bandwidth B is given by
r d k ,i (t ) = B log(1 + Sk ,i (t ))
(10)
Suppose MS k decides to access the BS i in a two-hop way c through RN m, then the upper bond r k , m , i (t ) of the average achievable rate of bandwidth B is given by
r ck ,m,i (t ) =
B min {log(1 + Sk ,m (t )),log(1+ Sk ,i (t ) + Sm,i (t ))} (11) 2
With ergodic assumption, the long-term mean throughput of MS k by the end of t-th slot can be written as 1 t N 6 Tk ( I (t )) = Tk (t ) = ∑∑∑ max r d k ,i (τ ), r c k ,m,i (τ ) I k ,m,i (τ ) (12) t τ =1 i =1 m=1 From formulation (12), it can be derived that the average throughput of MS k at time t not only depends on achievable rate, but also decided by the assignment indicator variable Ik,m,i(t). In addtion, Ik,m,i(t) is then affected by the resource
{
}
assignment methods, scheduling schemes and total user numbers that BS and RN serve at time t. Ideally, to maximize each use’s throughput, a centralized relay selection algorithm carried out by BS should select the optimal RN for each MS. This should be executed with regard to the CSI condition of the MS, current user numbers that RN serves, and resource allocation schemes. Assume the size of each time slot t is small. For a concave and non-decreasing utility function, the optimal RN assignment I*(t) at time t may proceed slot-by-slot along the steepest gradient ascent, as in the domain of continuous time. This RN assignment problem requires a maximum-weight 0-1 perfect matching among the BS set, RN set and the MS set: K
∂U k (Tk (t )) max {r d k ,i (t ), r c k ,m ,i (t )}I k ,m ,i (t ) ∂ T ( t ) i =1 m =1 k N
6
I* (t ) = arg max ∑∑∑ I ( t )∈I
k =1
(13) where Tk (t ) = (1 −
1
)Tk (t − 1) +
1
{
d
c
}
max r (t ), r (t ) Ik ,m,i (t )
[8]
1000 1000 (The estimation considers the relationship between the throughput of current time slot and that of the previous time slot). Moreover, Ik,m,i(t) follows the constraints given by (4),(5) and (6). Note that the feasible relay selection assignments I*(t) given in formulation (13) represents the optimal MS-RN-BS matching that maximize MS’s throughput at time t. For the sake of choosing the optimal relay selection results Ik,m,i(t)for each MS, BS should jointly considers the CSI condition of the MS, current user numbers that RN serves, resource allocation schemes, and the past throughput. Therefore, the optimal RN assignment I*(t) reflects the most efficient assignment, or resource allocation, of the whole system. Hence, it has an inherent load balancing effect. It can be inferred that if carried out by the BS, the optimal RN assignment I*(t) can be approximated by the Hungarian Method[9] in a polynomial time, while an exhaustive search takes O(K6N)steps in the worst case. However, a dilemma exists as follows: to find I*(t) requires the global knowledge of the system, including the instantaneous achievable rate between any BS-MS pairs at time t; and the past mean throughput Tk(t−1) of all MS k. In addition, the optimization is centrally computed by BS at each time slot, which is not practical in multi-cell systems. Therefore, in spite of being ideal, this formula (13) is too complicated, if feasible at all, to realize in practice. k ,i
k ,m ,i
C. A distributed load balancing relay selection (LB-RS) algorithm Motivated by the observation that the above centralized approach is too complex to be implemented, we propose a distributed load balancing relay selection scheme (LB-RS) in this paper. The more detailed procedure of LB-RS is as follows: 1) A BS periodically broadcasts pilot signals to assist MTs and RNs in estimating the channel gain between them and the associated BS. Similarly, RNs periodically broadcast pilot signals to assist MTs in estimating the channel gain between them and the neighboring RNs. RNs also
broadcast information to surrounding MTs about the user numbers it serves. Each MT takes advantage of such information to individually decide on relay selection. 2) If a MT needs to set up a new call with the BS, or to perform a handover to another cell, it checks for pilot signals from the BS and the RNs in the cell. According to the information from channel gain between the RNs and the associated BS, a MT will decide to either communicate with the BS directly or via a two-hop relay. If direct transmission to the associated BS is more beneficial, the MT sends a capacity request to the BS directly. The BS then decides whether to receive or reject its request according to admission control policy. 3) If the MT decides to transmit via a two-hop relay (e.g. two-hop relays can bring larger channel gain), it will first calculate the received SINR from each RN within the home cell. It will also obtain the user serving condition of each RN by listening to the pilot signal. Then it selects another RN from the neighboring cells which has the largest SINR, and records its user serving information. 4) By adopting formula (11), MS calculates the achievable c
rate rk that can be obtained through cooperative relay transmission by selecting different RNs, and then builds a distributed load-aware RN selection function as shown in formula (14) to select the optimal relay node which lead to the maximum β*.
⎧ E [ r c k , m , i (t ) ] ⎫ ⎬ ⎩ E [ K m (t ) ] + 1 ⎭
β (t ) = arg max ⎨ *
i,m
(14)
5) According to current scheduling policy, MS will transmit on the allocated sub-carriers to perform two-hop cooperative transmission. In function (14),
c
E[ rk , m ,i (t )] represents
the mean
achievable rate that MS k can achieve by selecting RN m as the relay node at time slot t, and is measured by MS k from pilot signals as illustrated by formula (11). E [ Km (t)] is the mean population served by RN m , constantly measured by RN m and advertised to MS k through a signaling channel. In order to achieve the throughput, MS k has to compete with the other MSs, which are already served by RN m, for cooperative c E [ r k , m , i (t ) ] transmission. Consequently, represent the E [ K m (t ) ] + 1
throughput Tk(t) predicted by MS k by choosing RN m as the serving RN node. Thus, the object of relay selection is not only to choose the optimal relay node that can maximize the predict throughput of MS k, but also to avoid “hot-spot” RNs at the same time. For the sake of avoiding complicated computations, the potential RN selection set only include six RNs that are deployed in the home cell and another RN in the neighboring cells which has the maximum received SINR. With proposed LB-RS algorithm, each MS can selected the optimal RN according to the current CSI conditions as well as the user numbers that RN serves, thereby implicitly balances asymmetric load across relay nodes in a distributed manner. Moreover, our scheme takes both user’ throughput and load
balancing into account, by fully utilizing cooperative communication so as to strike a balance between cell throughput and fairness among users. III.
SIMULATION RESULTS AND PERFORMANCE ANALYSIS
To test the performance of the proposed LB-RS scheme, we consider an OFDMA cellular system working over 2 GHZ bands. In the system evaluation, the simulation scenario comprises of 27 hexagonal cells is shown in Fig.2. To avoid border effects in the simulation results, the wrap-around technique is adopted at the cell edge region. In each cell, a BS is located in the cell centre with a radius of 1Km, and six RNs are deployed with a distance of 2/3Km far from the BS.
covered by RNs also increases. Since more MS will choose to perform cooperative transmission via a RN, hence leading to a great increase of RN serving user numbers. Nevertheless, neither MSINR-RS nor SD-RS can avoid the “hot-spot” RN problem, since these relay selection algorithm only focus on physical-layer radio closeness, and cause local congestion and asymmetric blocking of MSs across different RNs. While as far as the proposed LB-RS scheme is concerned, each MS will select the optimal RN according to its current channel conditions as well as the RN serving conditions in a distributed way. Owing to potential balancing the load among RNs, those RNs serving with fewer MS will gradually deal with more user access requirements. This is achieved by helping more MS to achieve cooperative transmission, hence leading to the improvement of system performance.
6000 20
5000
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3000 11
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1000
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1
-1000
15
5
4
3
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7
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-2000
-3000 -2000
0
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Figure 2. Simulation Scenario
OFDMA is adopted as the multiple access technique. Other simulation parameters are chosen in accordance with 3GPP LTE regulation for OFDMA system [10]: one time slots equals to 1ms, and one timeslot contains 14 OFDM symbols. Each scheduling timeslot contains 24 sub-channels, each subchannel contains 12 sub-carriers, and the bandwidth of each sub-carrier is 15 kHz. The transmission power of a MT per sub-carrier and that of RN is PMT=50mW, PRN=1W, 2 −10 respectively. The thermal noise power is σ = 10 W, and the [11] path-loss model adopted in the simulation is
Figure 3. Throughput VS number of users
⎧PL = 38.4 + 35lg(d ) + 20lg( fc / 5) + Xσ MS → BS, σ = 8 ⎪ ⎨PL = 36.5 + 23.5lg(d ) + 20lg( fc / 2.5) + Xσ RN → BS, σ = 3.4 (15) ⎪PL = 41 + 22.7 lg(d ) + 20lg( f / 5) + X MS → RN, σ = 2.3 ⎩ c σ Here the random variable X σ is used to model the shadow fading and independent multi-path fading. To make a comparison, we will evaluated the throughput and fairness performances of the following four schemes: ①without relay, w/o relay; shortest distance based relay selection, SD-RS; ③maximum SINR based relay selection, MSINR-RS; ④the proposed load balancing based relay selection, LB-RS. Assuming that in each resource scheduling timeslot, one RN can serve at most 8 MSs at the same time. And the scheduling method is round-robin (RR) [12], which has the characteristic of low complexity. Figure 3 shows the cell throughput when the number of users within the cell varies. As can be observed, when there are fewer MSs in the cell (below 20), all three relay selection scheme SD-RS, MSINR-RS and LB-RS can provide better performance as compared with w/o relay scheme. As user number increases, the number of MSs within the region
Figure 4. Fairness index VS number of users
In Fig. 4 the fairness index with vary user numbers is shown. The definition of fairness index F is given by 2
K [13] ⎛ K ⎞ , where rk is the throughput of MS k. ⎝ k =1 ⎠ k =1 It is observed that with LB-RS scheme, the fairness among users does not apparently affected by the increasing number of MSs. This phenomenon can be explained by the fact that the proposed LB-RS jointly considers the channel conditions together with the network conditions. Therefore, it will consider user’s throughput by implicitly balance asymmetric load across relay nodes. However, with the increase number of users, the fairness performances with MSINR-RS and that of SD-RS have gradually becomes worse. This is owing to the fact that those two schemes choose the optimal RN only based
F = ⎜ ∑ rk ⎟ / K ∑ rk 2
on physical layer conditions, while omit the user conditions within the cell. Consequently, with the increase of users, the possibility of local congestion at certain RNs also rises which leads to the decrease of fairness.
Figure 5. Edge user throughput VS number of users
Figure 5 illustrates the cell-edge throughput when the number of users within the cell varies. It can be concluded that, when user number is small, the performance of MSINR-RS is better than LB-RS. This is owing to the proposed LB-RS considers the existing load of different RNs when selecting the optimal RN. In particular, it might choose some sub-optimal relay node in order to balancing the load. Hence, there is a tradeoff between the system throughput and user’s fairness. However, with the increase of users, the load balancing effected on throughput improvement has gradually becoming obviously. On the other hand, as for MSINR-RS and SD-RS schemes, since each RN has limited resources, with the increasing of serving users, certain RN will suffer with overloaded traffic, while some RN will have lighter load, which lead to the decrease of system performances.
not adapt with the varying load, which finally leads to decreased resource utilization efficiency. IV.
CONCLUSIONS
In this paper, we propose a distributed load balancing relay selection scheme for relay based cellular systems. We first present a utility based centralized load-aware relay selection algorithm, and analyze its feasibility and the inherent problem. To overcome its shortcoming, a distributed load balancing based relay selection (LB-RS) algorithm is then present. For the sake of leverage the asymmetric traffic load across RNs, the proposed LB-RS will select the optimal RN for each MS independently, according to the current CSI as well as the user numbers that RN serves. It is shown that the proposed scheme could reduce regional congestions, and leverage asymmetric load variations among RNs, which significantly improve the cell throughput compared with the reference schemes. Moreover, the proposed scheme can also provides a flexible way to strike a balance between cell throughput and user fairness, hence better user experience can be obtained. REFERENCES [1]
[2]
[3]
[4]
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[6]
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[8]
Figure 6. Relay serving users VS number of users
[9]
Figure 6 shows the relay serving numbers versus user numbers. In the figure, as user number increases, the number of MSs serving by RN also increase. For the proposed LB-RS, as can be seen, the user number served by RN gradually approach 8, which is the limit number set by our simulation experiment. This is owing to the inherent load balancing between RNs, which result in uniform distribution of traffic. On the other hand, for the MSINR-RS and SD-RS schemes, since they can
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[13]
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