Power Fairness in A Scalable Ring-based Wireless
Mesh Network
Jane-Hwa Huang, Li-Chun Wang, and Chung-Ju Chang, Fellow, IEEE
Department of Communication EngineeringNational Chiao-Tung University, Taiwan, R.O.C.
E-mail: hjh@mail.nctu.edu.tw; lichun@cc.nctu.edu.tw; cjchang@cc.nctu.edu.tw
Abstract—The wireless mesh network (WMN) is an essential low-power solution to support ubiquitous broadband services. However, mesh networks face the power unfairness and through-put bottleneck issues. Compared to the users far away from the gateway, the users near the gateway need to relay more traffic and consume more power. This paper proposes a scalable ring-based WMN that can ensure power fairness among users by adjusting the ring widths. On top of the ring-based WMN, frequency planning is suggested to overcome the throughput bottleneck issue for the inner-ring users near the gateway, thereby making the system more scalable to accommodate more users and facilitating coverage extension. We also investigate the overall tradeoffs of the ring-based WMN in terms of power fairness, capacity, and coverage. An analytical model is developed to evaluate the throughput and power consumption of the ring-based WMN using carrier sense multiple access (CSMA) MAC protocol in the unsaturated situation. Then, a mixed-integer nonlinear optimization problem aiming to maximize cell capacity and coverage subject to the constraint of power fairness is formulated. Applying this optimization approach, we obtain the optimal number of rings and the associated ring widths of the ring-based WMN.
Index Terms—Power fairness, capacity and coverage, wireless mesh network (WMN).
I. INTRODUCTION
Thanks to the capabilities of enhancing coverage and ca-pacity by low transmission power, the wireless mesh net-work (WMN) is an economical solution to support ubiquitous broadband access [1], [2]. Figure 1 shows a multi-hop WMN, where each user relays other users’ traffic toward the central gateway and only the gateway directly connects to the Internet. WMN have many advantages over the infrastructure-based network, including low-power communication, rapid network deployment with less cabling engineering, and less cost.
However, due to multi-hop transmission, wireless mesh networks face the power unfairness problem. Specifically, the inner users near the gateway have to consume more power to relay more traffic for others, which induces the power unfairness problem for the inner users. When the users close to the gateway rapidly exhaust their battery energy, the whole mesh network will not function normally. As the number of users increases, the power unfairness problem becomes even more serious for the inner users. Therefore, while extending
This work was supported in part by the MoE ATU Program, the Program for Promoting Academic Excellence of Universities (Phase II), and the National Science Council under Grant 95W803C, Grant NSC 95-2752-E-009-014-PAE, Grant NSC 95-2221-E-009-155, and Grant NSC 95-2221-E-009-148.
r1 r2 r3 r4 A1 A2 A4 A3 Gateway (Central AP) Mesh Cell 0 Mesh Cell 1 Mesh Cell 2 f1 f2 f3 f4 Switch/Router Internet
Fig. 1. Ring-based cell architecture for a scalable wireless mesh network, where each ring is allocated with different channel.
the coverage area to serve more users, maintaining power fairness among users is a key challenge for WMNs.
In the literature, the performances of WMNs have mainly been studied from two directions. On the one hand, authors in [3] demonstrated the advantage of a multihop WMN over a single-hop network in terms of coverage by simulations. On the other hand, the results in [2] showed that withk users in
a WMN, the user’s throughput decreases sharply as O(1/k)
due to the throughput bottleneck at the gateway. [4] and [5] investigated the tradeoff between throughput and coverage in a scalable WMN. In addition, [6] focused on analyzing the power unfairness problem in the context of mesh sensor networks. [7] further suggested a specific approach to resolve the power unfair issue by reducing the hop distances of the nodes near the gateway (sink). These works considered the cases using the ideal medium access control (MAC) protocol without collisions and retransmissions, and assumed sufficient link throughput for each node. To our knowledge, fewer papers have studied the overall performances in terms of power fairness, coverage and throughput in the WMN.
To overcome the throughput bottleneck and power unfair-ness issues, we employ a scalable ring-based WMN where the rings in a cell are allocated with different channels as shown in Fig. 1 [5]. Under the ring-based cell structure, frequency planning can reduce the number of contending users, and thus make the system more scalable to accommodate more users and facilitate coverage extension. With the capability
of adjusting the ring width to control the hop distance and the data rate in the relay link between users, this ring-based cell structure also facilitates the management of coverage and throughput. In addition, by properly reducing the ring widths of inner rings, the users near the gateway can transmit at higher data rate due to shorter hop distance. Therefore, the power efficiency of WMN is improved and in turn the power unfairness issue can be resolved.
This paper also investigates the optimal tradeoff among throughput, coverage, and power fairness in the WMN. We develop an analytical model to evaluate the throughput and power consumption in the WMN considering the impacts of ring-based cell structure and frame contentions in the carrier sense multiple access (CSMA) MAC protocol. This model considers a general unsaturated case where the users are not always busy in sending traffic. Then, we formulate a mixed-integer nonlinear programming (MINLP) optimization prob-lem aiming to improve the overall performance tradeoff among coverage, capacity, and power fairness. With this optimization technique, we find a systematic approach to determine the optimal number of rings and the associated ring widths in a mesh cell.
The rest of this paper is organized as follows. Sections II discusses the proposed WMN and the impact of ring struc-ture on frame contentions. In Section III, we formulate an optimization problem to maximize cell capacity and coverage with the power fairness constraint. Section IV discusses the channel activity, and Section V elaborates the developed model for evaluating the throughput and power consumption in the considered WMN. Numerical examples are shown in Section VI. Concluding remarks are given in Section VII.
II. SCALABLERING-BASEDWIRELESSMESHNETWORK A. Network Architecture
Figure 1 shows the ring-based WMN, where stationary mesh users with the relay capability form a multihop network to extend the cell coverage. In the figure, the mesh cell is divided into several rings Ai, i = 1, 2, · · · , n, determined
by n concentric circles centered at the gateway with radii r1 < r2 < · · · < rn. The user in ring Ai connects to the
gateway via an i-hop communication, and only the gateway
connects to the Internet directly. Clearly, this WMN can be rapidly deployed in a large-scale area with less cabling engineering work.
The ring-based WMN operates in a multichannel with multi-interface fashion. Recall that there are multiple chan-nels available in the wireless networks, e.g., twelve non-overlapping channels in the IEEE 802.11a WLANs. Thus we can allocate the rings in a cell with different channels to avoid co-channel interference and improve the throughput. This frequency planning is simple because it only needs to design each ring width to ensure a sufficient co-channel reuse distance without interference. Moreover, we assume that each node is equipped with two radio interfaces. Thus, the user in ring Ai can concurrently communicate with the users
in rings Ai−1 and Ai+1 at different channels fi and fi+1,
ri Gateway (Central AP) lRC Ai Ai-1 A B θW,i θS,i P ri-1 Q ri-2 θS,i-1 VR (ri+ ri-1)/2 C D θS,i
Wireless Collision Domain, θW,i in Ai
Mutually-Interfered Region, θS,i in Ai
Mutually-Interfered Region, θS,i-1in Ai-1
Working-in-Vain Region VRof User P
θS,i-1
Fig. 2. Examples of wireless collision domain and mutually-interfered region.
respectively. By multichannel and multi-interface operations, the users can concurrently receive and deliver the relay traffic to improve throughput and delay. Besides, the system works well even employing the widely-used distributed CSMA/CA MAC protocol, thereby avoiding the compatibility issues.
Generally, spectrum and hardware costs are major concerns in the multichannel with multi-interface systems. However, there are multiple channels available in the wireless networks, e.g., twelve non-overlapping channels assigned for the IEEE 802.11a WLAN. The price of radio interface also goes down very rapidly, since the WLAN has become an off-the-shelf product.
B. Frame Contention under Ring-based Cell Structure
To describe frame contention under the ring-based cell structure, we first define the mutually-interfered region as an area in which any two users can sense the activity of each other. In Fig. 2, the area including usersC and D is an example
of mutually-interfered region. For simplicity, we assume that the mutually-interfered region in ringAi can be approximated
as an annulus sector with a central angle ofθS,i. LetlRC be
the interference distance. Referring to Fig. 2, the central angle
θS,i of a mutually-interfered region in ringAi is equal to
θS,i= 2 sin−1 lRC ri+ ri−1 , for lRC< (ri+ ri−1). (1)
IflRC≥ (ri+ri−1), we define θS,i= 2π which means that the
whole ring is in the same mutually-interfered region. Clearly, the area of a mutually-interfered region isAS,i= (θS,i/2π)ai
andai= π(ri2− ri−12 ) is the area of ring Ai.
Then, we define the wireless collision domain as the area in which at any instant at most one user can successfully transmit data traffic at a particular frequency. In Fig. 2, the wireless collision domain in ringAi is also approximated as
an annulus sector with a central angle of θW,i= θS,i−1, and
its area is AW,i = (θW,i/2π)ai. The phenomenon ofθW,i =
θS,i−1 is due to the fact that the request-to-send/clear-to-send
(RTS/CTS) mechanism is employed to avoid the hidden node problem. Referring to the example in Fig. 2, userA in ring Ai
is sending data to userB in ring Ai−1. In the meantime, since
usersP and A are not in the same mutually-interfered region,
userP in ring Ai can send an RTS request to usersQ in ring
because it has overheard the CTS of B and determined that
the channel is busy. This example shows that nodesP and A
are in the same wireless collision domain even though they are not in the same mutually-interfered region. Furthermore, the central angle θW,i of wireless collision domain in ring Ai is
determined by the angle θS,i−1 of mutually-interfered region
in the inner ring Ai−1, that is,θW,i= θS,i−1.
The example in Fig. 2 also shows that the existence of transmitter in region VR invalidates the RTS request of P .
Hence, we define the region VR with a central angle of
(θW,i− θS,i) as the working-in-vain region of P . Such an
impact of the ring structure on frame contention will be incorporated into the analytical throughput model later.
III. CAPACITY ANDCOVERAGEMAXIMIZATION A. Problem Formulation
All the issues of throughput, coverage, and power fairness will impact the design of WMNs. From a deployment cost perspective, a larger cell coverage is better because of fewer gateways. From a throughput viewpoint, however, a smaller cell is preferred since fewer users contend for the same channel. This paper mainly focuses on the power fairness. To achieve the power fairness, a shorter hop distance is better, since it can improve the link capacity and power efficiency, especially for the heavy-loaded users in the inner rings. To find the optimal tradeoff among throughput, coverage, and power fairness, we formulate an optimization problem to determine the best number of rings and the optimal ring widths in a cell. To begin with, we discuss the constraints in the considered optimization problem:
To guarantee a minimum throughput for each user, the
link capacityHi(d) of a user in ring Aishould be greater
than the carried traffic load Ri, i.e.,
Hi(d) ≥ Ri. (2)
The hop distances for the users in ring Ai may vary.
For simplicity, we assume that the average hop distance is d = (ri − ri−2)/2. In a real system, the next-hop
node may be too far away from the current node. In this situation, it may need to deploy a pure relay station.
To ensure the power fairness, it is required that
P F I ≥ P Freq, (3)
where P F I is the power fairness index defined in (19)
andP Freq stands for the power fairness requirement.
To ensure that the user at the boundary of ring can
find a next-hop node in the inner ring to forward the traffic, the ring width (ri − ri−1) should be less than
the maximum reception range dmax. In this WMN, the
channel allocated for the inner ring can be reused by the outer ring, if with a sufficient co-channel reuse distance. Hence, the ring width should be greater than a threshold
dmin to ensure a sufficient co-channel reuse distance.
Accordingly, dmin≤ (ri− ri−1) ≤ dmax. (4) ΦX XR θW,i P Q θW,i θS,i θW,i Gateway (Central AP) XL QR PR QL PL θS,i Working-in-Vain Region L R Ai Ai-1 ri-2 ri-1 ri θS,i-1 θS,i-1 θS,i PL’ PR’ θS,i θS,i
Considered user P and area with 2θW,i
Fig. 3. The considered userP and two adjacent wireless collision domains, where userP is contending for the radio channel.
B. MINLP Optimization Approach
The optimal capacity and coverage issues in a WMN can be formulated as a mixed-integer nonlinear programming problem with the following decision variables:n (the number of rings
in a mesh cell) andr1,r2,. . ., rn. The objective is to maximize
the cell capacity. In this ring-based WMN, optimal coverage and capacity can be achieved simultaneously since more users in a cell leads to higher cell capacity. Let the cell radiusrnbe
the cell coverage. Suppose thatρ is the user density and RDis
the traffic generated by each user. The cell capacity is defined asρπr2nRD. Then, the optimal ring widths can be determined
by solving the following optimization problem. MAX
n,r1,r2,...,rn ρπr 2
nRD (Overall throughput of a mesh cell)
subject to
Hi(d) ≥ Ri (5)
P F I ≥ P Freq (6)
dmin≤ (ri− ri−1) ≤ dmax. (7)
IV. CHANNELACTIVITY IN THERING-BASEDWMN From a user’s viewpoint, there are five types of channel activities in a WMN: (1) successful frame transmission; (2) unsuccessful frame transmission; (3) empty slot, where all users are in backoff or idle; (4) successful frame transmission from other users; (5) unsuccessful frame transmission from other users. For clarity, the channel activity is described by a sequence of activity time slots [8], [9]. Subject to the backoff procedures, the duration Tj for channel activity type j is
defined as T1 = T4 = TS, T2 = T5 = TC, T3 = σ, where σ
is the empty slot, TS and TC are the successful transmission
time and collision duration, respectively. The average duration
Tv of activity time slot is equal to
Tv=
5
j=1
νjTj . (8)
Here, νj is the probability of channel activity type as
calcu-lated in the following, and5j=1νj = 1.
At first, we derive the probabilitiesν1 andν2of a user
suc-cessfully/unsuccessfully sending a frame. In Fig.3, userP can
in the adjacent wireless collision domains ofP . Consider user P and its two wireless collision domains influenced by two
closest neighboring transmittersPL andPR, which are out of
the mutually-interfered regions of P as shown in Fig. 3. Let ψLandψRbe the positions ofPLandPR, respectively. If one
of the transmitters PL andPR is within the working-in-vain
regions ofP , i.e., ψL,ψR∈ [θS,i, θW,i], user P can still send
the RTS request to user Q, but user Q cannot reply the CTS
response, as discussed in Section II-B. Suppose that ZW,i is
the probability (average fraction of time) of a wireless collision domain in which a user is delivering data, as defined in (16). Clearly, the probability that there is a transmitter (like PL or
PR) affecting the considered area, and this transmitter is within
the working-in-vain region of P is equal to ZW,iθW,iθW,i−θS,i.
Hence, the working-in-vain probability pv of userP is
pv = 1 − Pr {ψL, ψR∈ [θ/ S,i, θW,i]}
= 1 −
1 − ZW,iθW,i− θS,i
θW,i
2
. (9)
Now, we consider the case that both transmittersPLandPR
are not in the working-in-vain regions of userP , i.e., ψL, ψR∈
[0, θS,i]. In the considered area of angle 2θW,i, only the users
in the area {2AW,i− (XL+ XR)} can send RTS frames as
shown in Fig. 3. Those users in regionsXL andXR will not
send their requests since they can sense the transmissions of
PL and PR. Let φX be the average central angle for region
XL, and AW,i be the area of a wireless collision domain of
user P . Therefore, the average number of contending users
in the considered area of angle 2θW,i is equal to the average
number of users in the area of {2AW,i− (XL+ XR)}, i.e.,
c1,i = ρai 2π2(θW,i− ZW,iφX) = ρai π (θW,i− ZW,i θW,i θS,i 0 ψLdψL) = ρ(ri2− r2r−1)(θW,i− ZW,iθS,i2 2θW,i ) (10) where ρ is the user density; ai = π(r2i − ri−12 ) is the area
of ring Ai;θS,i is the central angle of the mutually-interfered
region as defined in (1);φX= (ψL+ θS,i) − θS,i= ψL is the
central angle of region XL and ψL is uniformly distributed
in [0, θW,i] as shown in Fig. 3. Subject to the RTS/CTS
procedures, the frame collisions may only occur when the contending users concurrently deliver their RTS requests. Let
τ be the average probability of an active user sending the RTS
request at the beginning of an activity slot. Suppose that Ri
andHi(d) are the carried traffic load and the link capacity of
a node. Then, P0= 1 − Ri/Hi(d) is the average probability
of a user being idle due to empty queue [10]. Under the impact of ring structure on frame contention, the unsuccessful transmission probability pu is equal to
pu= pv+ (1 − pv)[1 − (1 − τ (1 − P0))C1,i−1], (11)
wherepvis the probability that at least one transmitter is inside
the working-in-vain regions ofP , and user P will not receive
the CTS response. The second term represents the probability that the RTS request fromP is collided with other RTS frames.
Thus, given that the considered user has a non-empty queue, the probability that this user successfully/unsuccessfully sends data frame in an activity slot can be expressed as
ν1= τ (1 − pu) and ν2= τ pu . (12)
By the same reasoning, one can also calculate the probabil-itiesνj, forj = 3, 4, 5, as detailed in [5].
V. THROUGHPUT ANDPOWERCONSUMPTIONANALYSIS
This section suggests an analytical method to evaluate the throughput and power consumption for the ring-based WMN, where the 802.11a WLAN is used as an example.
A. Carried Traffic Load of a User Node
The traffic load of mesh node includes its own traffic and the forwarded traffic from other users. Assume that all the nodes in the inner ring Ai share the relayed traffic from the outer
ringAi+1. Letci= ρπ(r2i − r2i−1) be the average number of
nodes in ringAi andρ be the user density. Suppose that RD
andRi represent the traffic load generated by each node and
the total carried traffic load per node in ringAi, respectively.
For the outermost ring An,Rn= RD. Besides, we have that
Ri= ci+1 ci Ri+1+ RD= n j=i+1cj ci + 1 RD. (13) B. MAC Throughput
To evaluate the MAC throughput in the ring-based wireless mesh network, we should consider the impacts of the physical layer ring structure on frame contention. Consider a binary exponential backoff procedure with the initial backoff window size of W . Let mbk be the maximum backoff stage. The
average backoff time can be calculated by [11]
Bk = (1 − pu)W − 1 2 + pu(1 − pu) 2W − 1 2 + · · · +pumbk(1 − pu)2 mbkW − 1 2 +pu(mbk+1)(1 − pu)2 mbkW − 1 2 + · · · = [1 − pu− pu(2pu) mbk]W − (1 − 2p u) 2(1 − 2pu) , (14) where pu is the unsuccessful transmission probability with
considering the impacts of ring structure in the physical layer, as defined in (11). Since a user sends RTS requests every (Bk+ 1) slots on average [11], the transmission probability τ
for an active user can be written as
τ = 1 Bk+ 1 = 2 1 + W + puW mbk−1 i=0 (2pu)i . (15)
From (11) and (15), we can obtain the solution ofτ and pu.
Then we evaluate the MAC throughput of one user. With the activity slot concept, the average busy probability (average
fraction of time) ZO,i of one user being sending data and the
channel utilization ZW,i of a wireless collision domain are
ZO,i= ν1T1
Tv (1 − P0) and ZW,i= ρAW,iZO,i
(16) where ν1 is the probability that one user successfully sends
a frame in an activity slot, T1 = TS is the successful
frame transmission time, Tv is the average duration of an
activity slot, and ρAW,i is the number of users in a wireless
collision domain. According to the IEEE 802.11a standard, the successful transmission timeTS and collision durationTCcan
be calculated as in [5]. Then, the link capacityHi(d) between
two nodes at separation distance d can be expressed as Hi(d) = ν1T1 Tv · l TS = ν1l Tv (17) where l is the payload size of data frame. From (8)-(17), we
can numerically obtain ν1,Tv,P0, andHi(d).
The hop distance also impacts the throughput in WMNs. Assume that the average reception ranges for eight PHY modes are dj, j = 1, 2, . . . , 8, and d1>d2>. . .>d8. In principle,
two users with a shorter separation distance can transmit at a higher data rate. Therefore, the transmission PHY mode
ma is determined according to the separation distance d
between two users, i.e., ma = j, if dj+1 < d ≤ dj. To
achieve fairness from resource allocation perspective and avoid throughput degradation due to low-rate transmissions [12] and [13], we also suggest that all data frames have the same transmission time TDAT A(l, ma). Thus, the data payload l
will be determined by the adopted PHY modema.
C. Power Consumption
Now we evaluate the average power consumption in the con-sidered WMN. Generally, there are three power consumption modes for a mesh user, including the transmitting, receiving, and idle modes [14]. Suppose that all the users transmit at a fixed higher power to extend the cell coverage. Let ptx and
prx be the average consumed power in the transmitting and
receiving modes; pidle be the power consumption when the
user is idle due to empty queue. With the activity slot concept, the average power consumption pavg,i for a user in ring Ai
can be expressed as pavg,i = j jνjTj jνjTj (1 − P0) + pidleP0 (18) = 2 j=1 ptxνjTj+ 5 j=3 prxνjTj Tv (1 − P0) + pidleP0
where the first term represents the average power consumption for an active user. j means the average consumed power for
channel activity type j. Specifically, 1= 2= ptx, and 3=
4= 5= prx.
Referring to [15], we define the power fairness indexP F I
for the ring-based WMN as
P F I = ( n i=1pavg,i)2 n(nj=1p2avg,i) , (19) TABLE I
SYSTEM PARAMETERS FOR NUMERICAL EXAMPLES.
Symbol Item Nominal value
ρ User node density 10−4users/m2
RD Demanded traffic of each user 0.4 Mbps
dmin Min. of ring width 100 (m)
dmax Max. reception range 300 (m)
lRC Interference distance (γIdmax) 400 (m)
ptx, prx Consumed power for Tx/Rx modes 1, 0.5 (power unit)
pidle Power consumption for IDLE mode 0.2 (power unit) where n is the number of rings in a cell. By (19), P F I = 1
means the perfect fairness, i.e., all the user have the same power consumption. In addition, P F I = 1/n stands for the
absolute unfairness.
VI. NUMERICALRESULTS
This section investigates the interactions among power fairness, capacity and coverage in a ring-based WMN. We consider a simple case where all the ring widths in a cell are the same. The system parameters are summarized in Table I. The chosen frame payload sizes for eight PHY modes are
{425, 653, 881, 1337, 1793, 2705, 3617, 4067} bytes [13].
Suppose that all the users transmitted at the same power. For this fixed transmission power system, referring to the measured results [16], the corresponding reception ranges are dj =
{300, 263, 224, 183, 146, 107, 68, 30} meters. In addition,
the power consumption for transmitting/receiving/idle modes are assumed to be (ptx, prx, pidle) = (1, 0.5, 0.2) (power
unit), which are normalized to ptx. These reception ranges
and power consumption may vary for different environments, hardware, and power-saving methods. However, the proposed optimization approach is general enough for different WMNs with various reception ranges and power consumption.
Figure 4 shows the cell coverage and capacity against the number of rings (n) in a cell under different power fairness requirements. In the figure, the optimal cell coverage and capacity for the case without power fairness requirement are 444 (m) and 24.8 (Mbps) at n = 4. To meet the power fairness requirement P F I = 0.9, the optimal coverage and
capacity diminish to 410 (m) and 21 (Mbps), respectively. In this figure, one can observe that the more the rings in a mesh cell, the better the coverage and capacity. However, the optimal solution is determined by the constrains of the power fairness requirement, mesh link throughput, and the hop distance.
Figure 4 also shows that the number of ringsn in a cell has
a maximum value. For handling the increasing relay traffic as
n increases, the ring width will be reduced to shorten the hop
distance and then improve the link capacity. However, since the ring width should be larger than dmin as discussed in
Section III-A, there will exist a maximum value ofn. In this
example, the maximum allowable number of rings is n = 4
for both cases.
In Fig. 5, the achieved power fairness against the number of rings is shown. If without any power fairness requirement, the achieved power fairness degrades as n increases. This
phenomenon is due to the fact that the users in the inner rings get more and more busy in forwarding the increasing relay traffic as n increases. However, shrinking the ring
1 2 3 4 200 250 300 350 400 450
Number of rings in a cell, n
Coverage of a mesh cell,
r n
(m)
NO Power Fairness Requirement Power Fairness Required, PFreq=0.9
10 15 20 25
Cell Capacity (Mbps)
Fig. 4. Cell coverage and capacity (aggregated throughput) versus the number of ringsn in a cell under different power fairness requirements.
1 2 3 4
0.85 0.9 0.95 1
Number of rings in a cell, n
Achieved power fairness,
PFI
NO Power Fairness Requirement Power Fairness Required, PFreq=0.9
Fig. 5. Achieved power fairnessP F I versus the number of rings in a cell.
width can improve the power fairness, since a shorter hop distance can raise the link capacity and power efficiency, especially for the heavy-loaded users near the gateway. From Fig. 5, it is observed that with the optimization approach to design the optimal ring width, the power fairness requirement
P Freq = 0.9 can be fulfilled at the cost of cell coverage as
shown in Fig. 4. For example, if the cell coverage is 444 (m) at n = 4, the average power consumption for the user
in ring Ai is pavg,i = (0.62, 0.38, 0.24, 0.21) (power unit).
If the cell coverage diminishes to 410 (m), the hop distance decreases with a higher power efficiency. Then, the average power consumption can decrease topavg,i= (0.47, 0.29, 0.23,
0.21), and thus the power fairness increases from 0.83 to 0.9. Clearly, since the power consumption is reduced, the network lifetime can be prolonged.
In these figures, we investigate the interactions among the power fairness, capacity, and coverage in a WMN. It is shown that the capacity and coverage can be enhanced simul-taneously. Besides, with properly designing the deployment parameters, the power fairness can be ensured at the expense of lower coverage and capacity.
VII. CONCLUSIONS
This paper has investigated a scalable ring-based WMN with power fairness guarantee. Subject to power fairness require-ment, a mixed-integer nonlinear programming optimization problem has been formulated, aiming at maximizing the cell capacity and coverage. We have suggests frequency planning to improve the throughput, and to make the system more scalable to coverage. With properly adjusting the ring widths, power fairness among users can be also ensured. An analytical model has been developed to evaluate the throughput and power consumption. On top of the developed analytical model, the optimization approach has been applied to determine the optimal number of rings and the associated ring widths. Numerical results have shown that the goal of capacity en-hancement with power fairness guarantee can be fulfilled at a cost of coverage performance.
Many interesting issues are worthwhile for future investi-gation form this work. These topics includes investigating the case with variable ring widths in a cell, the impacts of power control, and the power efficiency issues.
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