On the Uplink Performance and Optimization of a
Relay-assisted Cellular Network
Shiang-Jiun Lin
∗‡, Wern-Ho Sheen
†, and Chia-Chi Huang
∗ ∗Department of Communication Engineering,National Chiao Tung University, Hsinchu, 300 Taiwan †Department of Information and Communication Engineering, Chaoyang University of Technology, Taichung County, 413 Taiwan
‡Industrial Technology Research Institute, Hsinchu, 310 Taiwan
Abstract—Using relay stations (RSs) has been known as a
promising technology to improve the system performance of a traditional cellular network. This paper aims to investigate the uplink performance of a relay-assisted cellular network with optimal system parameters. Two performance measures, average power consumption of mobile stations and uplink system spec-tral efficiency, are optimized by jointly considering the system parameters of RSs’ locations, reuse patterns, path selections and resource allocation. A genetic algorithm along with a method of MAI (multiple access interference) estimation is proposed to solve the optimization problem. Numerical results show that significant improvement on system performance can be achieved from both power consumption and system spectral efficiency aspects if RSs are deployed and used in the optimal way.
I. INTRODUCTION
Using fixed relay stations (RSs) in the traditional cellular network is an emerging technology to improve system per-formance and has recently drawn research interest in both academia and industry [1]-[11]. By reducing the propagation loss between the base station (BS) and a mobile station (MS), RSs can significantly improve the cell coverage, increase the user throughput, and save the MS’s transmit power [2]-[10]. In addition, the system capacity can also be largely enhanced if RSs are deployed and used in an optimal way [7]. The performance of the relay-assisted cellular network has been investigated extensively from both theoretical and practical points of view [5]-[10]. These studies, however, have been done for very limited system scenarios: fixed number of RSs and locations, fixed reuse pattern, or seeking optimal RSs’ positions with a simplified one-dimensional model, except the one by the authors in [7], where the downlink performance was optimized for a general relay-assisted cellular network. In this work, we investigate the uplink performance and optimization. There have been few studies on the uplink performance of the relay-assisted cellular systems [8]-[10]. In [8], the issues of capacity, cell coverage, and MS transmit power were considered in a relay-assisted CDMA network with six RSs under different frequency allocation methods. In [9], the uplink capacity of an 802.16j system was discussed, where a simplified one-dimensional model is analyzed for the maximal capacity gains, and fixed number of RSs with uniform placement is also simulated. In [10], the issues of RS positioning and spectrum partitioning were studied by
searching optimal RSs locations along the lines connecting BS and the six vertices of a hexagonal cell to maximize the mean user data rate.
In this work, the uplink performance is evaluated for a general relay-assisted cellular system. Two performance mea-sures, average MS’s power consumption and uplink system spectral efficiency, are optimized by jointly considering RSs’ locations, reuse patterns, path selections and resource alloca-tion. The optimization is done based on a genetic algorithm (GA) and a method for MAI (multiple access interference) estimation. MAI estimation is important when applying intra-cell frequency reuse among MS to RS links, where locations of interferer are usually unknown to MSs. Numerical results show that the average MS’s transmit power is significantly reduced and the uplink system spectral efficiency is largely enhanced.
The rest of the paper is organized as follows. Section II describes the system setups. Section III formulates the objective functions under different criteria. The optimization algorithm is described in Section IV. Section V provides the numerical results, and finally, Section VI concludes this paper.
II. SYSTEMSETUPS
A. Cell Architecture
Fig. 1(a) depicts a hexagon cell structure with radiusD and
coverage Ω investigated in this paper. The BS is located at the cell center.N RSs are deployed into the cell with the position
vectorrjofRj, thejthRS, and Υ .= {rj} denotes the set of N
RSs’ positions. In addition, MSs are uniformly distributed over Ω with position vector m. MS can communicate with BS either through a direct path (the MS-BS link) or a 2-hop path (the MS-RS link and the RS-BS link). All stations are equipped with an omni-directional antenna and one RF transceiver.
B. Relaying Technique
We consider RSs which operate in the in-band decode-and-forward mode, where the received signal is fully decoded and forwarded to the destination using the same frequency band as BS. Besides, the orthogonal radio resources are allocated for direct paths and 2-hop paths respectively. A practical scheme is shown in Fig. 1(b), where resource for 2-hop links is
1 R 2 R mG 2 rG D 'LUHFW3DWK KRS 3DWK MS BS Ω 2 m rG G− 1 rG Ο 7LPH )UHTXHQF\ 5DGLR5HVRXUFHIRU 'LUHFW3DWK 06%6/LQN 5DGLR 5HVRXUFHIRU KRS3DWK 56%6 /LQN 5DGLR5HVRXUFHIRU KRS3DWK 0656/LQN 8SOLQNVXEIUDPH D E
Fig. 1. (a) Cell architecture, (b) radio resource allocation. further divided into one for MS-RS and the other for RS-BS transmissions. With this allocation, RSs do not need to transmit and receive at the same time (half-duplex relaying).
C. Propagation Models
The line-of-sight (LOS) and non-line-of-sight (NLOS) path-loss models for suburban macro-cell environment in [11] are adopted, which are given in (1) and (2), respectively.
LLOS(d) = 23.8 log10(d) + 41.9 dB, (1)
LNLOS(d) = 40.2 log10(d) + 27.7 dB, (2)
whered is the separation (in meters) between the transmitter
and the receiver. The LOS model is used for RS-BS links be-cause RSs are usually installed in the relatively high position, e.g. on the rooftop, while the NLOS one is for MS-BS links and MS-RS links.
D. Power Setup for RSs
The transmit power of each RS is set to achieve a pre-specified spectral efficiency,St, for users at the cell boundary
in the downlink. We assume RSs use the same power level to communicate with BS in the uplink. In this work, the AWGN channel is taken as an example to demonstrate the uplink theoretic performance. Hence,St can be expressed as
St= log2(1 +
pRj · L−1NLOS(D − rj)
N0+ I0 ), (3)
where pRj is the transmit power spectral density (PSD) for
Rj,L(d) is propagation loss in linear scale, rj denotes the
Euclidean distance of the position vectorrj, and N0 andI0
are the PSDs of AWGN and MAI, respectively. Accordingly,
pRj is setup by pRj=
(2St− 1) · (N 0+ I0)
L−1NLOS(D − rj) watts/Hz. (4)
The transmit power PRj is then equal to pRj · W , where W
is the link bandwidth.
E. Frequency Reuse over MS-RS Links
In Fig. 1(a), the radio resource can be further reused over the MS-RS links to increase the spectral efficiency because of the spatial separation between RSs. To exploit this advantage, let RSs be divided intoL groups, where L ≤ N , and each group
shares the same radio resource. The reuse pattern then can be specified by the set G .= {Gl}Ll=1, where Gl= {Rjl} is the
set of RSs in thelth group. It is clear that L
l=1|Gl| = N,
where|Gl| is the cardinality of the set Gl.
III. PROBLEMFORMULATION
In the uplink, in addition to the system spectral efficiency, MS’s power consumption is also an important performance measure due to the limited battery life. In this section, given a fixed amount of bandwidth for each MS, two system performance measures are investigated: 1. minimization of average MS’s transmit power for a specified throughput; 2. maximization the uplink spectral efficiency by given a fixed MS’s transmit power, by jointly searching optimal RSs’ posi-tions, reuse patterns, path selections and bandwidth allocation. Letwt(Hz per unit area) be the bandwidth allocated to MS
at any location m. Then, w t= wM →B(m) = wM →Rj(m) + wRj→B(m). Let SM →B(m), SM →Rj(m), and SRj→B(m)
denote the spectral efficiency for the MS-BS link, the MS-RS link, and the RS-BS link, respectively. In the AWGN channel,
SM→B( m) = log2 1 + PM→B( m) · L−1NLOS(m) (N0+ IM→B) · wt , (5) SM→Rj( m) = log2 1 +PM→Rj( m) · L−1NLOS(rj− m) (N0+ IM→Rj) · wM→Rj( m) , (6) and SRj→B( m) = log2 1 + PRj→B( m) · L−1LOS(rj) (N0+ IRj→B) · wRj→B( m) , (7)
where PM →B(m) and PM →Rj(m) are MS’s transmit power
of the MS-BS link, and the MS-RS link, respectively,
PRj→B(m) is the RS’s transmit power of the RS-BS link,
andIM →B,IM →Rj andIRj→Bare the PSDs of average MAI
appearing over the MS-BS link, the MS-RS link, and the RS-BS link, respectively. The throughput for each link is then expressed, respectively, by
tM→B( m) = wt· SM→B( m), (8)
tM→Rj( m) = wM→Rj( m) · SM→Rj( m), (9)
and
tRj→B( m) = wRj→B( m) · SRj→B( m). (10)
A. Measure 1-Minimization of Average MS’s Transmit Power
In this section, the average MS’s transmit power will be minimized to achieve a targeted throughputTt. From (5) and
(8), the MS’s transmit power for direct path is given by
PM→B( m) = (2
Tt
wt − 1) · (N0+ IM→B)
L−1NLOS(m) · wt. (11)
For a 2-hop path, since tM →Rj→B(m) =
min{tM →Rj(m), tRj→B(m)}, where tM →Rj→B(m) is
the effective throughput of a 2-hop link, the most efficient way is to make tM →Rj(m) = tRj→B(m) = Tt. As a result,
the bandwidth allocation for each hop is given by
wRj→B( m) = Tt SRj→B( m) , (12) and wM→Rj( m) = wt− wRj→B( m). (13)
Then, the MS’s transmit power toRj can be expressed as PM→Rj( m) = (2 Tt wM→Rj(m)−1)·(N 0+IM→Rj) L−1NLOS(rj− m) · wM→Rj( m). (14)
The optimal path selection is to select direct path if PM →B(m) ≤ PM →Rj(m), where PM →Rj(m) =
minRi{PM →Ri(m)}; otherwise the 2-hop path via Rj is
selected, where Rj = arg minRi{PM →Ri(m)}. Finally, the
objective function is given by min Υ,GPMavg, (15) with PMavg= m∈ΩB 1 ΩBPM→B( m)dA+ N j=1 m∈ΩRj 1 ΩRjPM→Rj( m)dA, (16)
where ΩB and ΩRj are the service area of BS and Rj.
B. Measure 2-Maximization of Uplink System Spectral Efficiency
In this section, given wt and a fixed MS’s transmit power
PM, the uplink system spectral efficiency will be maximized.
For direct path, by substituting PM into (5), the throughput
can be obtained by (8). For a 2-hop path, again,tM →Rj(m) = tRj→B(m) gives the highest spectral efficiency. Hence, when
wRj→B( m) = SM→Rj( m) SM→Rj( m) + SRj→B( m) · wt, (17) and wM→Rj( m) = SRj→B( m) SM→Rj( m) + SRj→B( m) · wt, (18)
the maximum attainable throughput is
tM→Rj→B( m) =
SM→Rj( m) · SRj→B( m) SM→Rj( m) + SRj→B( m)
· wt. (19)
Notice that from (6) and (18), we need to solve the following nonlinear equation for the optimalSM →Rj(m),
SM→Rj( m) = log2 aSM→Rj( m) + b , (20) where a = PM· L −1 NLOS(rj− m) (N0+ IM→Rj) · SRj→B( m) · wt , (21) and b = PM · L −1 NLOS(rj− m) (N0+ IM→Rj) · wt + 1. (22)
The optimal path selection is to select direct path if
tM →B(m) ≥ tM →Rj→B(m), where tM →Rj→B(m) =
maxRi{tM →Ri→B(m)} ; otherwise, the 2-hop path via Rjis
selected, where Rj = arg maxRi{tM →Ri→B(m)}. Let SΩ, TΩ, and WΩ denote the uplink system spectral efficiency,
system throughput, and system bandwidth consumption, re-spectively. The objective function is then expressed by
max Υ,GSΩ .= T Ω WΩ (bps/Hz), (23) 2SWLPDOVROXWLRQRU PD[LWHUDWLRQQR" *HQHUDWLRQRILQLWLDOSRSXODWLRQ 6XUYLYRU VHOHFWLRQ 1 'RQH < )LWQHVVHYDOXDWLRQ 0D[ LWHUDWLRQQR" 6HUYLFHDUHD GHWHUPLQDWLRQ 0$,HVWLPDWLRQ 06SRZHU8/WKURXJKSXW FDOFXODWLRQ 1 < 2EMHFWLYH IXQFWLRQ 0$,HVWLPDWLRQDOJRULWKP 0DWHVHOHFWLRQ *HQHWLFHYROXWLRQ &URVVRYHU 0XWDWLRQ 5RRP DYDLODEOH" 1 <
Fig. 2. The GA operation flowchart. with TΩ= m∈ΩB tM→B( m)dA + m∈ΩRjtM→Rj→B( m)dA, (24) and WΩ = m∈ΩB wtdA + N j=1 m∈ΩRj wRj→B(m)dA + L l=1 max Rj∈Gl{ m∈ΩRj wM →Rj(m)dA}. (25)
IV. OPTIMIZATIONALGORITHM
It is observed that both (15) and (23) are highly nonlinear functions for RSs’ positions Υ and the reuse pattern G, and the analytic solutions are not available in general. To resolve these issues, a particular design of GA based optimization together with an MAI estimation method for uplink are proposed. Fig. 2 illustrates the GA operation flowchart.
A. GA Operation
The Cartesian coordinate and the reuse group of a RS, (rj, Gl), is encoded as a gene, and the set of N RSs’
positions and the corresponding reuse pattern, (Υ, G), denotes
a chromosome. As shown in Fig. 2, in the beginning Npop
chromosomes are randomly generated and used as the initial
population involved in the evolution. Each chromosome is
evaluated against the objective function, called fitness
evalua-tion. Then, survivor selection selects the best Nsur= β ·Npop
chromosomes and the rest is discarded to make room for the new offspring, whereβ is the survival rate.
In the genetic evolution, Roulette wheel selection [13] is adopted to select two mates from the survival chromosomes to produce two new offspring. Uniform crossover [13] is then applied to produce two offspring from two selected mates. In a real-valued encoding scheme, a small zero-mean random perturbation is suggested to add to each gene of the offspring to prevent the evolutions being dominated by few genes [14]. A mutation probability Pmut is set to determine whether
a gene is mutated or not. Once a mutation is performed, the coordinate of the corresponding RS will be regenerated. Sufficient offspring are produced until the total number of the survivors and the offspring equals Npop.
The GA operation iterates until the optimal solution is found or the maximum iteration number is reached.
B. MAI Estimation Algorithm
An MAI estimation algorithm, also shown in Fig. 2, is proposed to determine the MAI level when the frequency is reused over MS-RS links. Initially, MS chooses the nearest BS or RS as its serving station, hence the ΩB and ΩRj are
pre-determined. Given a MS served by thekthRS in the reuse
group l, i.e., m ∈ ΩRkl, the MAI for this MS is caused by
the co-channel user in Gl. We calculate the MAI level for the
MS by averaging over the potential location of the interferer, which is expressed by IM→Rk= Ri∈Gl i=k mI ∈ΩRi 1 ΩRi · pMI →Ri( mI) · L −1 NLOS( mI− rk)dA, (26)
wheremI is the location of interferer and Ri is the serving
station ofmI.
In Measure 1, assume I0 = N0 for the PSD setup of the
interferer, which is pMI→Ri( mI) = (2 Tt wMI →Ri ( mI ) − 1) · 2N0 L−1NLOS(ri− mI) . (27)
By substituting (27) into (26), the average MAI for the MS can be obtained. Then, the transmit power ofm for the 2-hop
path can be determined by
PM→Rk( m) = (2 Tt wM→Rk ( m) − 1) · (N 0+ IM→Rk) L−1NLOS(rk− m) ·wM→Rk( m). (28)
Each MS can decide its new serving station by choosing minimal transmit power among the direct path and 2-hop paths. Then, ΩB and ΩRj can be re-determined.
In Measure 2, since PMI→Ri(mI) = PM, the throughput
for the 2-hop path can be determined according to Section III-B. Again, each MS can decide its new serving station by choosing maximal throughput among the direct path and 2-hop paths, and ΩB and ΩRj can be re-decided.
The process is repeated until the service area is converged or the maximum iteration number is reached.
V. NUMERICALRESULTS
In our numerical results, the cell radius is set as 1400 meters, the cell region is divided into grids with each side equal to 20 meters, and the locations of all stations are rounded into the nearest grid vertices. LetSt be set as 0.5 for PSD setup
of RSs. In GA, Npop = 200, β = 0.5 and Pmut = 0.05 are
adopted. The Gaussian variable with variance equal to a grid length is used as the perturbation when performing crossover operations. Through the work, wt= 28.5 KHz per unit area
is allocated to MS. Newton’s method is adopted to solve the nonlinear equation mentioned in (20) to (22). Besides, the inter-cell interference is assumed to be constant and embedded into the thermal noise, while the effect of intra-cell interference caused by frequency reuse over MS-RS links is considered. Note that more generations (iterations) are needed in GA for a larger number of RSs. X (m) Y (m) −1000 −500 0 500 1000 −1000 −500 0 500 1000 −50 −40 −30 −20 −10 0 10 (a)N=0 X (m) Y (m) −1000 −500 0 500 1000 −1000 −500 0 500 1000 −50 −40 −30 −20 −10 0 10 (b)N=2 X (m) Y (m) −1000 −500 0 500 1000 −1000 −500 0 500 1000 −50 −40 −30 −20 −10 0 10 (c)N=4 X (m) Y (m) −1000 −500 0 500 1000 −1000 −500 0 500 1000 −50 −40 −30 −20 −10 0 10 (d)N=6
Fig. 3. Optimal RSs’ positions and MS’s transmit power distribution (dBm).
A. Measure 1-Minimization of Average MS’s Transmit Power
The targeted throughput, Tt = 14.25 (Kbps per unit area)
is set in this section. No frequency reuse is adopted among MS-RS links. Fig. 3 shows the optimal RSs’ placement and the distribution of MS’s transmit power (in dBm). Fig. 3(a) is the case for no RS (N = 0). Clearly, more transmit power is
needed for a more distant MS. The average transmit power,
PMavg, is 14.54 dBm, shown in Table I(a). Fig. 3(b) is the
case of N = 2. The optimal RSs positions are in (±660, 0).
The service area of BS and RSs is indicated by the black lines, where ΩB = 31% and ΩR = 69% with ΩR= ∪jΩRj.
Besides,PMavg= 10.75 dBm in this case. Fig. 3(c) shows the
case of N = 4, where ΩR = 86% and PMavg = 3.18 dBm.
Fig. 3(d) is the case of 6 RSs. As can be seen, the optimal RSs’ positions are on the lines connecting the cell center and six vertices of the hexagonal cell with distance 900m from BS, and the whole area is almost evenly partitioned by BS and 6 RSs, where each station serves about 14% of total area. In this case,PMavg = −2.05 dBm, which is reduced 16.59 dB
compared to N = 0. Table I(a) summarizes the service area
ratio of BS and RSs, bandwidth allocation ratio for each link, and the average uplink transmit power forN = 0 to N = 10.
To explore frequency reuse over MS-RS links, the case of N = 6 is taken as an example with reuse
patterns G ={G1, G2, G3, G4, G5, G6}, G = {G1, G2, G3},
G = {G1, G2}, and G = {G1}, where each group has equal
number of RSs. The optimal RSs are symmetrically placed on the line connecting the cell center to six vertices of the cell with RSs in the same reuse group being pulled as far apart as possible. Table II(a) provides more detailed results of all cases. The uplink system spectral efficiency is getting better when the frequency is more aggressively reused (i.e., G = {G1} ); however, it costs more transmit power to achieve
the same targeted throughput due to larger MAI.
B. Measure 2-Maximization of Uplink System Spectral Efficiency
In this section,PM is set as 15 dBm and no frequency reuse
is adopted among MS-RS links. Fig. 4 describes the optimal RSs’ positions and the distribution of link spectral efficiency
TABLE I
IMPORTANT SYSTEM PARAMETERS FORN = 0TON = 10.
N 0 2 4 6 8 10 (a). Ω B:ΩR(%) 100:0 31:69 14:86 14:86 14:86 11:89 WM→B:WM→R:WR→B(%) 100:0:0 31:65:4 14:80:6 14:80:6 14:79:7 11:82:7 Measure 1 PMavg(dBm) 14.54 10.75 3.18 -2.05 -3.75 -5.07 (b). ΩB:ΩR(%) 100:0 36:64 14:86 13:87 12:88 11:89 WM→B:WM→R:WR→B(%) 100:0:0 36:49:15 14:59:27 13:53:34 12:51:37 11:50:39 Measure 2 SΩ(bps/Hz) 1.58 2.54 3.37 3.83 4.02 4.16 TABLE II
IMPORTANT PARAMETERS FOR FREQUENCY-REUSE PATTERNS,N =6.
G {G1, G2, G3, {G1, G2, G3} {G1, G2} {G1} G4, G5, G6} (a). Ω B:ΩR(%) 14:86 14:86 14:86 15:85 WM→B:WM→R:WR→B(%) 14:80:6 23:66:11 29:57:14 42:39:19 Measure 1 PMavg (dBm) -2.05 -2.03 -2.02 -1.57 SΩ(bps/Hz) 0.5 0.83 1.07 1.46 (b). Ω B:ΩR(%) 13:87 10:90 9:91 13:87 WM→B:WM→R:WR→B(%) 13:53:34 14:44:42 16:39:45 31:27:42 Measure 2 SΩ(bps/Hz) 3.83 5.31 6.08 6.23 X (m) Y (m) −1000 −500 0 500 1000 −1000 −500 0 500 1000 2 4 6 8 10 12 14 16 18 20 (a)N=0 X (m) Y (m) −1000 −500 0 500 1000 −1000 −500 0 500 1000 2 4 6 8 10 12 14 16 18 20 (b)N=2 X (m) Y (m) −1000 −500 0 500 1000 −1000 −500 0 500 1000 2 4 6 8 10 12 14 16 18 20 (c)N=4 X (m) Y (m) −1000 −500 0 500 1000 −1000 −500 0 500 1000 2 4 6 8 10 12 14 16 18 20 (d)N=6
Fig. 4. Optimal RSs’ positions and distribution of uplink spectral efficiency (bps/Hz),PM = 15 dBm.
(in bps/Hz). Fig. 4(a) is forN = 0, where SΩ= 1.58 bps/Hz
given in Table I(b). Fig. 4(b) is the case of N = 2. The
optimal RS positions are at (±700, 0) and SΩ= 2.54 bps/Hz. Fig. 4(c) shows the case of N = 4, where ΩR = 86% and
SΩ= 3.37 bps/Hz. Fig. 4(d) is for N = 6, where the optimal
RSs’ positions are on the line connecting the cell center to the six vertices of the cell with distance 740m from BS. Note that since the RS-BS link is not perfect, the maximum throughput for a 2-hop link is limited by the RS-BS link no matter how close the MS and the RS is. Obviously, more uniform data rate to MS can be provided with RSs’ assistance. Important system parameters are summarized in Table I(b).
Table II(b) shows the results of different reuse patterns for
N = 6 with equal number of RSs in each reuse group. The
system spectral efficiency is getting better if the frequency is more aggressively reused (i.e., G ={G1}). With respect to the service area ratio, ΩR becomes larger in G = {G1, G2, G3}
and G = {G1, G2} cases. However, in G = {G1}, ΩR is
shrunk due to large MAI.
VI. CONCLUSIONS
In this work, the uplink performance of relay-assisted cellu-lar networks is investigated with optimized system parameters.
The optimal RSs’ positions, reuse patterns, path selections and bandwidth allocation are jointly considered under two criteria: one is to minimize the average MS’s transmit power for a specified throughput, and the other is to maximize the uplink system spectral efficiency by given a fixed MS’s transmit power. Genetic algorithm approach along with a multiple access interference estimation method designed for the uplink performance evaluation are adopted. Numerical results conclude that given a fixed allocated bandwidth, the average uplink transmit power is significantly reduced for a targeted throughput, and the user throughput as well as the system spectral efficiency are largely enhanced for a fixed uplink transmit power with the assistance of RSs compared to the conventional cellular system.
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