1
Optimal Resource Allocation in Random Access
Cooperative Cognitive Radio Networks
Mani Bharathi Pandian, Mihail L. Sichitiu, Huaiyu Dai
Abstract—Cooperative Cognitive Radio Networks (CCRNs) incorporates cooperative communication into cognitive radio networks,
in which, primary users lease their spectrum to secondary users, and in exchange, the primary users leverage secondary users as
cooperative relays to enhance their own throughput. Mobile operators offload their Internet traffic to privately owned WiFi access points
(APs), much to the inconvenience of non-cellular users served by the APs. However, by employing the CCRN scheme, the mobile
operator can lease a licensed channel to the AP, effectively doubling its capacity. In this paper, we propose an implementation of the
CCRN framework applied to IEEE 802.11 WLANs. The cooperation is cast as a two-player bargaining game where the two players
are the primary users (users of the mobile operator) and the secondary users (users of the AP before spectrum leasing) who bargain
for either throughput share or channel access time share. The optimal resource allocation that ensures efficiency as well as fairness
among users is provided by the Nash solution. Simulation results show that the users achieve higher throughput via the proposed
CCRN scheme, thus providing the mobile operator (e.g., AT&T) and the private WiFi provider (e.g., a Starbucks coffee shop) with
incentives for cooperation.
Index Terms—Cooperative Cognitive Radio Networks, WLAN Optimization, WiFi, spectrum leasing, Game theory.
F
1
I NTRODUCTION
M
O bile
data offload to small cell technology such as
WiFi or femtocell provides a compelling solution
for mobile operators who want to relieve the strain on
their core networks. Compared to cellular macrocells,
small cells provide increased spectrum reuse in the coverage area, higher signal to noise ratio in the cell (hence
superior link bit rate for its users), and are highly cost
effective even for large scale deployments. Furthermore,
the reduced transmission times enabled by the superior
link bit rates in the small cells directly translate into
battery power saving for the user devices. WiFi hotspots
operate in the unlicensed bands and suffer from severe
interference due to scarce spectrum availability. On the
other hand, macrocells and femtocells require the use of
the same costly and scarce licensed spectrum and suffer
from co-site interference problems.
To unlock new spectrum for small cell technology, a
new regulatory spectrum sharing framework [1] is being
proposed by the Federal Communications Commission
(FCC), where non-mobile incumbent owners, such as
military who do not use their spectrum at all times
and locations are allowed to grant exclusive access of
their spectrum to mobile operators in regions where
there is no incumbent activity. Recently, FCC and the
US Federal government have identified the 3550-3650
MHz band [2] (3.5 GHz Band), currently utilized for
military and satellite operations localized to the U.S.
coastline, as an ideal spectrum band for shared use with
• Mani Bharathi Pandian, Mihail L. Sichitiu, Huaiyu Dai are with
the Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC, USA. E-mails: {mpandia, mlsichit,
hdai}@ncsu.edu.
mobile operators for small cell operations. The European
Commission is working on a similar proposal in the 2.32.4 GHz band that has very localized incumbent military
telemetry use. Such a spectrum sharing approach regime
can potentially unlock more than 100 MHz of highquality spectrum, specially in higher spectrum bands (>
2 GHz) that are ideal for small cells.
To expedite spectrum sharing in small cells, FCC in
its recent ruling [3] has eliminated spectrum sensing
as a requisite for cognitive radio devices. Instead, FCC
mandates that devices learn of spectrum availability at
their respective locations from an external source such as
a location-based query to the database of the incumbent,
for example the Google Spectrum Database [4]. Devices
with such “cognitive” or “frequency-agile” transceivers
are regarded as the main enabler of spectrum sharing
in small cell technology. Although, spectrum leasing
simplifies commercial deployment and promotes better spectrum utilization, developing a workable pricing
model between the primary network (owner of the
spectrum) and the secondary network (beneficiary of
the leased spectrum) is not trivial. To expedite spectrum
leasing in real-world deployments, researchers have recently advocated for schemes that employ spectrum
leasing, not necessarily on the basis of fees or charge, but
in return for improved quality-of-service of the primary
network via cooperation with secondary network. One
such proposal is the new cognitive radio paradigm in [5]
termed Cooperative Cognitive Radio Networks (CCRNs). In
CCRNs, the primary users select a set of secondary users
(which have better channel conditions) to relay the primary traffic cooperatively, and in return the secondary
users are granted channel access opportunities in the
licensed (leased) spectrum. CCRNs exploit cooperative
2
diversity in cognitive radio networks by combining cooperative communication [6], a physical layer technology, and
the spectrum leasing feature enabled by cognitive radios.
Consider the scenario in Fig. 1-(a) where the primary
users initially connect to their cellular base station (BS)
using cellular technology such as LTE in the licensed
spectrum, while the secondary users connect to the
IEEE 802.11 WiFi AP and use the standard 802.11 DCF
protocol for channel access in the unlicensed bands. The
primary users along with the BS form the primary network, while the secondary users along with the AP form
the secondary network. If all primary users offload their
traffic to the WiFi AP, although they might connect to the
AP at superior link bit rate, the corresponding increase
in contention can significantly degrade throughput of all
the users (both primary and secondary). Instead, assume
that spectrum leasing is enabled via the CCRN scheme
for the network in Fig. 1. The primary network (i.e.,
the mobile operator) leases an additional channel from
the licensed spectrum to the secondary AP. In exchange,
the secondary AP adds the extra channel to its auxiliary
interface and reassigns both the primary and secondary
users in the two resulting WLAN cells - the original cell
that continues to operate in the unlicensed channel and
the new cell operating in the newly leased channel as
shown in Fig. 1-(b). With the capacity of the AP now
effectively doubled, both primary and secondary users
can expect significant improvements in their achievable
throughput, as well as power savings (owing to reduced
transmission time). Hence the CCRN scheme offers a
win-win scenario for both the cellular network operator (e.g., AT&T) as well as the WLAN owner (e.g., a
Starbucks coffee shop).
Leased
Spectrum (WLAN-1)
Licensed Spectrum (LTE)
PU
PU
PU
SU
SU
AP
BS
PU
SU
INTERNET
(a)
Unlicensed
Spectrum
(WLAN)
SU
AP
BS
INTERNET
Unlicensed
Spectrum
(WLAN-2)
(b)
Fig. 1: Network diagram showing the base station (BS) of
the primary network, the access point (AP) of the secondary
network, and the primary and secondary users (PUs and SUs)
in the range of the AP (a) before, and (b) after spectrum sharing
under CCRN scheme.
Much of the existing CCRN schemes in the literature assume that the users access the spectrum
using TDMA [5], [7], [8], frequency division multiple access (FDMA) [9], space division multiple access
(SDMA) [10], orthogonal frequency division multiple
access (OFDMA) [11], or using other special orthogonal
schemes [12]. A random access scheme is presented
in [13], where secondary users access the spectrum us-
ing slotted Aloha. In contrast, WLANs have adopted
a contention-based medium access control such as the
IEEE 802.11 Distributed Coordination Function (DCF).
To leverage cooperative transmission and spectrum leasing in WLANs, such as the scenario in Fig. 1-(b), existing
CCRN schemes are no longer applicable.
In our work, we propose an implementation of the
CCRN framework for primary network that supports
any current cellular standard, such as LTE, and an
IEEE 802.11 multi-rate WLAN based secondary network.
When served by the secondary AP, all users (either primary and secondary) employ an IEEE 802.11 DCF based
channel contention mechanism. As shown in Fig. 1,
both the AP and the BS are connected to the Internet
over wireline channel (backhaul), as is common in the
present-day deployments. No backhaul capacity limitation is assumed for the wireline channel. The primary
network owns bandwidth in the form of “channels” of
certain size (e.g., 20 MHz channels in the 3.5 GHz band),
which it is willing to lease to the secondary network; in
exchange, the AP of the secondary network offloads data
traffic for the primary (cellular) users in its range. To enable spectrum leasing, the AP of the secondary network
is equipped with an auxiliary radio (shown in Fig. 1-(b))
that can be tuned to the frequency of the leased channel
(licensed spectrum). All the user equipments (primary
and secondary) are also equipped with radios that can
be tuned to the unlicensed frequency as well as the
leased channel and support dual-mode (WiFi + Cellular,
common in today’s smartphones). The setup in Fig. 1-(b)
resembles the cooperative communication scheme in a
mixed wireline/wireless network [6] where the sourceto-relay (Internet/BS-to-AP) is a wireline channel, and
the relay-to-destination (AP-to-users) is a wireless channel. The problem formulation for the proposed CCRN
scheme is discussed in Section 2.
2
S YSTEM M ODEL
In the proposed CCRN scheme, the primary network
agrees to lease the channel to the AP only if the AP
is offering a bargain that improves the primary network
throughput. The user devices are assumed to support
service differentiation (readily available for 802.11 devices implementing 802.11e). The AP has the freedom
to reassign any user in either of the two WLAN cells
(Fig. 1-(b)), and to assign different service weights to
different users. As a result, depending on the distribution of the users in the two cells and the service
weight of each user, different throughputs for the users
in the primary and secondary networks are achievable.
If we denote with Xp and Xs the aggregate throughputs
for the primary and secondary users respectively, we
can define the bargaining set (Xp , Xs ) ∈ B. Fig. 2-(a)
depicts the bargaining set B of achievable throughputs
as well as the disagreement point (Xpd , Xsd ) representing
the throughputs of the two networks in the absence of
cooperation (i.e., when the cellular users communicate
3
with the BS in the licensed channel, and the AP users
are all in the unlicensed channel). A bargaining point is
a recommended solution for the two players given the
bargaining set, the disagreement point and a bargaining
solution, which is a rule for finding the bargaining point.
A thorough treatment of various bargaining solutions
can be found in [14]; however, we restrict our discussion
to the well-known Nash bargaining solution [15].
(Xpb , Xsb )
N
N
Xs
Xs
(Xpd , Xsd )
B
Xp
(a)
B
ւ
(Xpb , Xsb )
(Xpd , Xsd )
◮
Xp
◮
(b)
Fig. 2: The bargaining set B, bargaining point (Xpb , Xsb ) and
disagreement point (Xpd , Xsd ) for the CCRN problem without
(a), and with (b) fairness constraint (time or throughput)
coupled with the use of the optimized contention window.
Achieving fairness and efficient use of resources
(channel time or achievable throughput) are essential
in WLANs. For this reason, in the proposed CCRN
scheme, we impose either a weighted time or a weighted
throughput fairness constraint in the WLAN. When
served by the WLAN AP, the primary and secondary
users are assigned separate service classes, classp and
classs respectively, with wp and ws representing the
weights for the service classes. Under the weighted time
fairness constraint, users share their channel occupancy
time in proportion to their assigned weights; while
under weighted throughput fairness constraint, the user
share their achievable throughput in proportion to their
assigned weights. Our CCRN algorithm attempts to find
the
1) service weights (wpb , wsb ) and,
2) the distribution of the users in the two WLAN cells,
that will achieve the aggregate network throughputs
(Xpb , Xsb ) at the Nash bargaining solution.
Our CCRN scheme requires an IEEE 802.11 DCF like
contention based channel access mechanism that will
achieve the chosen fairness constraint (weighted time
or weighted throughput) in the WLAN. The proposed
WLAN model for our CCRN scheme is built on the
recent work in [16] that calculates an optimal fixed
contention window for each contending station in an
IEEE 802.11 multi-rate WLAN to jointly achieve aggregate WLAN throughput maximization and time fairness
(equal channel occupancy time for all stations). To fit
our CCRN needs, the WLAN model in [16] is extended
in the following directions in Section 3:
1) to support weighted time or weighted throughput
fairness constraint among stations in the WLAN,
and
2) to support both uplink as well as downlink traffic.
Although the extended WLAN models are able to find
the optimal contention window, they however require
solving an order n polynomial where n is the number of
stations in the WLAN. To reduce the computation complexity, we derive a computationally inexpensive closedform approximation for the optimal contention window
in Section 3. Using the closed-form approximation, we
show that under a chosen fairness constraint (time or
throughput), when all stations adopt optimal contention
window sizes, the aggregate throughputs of the two
service classes, Xp and Xs , evaluated for all feasible
weights, wp and ws , closely follow a straight line of the
form:
cp Xp + cs Xs = 1,
(1)
where cp and cs are constants that are only a function of
the bit rates of the links in the WLAN. The expressions
for cp and cs are different under weighted time and
weighted throughput fairness constraints. In Section 4,
we take advantage of the result in (1) to show that
when all users in the WLAN use optimized contention
window under a fairness constraint (time or throughput), the bargaining set of the CCRN problem can be
approximated by a straight line (as shown in Fig. 2-(b)).
The expression for the approximate linear bargaining set
is only a function of bit rates of the participating users
(primary and secondary users which are being served
by the AP) and hence easily calculated. Also, a closedform expression for the network aggregate throughputs
(Xpb , Xsb ) and their service weights (wpb , wsb ) at the Nash
bargaining solution exists and is a function of the disagreement point and the bit rates of users. Finally, a
method to find an effective user distribution in the
two WLAN cells is proposed that will achieve aggregate network throughputs close to the Nash solution
(Xpb , Xsb ), while maintaining the weights wpb and wsb for
the service classes. Section 3 introduces the necessary
WLAN models, while Section 4 discusses the proposed
CCRN scheme under both the time and throughput
fairness constraints.
3
WLAN O PTIMIZATION
The recent work in [16] proposes a MAC algorithm
for IEEE 802.11 multi-rate WLAN that computes an
optimal contention window for every contending station
in the network to jointly achieve network throughput
maximization and time fairness among stations. The time
fairness constraint requires each competing station to
receive approximately equal channel occupancy time. We
build on the work in [16] and extend their WLAN
model to support service differentiation in terms of
weighted time and weighted throughput fairness where
the stations share the available channel occupancy time
and achievable throughput respectively in proportion
4
to their assigned weights. The proposed WLAN model
adopts a medium access mechanism very closely related
to 802.11 DCF access mechanism, but which, instead of
the binary exponentially backoff mechanism in DCF uses
a fixed contention window for every access attempt. This
approach improves short-term fairness1 and has been
adopted in several works on WLAN optimization [16]–
[20].
Consider a typical 802.11 multi-rate WLAN with one
AP and n competing stations. We assume a saturated
network where each competing station always has packets to transmit. Each station uses the same packet payload size, sd (in our numerical results we use sd = 12000
bits), although, our work can be easily extended to
accommodate heterogeneous payloads. Also, an ideal
channel is assumed where packet losses are only due
to packet collisions. Notations are defined in Table 1.
pi
CWi
Pt i
Pidle
Pc
Tc
Tti
Tslot
sd
n
(2)
The expression for Pti , Pidle , Pc can be calculated as [19]:
Y
Pti = pi (1 − pj ),
(3)
Pidle =
(1 − pi ),
(4)
i=1
Pc = 1 − Pidle −
n
X
Pti .
(5)
i=1
The per station throughput [19] of station i is:
Pti sd
,
P
T
+
Pc Tc + Pidle Tslot
j=1 tj tj
xi = Pn
(8)
where wi and wj are the weights assigned to station i and
j respectively. The relationship between contention windows of station i and j is obtained by combining (2), (3)
and (8):
Consider the event where station i is attempting to
transmit a packet of size sd in a given time slot. The
attempt probability can be calculated as in [19] when
the exponential binary backoff is disabled:
j6=i
n
Y
Time Fairness in WLANs
wi
Pti Tti
=
,
Ptj Ttj
wj
TABLE 1: Notations used throughout the paper.
2
.
CWi + 1
3.1
Under weighted time fairness constraint, the stations
share the channel occupancy time in proportion to their
assigned weights. Therefore, any two stations i and j
must satisfy the condition:
channel access probability of station i
contention window of station i
successful transmission probability of station i
probability that a slot is idle
probability of collision in a slot time
average collision duration
transmission duration for station i
duration of an empty slot
packet payload size in bits
total user stations in the network
pi =
to support weighted time fairness constraint. However
the extended optimal WLAN model is computationally
expensive, and therefore, a computationally inexpensive
approximate WLAN model is developed in Section 3.1.1.
The optimal and the approximate WLAN model are
further extended in Section 3.1.2 to support downlink
traffic as well. In Section 3.1.3, we derive the closed-form
expression for constants cp and cs in (1) and show that
they are only a function of the bit rates of the links in the
WLAN. Using (1), the closed-form expression for the linear bargaining set B on the Xp − Xs plane (see Fig. 2-(b))
in the CCRN problem is easily obtained. In Section 3.2,
we repeat the same analysis as in Section 3.1 but for the
weighted throughput fairness constraint.
(6)
and the aggregate throughput of the WLAN, X, is:
Pn
n
X
i=1 Pti sd
X=
xi = Pn
. (7)
P
T
+
Pc Tc + Pidle Tslot
i=1 ti ti
i=1
In Section 3.1, the WLAN model in [16] is extended
1. With binary exponential backoff the collided stations choose long
backoffs with higher probability, thereby benefiting other stations from
increased channel access.
wi Ptj
Tti
wi pj (1 − pi )
wi (CWi − 1)
=
=
=
.
Ttj
wj Pti
wj pi (1 − pj )
wj (CWj − 1)
(9)
It can be shown that maximizing the network throughput X in (7) for the weighted time fairness constraint
in (8) is equivalent to minimizing the following cost
function:
Tc
1 − pi
C(pi ) =
+
(Tslot − Tc ).
(10)
Pt i
pi
When all stations use the same weight, i.e., w1 = w2 =
. . . = wn = 1, the WLAN model in [16] computes the
optimal contention window for every contending station
in the WLAN so that they share the channel occupancy
time equally and also simultaneously maximize the aggregate WLAN throughput. The optimized contention
window for station i is obtained by solving [16]:
λ2
2λ3
(n − 1)λn
Tslot
+
+···+
=
,
(CWi − 1)2
(CWi − 1)3
(CWi − 1)n
Tc
(11)
where hj =
λk =
2Tti
Ttj
is used to compute
X
hl1 hl2 · · · hlk ,
l1 <l2 <···<lk
1≤l1 ,l2 ,···,lk ≤n
k = 1, 2, · · ·, n. (12)
Uniqueness of CWi is shown in [16]. The work in [16]
can be easily extended to support weighted time fairness
constraint, where the optimal contention window is obtained by the same expression (11) with λk , k ∈ {1, .., n},
5
defined in (12) but with a new definition for hj given by:
2wj Tti
.
hj =
wi Ttj
pi =
(13)
W − ηe + 1
.
τi
(19)
Since −1/e < −η/e < 0 and W (−η/e) > −1 because the
access probability pi > 0 and τi > 0, we have:
3.1.1
Approximate WLAN Model
Computing
the
optimal
contention
window
using (11), (13) is relatively computationally expensive
as it requires finding the roots of an order n polynomial.
To overcome this constraint, we provide a simplified
equivalent solution that calculates the same optimal
contention window as in (11), (13) but at a greatly
reduced computation cost. Since the access probability
of any station pi 1, the following approximation
holds:
1 − pi
≈ 1.
(A1)
1 − pj
W0 − ηe + 1
pi =
,
τi
where W0 (·) is the principal branch of W and is a
single-valued function. The value of W0 (−η/e) is a fixed
constant for a given 802.11 variant since it takes η
and e as its arguments (Table 2). Hence the optimal
access probability pi in (20) is unique and its calculation
only requires performing an addition and a division as
opposed to solving the order n polynomial in (11).
Tslot [µs]
Tc [µs]
η
1+W0 − ηe
Using (A1) in (9),
pj = pi
wj Tti
.
wi Ttj
(14)
The first derivative (w.r.t pi ) of the cost function in (10)
is
Pn
1 − j=1 pj
1
0
C (pi ) = − 2 Qn
Tc − 2 (Tslot − Tc ). (15)
pi
pi j=1 (1 − pj )
When n −→ ∞,
n
Y
(1 − pj ) −→ e
−
Pn
j=1
pj
=e
−pi
wj Tt
i
j=1 wi Tt
j
Pn
(20)
a
9
861.06
0.9895
0.1380
b
20
5.7×103
0.9965
0.0816
g
9
855.06
0.9895
0.1385
n
9
1.6×103
0.9943
0.1035
TABLE 2: Parameters Tslot , Tc , η and 1+W0 − ηe
a/b/g/n.
for 802.11
By denoting
η
ζ = W0 −
+ 1,
e
we have, from (16), (20):
n
X
= e−τi pi ,
j=1
pi = τi pi = ζ.
(21)
(22)
i=1
(16)
Furthermore using (22) in (3), (4), (5), we obtain the
following approximations which we will use later in our
discussion:
(17)
Pidle ≈ e−ζ ,
n
X
Pti ≈ ζe−ζ ,
(23)
Pc ≈ 1 − ζe−ζ − e−ζ .
(25)
where
n
Tti X wj
.
τi =
wi j=1 Ttj
The transmission duration Tti depends on the bit rate of
station i, the parameters of MAC and PHY layers (802.11
a/b/g) and the data packet size sd . Consequently, the
transmission duration for all supported bit rates of the
chosen 802.11 variant can be precomputed and stored
in a lookup table. Then, calculating τi only requires the
knowledge of bit rates of all the links in the network. To
minimize the cost function, we set its derivative (15) to
zero, resulting in:
1 − τi pi = ηe−τi pi ,
(18)
can be calculated for a given
where η = 1 − TTslot
c
variant of 802.11 from the parameters of the MAC
and PHY layers (Table 2). Solving (18) results in the
optimal channel access probability pi that maximizes
the network throughput under time fairness condition,
however, (18) is a transcendental equation involving
exponential whose closed form solution is given in terms
of the Lambert W function (W ) [21]:
(24)
i=1
3.1.2
Support for Downlink
The analysis to this point only considers uplink traffic.
However, in a WLAN with n active stations and an AP,
there are n uplinks and n downlinks. The bit rates on
the uplink and downlink are determined by the rate
adaptation algorithm at the sending end, and can be
asymmetric. In this sub-section, we extend the WLAN
model to also support downlink traffic. Let qi denote
the access probability the AP assigns to station i for its
downlink traffic. We refer to AP as station n + 1. The
access probability of the AP is:
pn+1 =
n
X
i=1
qi .
(26)
6
The approximate channel utilization of a station in class1
and class2 using (8), (25), (23) and (32) is then:
The condition for weighted time fairness becomes:
Qtk Tt0k
Qtl Tt0l
Pt Tt
Pti Tti
= j j =
=
,
wi
wj
wd wk
wd wl
(27)
where Tt0i is the downlink transmission time of station i,
wd is the weight for downlink traffic relative to uplink
traffic, wi is the weight of station i for both its uplink
and downlink traffic, Pti follows expression (3) with i ∈
{1, . . . , n}; j ∈ {1, . . . , n + 1}, and Qti is the successful
transmission probability for AP to transmit a packet to
station i:
n
Y
Qti = qi
(1 − pj ), i = 1, . . . , n.
(28)
j=1
Using (27) and (28), it can be shown that the AP with
channel access probability pn+1 is in a separate service
class with a service weight of:
wn+1 = wd
n
X
wi ,
(29)
and transmission time defined by:
Pn
wi
Ttn+1 = Pni=1 wi .
(30)
i=1
u1 = Pn1 +n2
Ptj Ttj + Pc Tc + Pidle Tslot
r
≈
,
rn1 + n2 + κ(rα1 + α2 )
1
,
u2 ≈
rn1 + n2 + κ(rα1 + α2 )
P
where αj = i∈classj T1t and
j=1
κ=
3.1.3
qi
pn+1
wj
= Pn
j=1
wi
wi
×
Tt0
Ttn+1
= Pn i wj .
0
Tti
j=1 T 0
(31)
tj
Closed-form expression for the bargaining set
Consider a multi-rate WLAN with two service classes,
class1 and class2 , and weights w1 and w2 respectively.
Using the approximate WLAN model, we show that
when all stations in the service classes use optimized
contention window, the aggregate throughputs of the
service classes, (X1 , X2 ), when evaluated for all feasible
weights w1 and w2 and plotted on an X1 -X2 plane,
closely follow a straight line whose slope is independent
of the weights and is only a function of the bit rates of
the links. We take advantage of this result in the CCRN
scheme where separate service classes are assigned to
the primary and secondary networks, and as a result,
the bargaining game has a linear bargaining set.
Assume only uplink traffic in the WLAN. Let the
size and weights of class1 , class2 be n1 , n2 and r, 1
respectively. Under weighted time fairness, the channel
utilization is the same for every station within a class. We
first show that there exists a linear relationship between
the channel utilization of class1 and class2 . The channel
occupancy time is approximated using (17), (22), (23):
wi
Pti Tti ≈ e−ζ pi Tti = ζe−ζ Pn wj .
(32)
j=1 Ttj
(34)
(35)
(1 − ζe
− e−ζ )Tc + e−ζ Tslot
,
ζe−ζ
(36)
is a constant for an 802.11 variant (Table 2). Eliminating
r from (34) and (35):
(n1 + κα1 )u1 + (n2 + κα2 )u2 = 1.
(37)
The aggregate throughput of classi , is Xi = ui αi sd , i ∈
{1, 2}, and by expressing ui in terms of Xi in (37), we
have the linear equation in X1 , X2 that is independent
of the weight ratio r and a function of α1 , α2 ; where αi
depends on the bit rates of the links in classi :
n1 + κα1
n2 + κα2
X1 +
X2 = 1.
α1 sd
α2 sd
i
vi =
, i ∈ class1 (33)
i
−ζ
i=1 Tt0
The access probabilities p1 , . . . , pn+1 can be computed
using (11), (13) or (20), (17). Internally, the AP assumes
that there are n individual virtual stations contending for
a transmission opportunity each with access probability:
Pti Tti
(38)
With both uplinks and downlinks traffic in the WLAN,
the corresponding expression for (37) is:
[(1 + wd )n1 + κα1 ]u1 + [(1 + wd )n2 + κα2 ]u2 = 1, (39)
P
1
where αj = α̂j + wd α̌j , α̂j =
i∈classj Tti ,
P
1
α̌j =
i∈classj Tt0 , j ∈ {p, s}. The corresponding
i
expression in (X1 , X2 ) is
(1 + wd )n1 + κα1
(1 + wd )n2 + κα2
X1 +
X2 = 1. (40)
sd αp
sd αs
3.2
Throughput Fairness in WLANs
Under weighted throughput fairness constraint, the stations share their achievable throughput in proportion to
their assigned weights. Therefore, any two stations i and
j satisfy the condition:
Pt
pi (1 − pj )
wi
xi
= i =
=
,
xj
Pt j
pj (1 − pi )
wj
(41)
where wi and wj are the assigned weights to stations
i and j respectively. Comparing (41) and (8), weighted
time fairness and weighted throughput fairness are
equivalent upon rescaling the weights with the transmission time, i.e.,
Pt i
wi
Pt Tt
wi Tti
=
⇐⇒ i i =
, i, j ∈ {1, . . . , n}.
Pt j
wj
Ptj Ttj
wj Ttj
(42)
Therefore, by replacing wi with wi Tti in (13), the optimal
contention window under weighted throughput fairness
is obtained by the same expression in (11) with λk , k ∈
7
{1, .., n}, defined in (12) but with hj defined by:
hj =
3.2.1
2wj
.
wi
where βj =
and (50):
(43)
Approximate WLAN Model
By replacing wi with wi Tti in (17), the closed form expression for the approximate access probability pi is (20)
with:
n
1 X
wj ,
(44)
τi =
wi j=1
The closed form expression in (44) is identical to the expression for the optimal access probability in [18] whose
WLAN model supports weighted throughput fairness
for idle sense access method [17]. The only difference
is that in [18] the value of ζ in (21) is calculated for
the highest bit rate of the chosen 802.11 variant while ζ
in our model applies for all the bit rates of the 802.11
variant.
3.2.2
The condition for proportional throughput allocation is:
Pt
Qtk
Qtl
Pti
= j =
=
.
wi
wj
wd wk
wd wl
(45)
Using (28) and (45), the AP (station n+1) is in a separate
service class with a service weight wn+1 defined in (29)
and transmission time defined by
Pn
0
i=1 wi Tti
Ttn+1 = P
.
(46)
n
i=1 wi
The access probabilities p1 , · · ·, pn+1 is computed using (11), (43) or (20), (44). Internally, the AP assigns the
following probability to each station for their downlink
traffic:
wi
qi
= Pn
vi =
.
(47)
pn+1
j=1 wj
3.2.3
Closed-form expression for the bargaining set
As in Section 3.1.3, we derive the linear relationship
between the aggregate throughputs of class1 and class2 .
Under weighted throughput fairness constraint, the perstation throughputs are equal within a class. Using (41)
and (24), we have:
Pn
ζe−ζ
j=1 Ptj
(48)
Pti = Pn wj ≈ Pn wj ,
j=1 wi
j=1 wi
With only uplink traffic in the WLAN, the per-station
throughput for class1 and class2 using (6) is approximated by:
rsd
,
(49)
x1 ≈
rβ1 + β2 + κ(rn1 + n2 )
sd
x2 ≈
,
(50)
rβ1 + β2 + κ(rn1 + n2 )
i∈classj
Tti . Eliminating r from (49)
κn1 + β1
κn2 + β2
x1 +
x2 = 1.
sd
sd
(51)
The aggregate throughput of classi , is Xi = ni xi , i ∈
{1, 2}, and by expressing xi in terms of Xi in (51), we
have the linear equation in X1 , X2 that is independent
of r and a function of the bit rates of the links.
With both uplink and downlink traffic in the WLAN,
the counterpart expression for (51) is:
κ(1 + wd )n2 + β2
κ(1 + wd )n1 + β1
x1 +
x2 = 1, (52)
sd
sd
P
P
where βj = β̂j +wd β̌j , β̂j = i∈classj Tti , β̌j = i∈classj Tt0i
and the resulting expression in (X1 ,X2 ) is
κ(1 + wd )n1 + β1
κ(1 + wd )n2 + β2
X1 +
X2 = 1,
(1 + wd )n1 sd
(1 + wd )n2 sd
(53)
where Xi = (1 + wd )ni xi , i ∈ {1, 2}.
4
Support for Downlink
P
CCRN S CHEME
In this section we apply the models we developed in
Sections 3 to the CCRN problem we consider. Under the
CCRN scheme, a cellular operator acts as the primary
network and offloads traffic to a secondary network that
owns an AP. In exchange, the cellular operator leases
an additional (licensed) channel to the AP, effectively
doubling the capacity of the AP. We assume that there
are ns secondary users associated with the AP, and np
primary users that are initially cellular users, but which
are in the range of the AP and will be offloaded to the AP
if a suitable arrangement for both parties is found (Fig. 1(b)). In the rest of the section, we first determine a closedform expression for the bargaining set. We then find
the connected closed-form expression for the bargaining
point (Nash solution). Finally, we give the closed-form
expression for the service weights of the user classes at
the bargaining point and present a method to determine
a user distribution in the two WLAN cells that will
result in aggregate throughput of primary and secondary
network close to the bargaining point.
4.1
CCRN under Time Fairness
The aggregate throughput of the individual networks before cooperation is the disagreement point, d = (Xpd , Xsd ).
Let cell1 and cell2 denote the two WLAN cells (Fig. 1(b)) operating in the leased and the unlicensed spectrum
respectively. A user, primary or secondary, can be instructed by the AP to associate to one of the two cells.
The primary and secondary users in a cell belong to two
different service classes; we name them classp and classs
respectively. Note that under time fairness, the channel
occupancy time of any two users within a service class
are the same and so are their channel utilization2 . We
2. fraction of the time the station occupies the channel for a successful transmission of a packet.
8
place the following constraint on the channel utilization
of the classes in the two cells:
C1: The channel utilization of a primary user (secondary
user) in cell1 is equal to the channel utilization of a
primary user (secondary user) in cell2 .
This is the condition for cell fairness: two user having
same bit rate (we assume equal payload for all users) and
belonging to the same class but placed in different cells
will achieve same throughput3 . If we denote the target
time ratio between classp and classs by r and the channel utilization of primary and secondary users by up and
us respectively, then constraint C1 requires up : us = r : 1
in each cell (cell1 and cell2 ). In Section 3.1.3, (39) gives
the linear relationship between the channel utilization of
two service classes in a WLAN cell. Rewriting (39) for
each cell, cell1 and cell2 , and the two classes, classp and
classs , we have:
[(1 +
[(1 +
wd )n1p
wd )n2p
+
+
καp1 ]up
καp2 ]up
+ [(1 +
+ [(1 +
wd )n1s
wd )n2s
+
+
καs1 ]us
καs2 ]us
= 1, (54)
= 1, (55)
where nij is the number of users of classj in
celli , P
i∈{1, 2}, j∈{p, s}, αji = α̂ji + wd α̌ji where
1
i
α̂j =
k∈celli ∩classj Ttk is the sum of the reciprocal of
uplink transmission
times of all users of classj in celli
P
and α̌ji = k∈celli ∩classj T10 is the sum of the reciprocal
tk
of downlink transmission times of all users of classj
in celli , wd is the predetermined weight for downlink
traffic relative to uplink traffic and κ is a fixed constant
given by (36) for the parameters defined in Table 2. The
transmission duration, Tti or Tt0i , depends on the bit rate
of the link between the AP and station i, the parameters
of MAC and PHY layers (802.11 a/b/g) and the data
payload size sd . Hence expression in (54) and (55) are
only a function of bit rates of the users, sd , and the
WLAN variant employed (802.11a/b/g/n). Adding (54)
and (55):
[(1 + wd )np + καp ]up + [(1 + wd )ns + καs ]us = 2. (56)
P
1
where αj = α̂j + wd α̌j , α̂j =
i∈classj Tti ,
P
1
α̌j =
i∈classj T 0 , j ∈ {p, s}. The aggregate throughput
ti
of the primary and secondary networks are3 :
Xp = up sd αp ,
(57)
Xs = us sd αs .
(58)
Combining (57), (58) and (56):
(1 + wd )np + καp
(1 + wd )ns + καs
Xp +
Xs = 2. (59)
sd αp
sd αs
By denoting
ap =
(1 + wd )np + καp
,
sd αp
(60)
3. throughput of user i is ui × Tsd where ui and Tti are the channel
ti
utilization and transmission time of user i and sd is payload in bytes.
as =
(1 + wd )ns + καs
,
sd αs
(61)
the Nash bargaining problem is:
maximize (Xp − Xpd )(Xs − Xsd )
subject to
ap Xp + as Xs = 2,
Xp ≥ Xpd ,
(62)
Xs ≥ Xsd .
Since the bargaining set B defined in (59) is a straight
line, the Nash bargaining solution will be the mid-point
of the bargaining range, Bd = {(Xp , Xs ) ∈ B | Xp ≥
d
d
X
s }, which is the line segment joining points
p , Xs ≥ X
d
2−ap X
2−as Xsd
, Xsd . The bargaining point
Xpd , as p and
ap
(Xpb , Xsb ) is then:
2 − as Xsd
Xpd +
,
ap
!
2 − ap Xpd
1
d
b
Xs +
.
Xs =
2
as
Xpb =
1
2
u
(63)
(64)
X α
From (57) and (58), r = ups = Xps αps . Hence the target
ratio between the classes at the bargaining point is:
2−a X d
Xpd + asp s αs
.
rb = (65)
2−ap X d
Xsd + as p αp
The ratio rb is the solution of the bargaining problem
and can be computed using only the disagreement point
and the bit rates of all users in the WLAN. The next
step is to find a distribution of primary and secondary
users in each cell that will result in an operating point of
the system close to the Nash solution. At the bargaining
point, using (54) and (55):
1
,
ubs
1
[(1 + wd )n2p + καp2 ]rb + [(1 + wd )n2s + καs2 ] = b ,
us
[(1 + wd )n1p + καp1 ]rb + [(1 + wd )n1s + καs1 ] =
(66)
(67)
where ubs is the channel utilization of a secondary user
at the bargaining point. Hence, finding the user distribution is equivalent to solving the following partition
problem: partition the np + ns users into two subsets
corresponding to each cell such that the sum of the
weights in first subset equals the sum of weights in
the other
subset, where the
weight for a primary user i
wd
1
is rb 1 + wd + κ Tt + T 0
and for a secondary user
ti i
wd
1
i is 1 + wd + κ Tt + T 0
. The partition problem is
ti
i
NP complete, but there are efficient pseudo-polynomial
algorithms for solving it [22]. We implemented the dynamic programming based algorithm in C and found
the execution time to be less than 0.25 seconds for 40
users with a precision of 2 decimal digits. Algorithm 1
summarizes the steps for finding the distribution of users
in each cell and their channel access probabilities (line
9
4) that would result in the operating point of the system
close to the Nash solution.
Algorithm 1 CCRN Approach
Inputs: hRp , Rs i are the uplink and downlink bit rates of the
primary and secondary users respectively; w is the preassigned
weight of the downlink traffic relative to the uplink traffic;
(Xpd , Xsd ) is the disagreement point.
1: calculate rb using (65) for the inputs {Rp , Rs , Xpd , Xsd };
2: using {Rp , Rs , rb , w} in the pseudo-polynomial algorithm,
find the distribution, hC1b , C2b i, of the primary and secondary users in cell1 and cell2 , at the bargaining point.
3: find the corresponding optimal access probabilities,
hP1b , P2b i, for the users in cell1 and cell2 using the WLAN
model in Section 3.
4: return hC1b , P1b i, hC2b , P2b i;
. operating point.
4.2
CCRN under Throughput Fairness
For throughput fairness, we follow a similar approach
as for the time fairness covered in Section 4.1. The
corresponding throughput fairness constraints within a
class is:
C2: The throughput of a primary user (secondary user)
in cell1 is equal to the throughput of a primary user
(secondary user) in cell2 .
With this constraint, two users belonging to the same
class, but placed in different cells, will achieve equal
throughputs. As in the previous section, using C2, we
can show that the relative weights between the classes
in each cell are equal, and the corresponding linear
relationship between the aggregate throughput of the
primary and secondary networks, Xp and Xs , is:
βp + κ(1 + wd )np
βs + κ(1 + wd )ns
Xp +
Xs = 2, (68)
(1 + wd )np sd
(1 + wd )np sd
P
where βj = β̂j + wd β̌j , β̂j =
i∈classj Tti ,
P
0
.
The
method
to
compute
the
β̌j =
T
i∈classj ti
s
b
bargaining point (Xp , Xp ), throughput ratio between
classes rb , and the corresponding user distribution while
using C2 and (52) instead of (54) and (55) is similar to
the method presented in Section 4.1.
4.3
the aggregate throughput it provides to the cellular
users in WLAN coverage. The AP and BS will agree to
cooperate only when there is an improvement in their
aggregate throughput with respect to their disagreement
point. Algorithm 1 is then invoked and the AP broadcasts4 the user assignment information along with the
access probabilities of the users at the Nash solution.
All users move to their assigned cell and operate at
their assigned contention window size. The mechanism
is repeated periodically thereby allowing the protocol to
dynamically maintain the operating point of the system
close to the Nash solution under varying user activities
and channel conditions. All the the message exchanges
during the bargaining process between the AP and the
BS occurs over the wireline channel that connects them
to the Internet (Fig. 1).
Protocol Design
In this section we show how to integrate the proposed
CCRN scheme with a WLAN similar to current 802.11
systems. The AP first collects the bit rates of all the links
(for both primary and secondary users) in its WLAN4 .
The AP then calculates the aggregate throughput for
the primary and secondary network at the bargaining
point using (63) and (64). It then queries the BS for
4. The bit rate of a user on its uplink and downlink can be obtained
from the SINR or the rate adaptation algorithm at the respective
sender end. This information is then communicated to the AP by leveraging the provisions provided in IEEE 802.11 for Wireless Network
Management such as the 802.11v amendment to 802.11a/b/g/n. The
amendment also allows configuration of client devices and can be used
to configure the frequency channel and the contention window size of
the client.
5
P ERFORMANCE E VALUATION
In this section we evaluate the performance of our
proposed WLAN model in Section 3 and the CCRN
scheme in Section 4.
5.1
WLAN Model Validation
For the simulation experiments, we developed a discreteevent simulator that implements the standard 802.11
DCF (no RTS/CTS) for each independently transmitting
station. The simulator uses the MAC and PHY parameters of IEEE 802.11b standard for a packet size of 1500
bytes and each experiment is run for a simulation time
of 200 seconds. The support for the other channel access
mechanisms under consideration in the section are also
built in this simulator.
In Section 5.1.1, we evaluate the performance of the
proposed approximate WLAN model for time fairness
by considering the first simulation scenario from Section V in [16]. In Sections 5.1.2 and 5.1.3, we compare
the performance of the approximate WLAN model and
the optimal WLAN model under both weighted time
and weighted throughput fairness constraints. In Section 5.1.4, the correctness of the closed-form linear expression in X1 and X2 ( (40) and (53) derived in Sections 3.1.3 and 3.2.3 respectively) are validated using the
simulator.
5.1.1 Time Fairness
In this section we consider a 802.11b WLAN with n
stations where one slow station at 1 Mbps competes with
n − 1 fast stations all at 11 Mbps and with time fairness
constraint (all n stations receive equal channel occupancy
time) imposed on the WLAN. The performance of our
approximate WLAN model is compared with:
(i) the optimal WLAN model in [16];
(ii) The default 802.11 DCF backoff algorithm;
(iii) the proportional fair throughput allocation algorithm proposed by Banchs et al in [20];
(iv) the idle sense algorithm in [17].
10
6.5
1
5.5
0.9
Approximate
Optimal
DCF
Idle Sense
Banchs
2.5
1.5
2345
10
Total Stations
Approximate
Optimal
DCF
Idle Sense
Banchs
0.7
0.6
0.5
5.1.3
0.4
2345
20
10
Total Stations
(a)
20
(b)
Fig. 3: Performance comparison of the five MAC algorithms
under time fairness: (a) aggregate throughput of the WLAN,
(b) short-fairness of the channel occupancy time.
The experiment is same as scenario I in Section V
of [16]. Fig. 3 confirms that the approximate WLAN
model can achieve the same level of performance observed using the optimal WLAN model in [16] but at a
greatly reduced computation cost (note that Fig. 3 and
Figures 1a and 2a in [16] are similar). Our approximate
WLAN model is similar in nature and complexity to the
work in idle sense [17] but applies to multi-rate WLANs.
The access method proposed in idle sense [17] achieves
throughput enhancement in multi-rate 802.11 WLANs,
but compromises fairness as shown in Fig. 3 because the
optimization is performed for an equivalent single-rate
network.
Weighted Time Fairness
0.97
3
2.5
2
1.5
1
Class 1 − Approximate
Class 2 − Approximate
Class 1 − Optimal
Class 2 − Optimal
0.5
0
4
12
20
28
36
Total Stations
(a)
44
Jain Fairness Index
Aggregate Throughput (Mbps)
5.1.2
Approximate
Optimal
0.95
0.93
4
12
20
28
36
Total Stations
Weighted Throughput Fairness
44
(b)
Fig. 4: (a) Aggregate throughput per class vs. number of
stations and, (b) short-term fairness of the channel occupancy
time under weighted time fairness.
In this section we consider two service classes in a
802.11b WLAN of size n with weights w1 = 1 and
5. We fix the sliding window size to 20 × n so that the window size
varies with the WLAN size, n.
1.1
1
Class 1 − Approximate
Class 2 − Approximate
Class 1 − Optimal
Class 2 − Optimal
Class 1 − 802.11e
Class 2 − 802.11e
0.9
0.7
0.5
0.3
0.1
4
12
20
28
36
Total Stations
(a)
44
Jain Fairness Index
3.5
0.8
w2 = 0.5. Only one class is active in a station: half
of the stations send class1 traffic, while the other half
sends class2 traffic; and within each class, half of the
stations use 1 Mbps bit rate to send packets while
other half use 11 Mbps. Figures 4a and 4b show the
aggregate WLAN throughput of the two service classes
and the short-term fairness of channel occupancy time
measured using the modified sliding window method
of Jain fairness index in [26]. The results for the optimal
WLAN model (Section 3.1) for n > 20 is not shown due
to the intractability of solving the polynomial in (11) for
n > 20. Fig. 4 shows that the approximate WLAN model
agrees with the optimal WLAN model and that both the
models achieve the desired time ratio 1 : 0.5.
Aggregate Throughput (Mbps)
4.5
Jain Fairness Index
Aggregate Throughput (Mbps)
The following parameters are compared in Fig. 3:
(i) the aggregate WLAN throughput;
(ii) the average Jain fairness index [23] (or the shortterm fairness) of the channel occupancy time computed using the sliding window method5 in [24],
[25].
Approximate
Optimal
802.11e
0.95
4
12
20
28
36
Total Stations
44
(b)
Fig. 5: (a) Aggregate throughput per class vs. number of
stations and, (b) short-term fairness of the channel access
opportunities under weighted throughput fairness.
Consider the same WLAN in Section 5.1.2 with
weights w1 = 1 and w2 = 0.5 for the service classes
(this experiment is similar to the scenario in Figure 3
of [18]). In this experiment, the 802.11e EDCA model
in idle sense [18] is compared with both our WLAN
models (optimal and approximate) in Section 3.2. With
802.11e, a throughput ratio of 1:0.5 between the classes
can be obtained by setting CW1 ∈ [16, 48] for class1
and CW2 ∈ [31, 93] for class2 (from [18]) in the simulator. In Fig. 5, the aggregate WLAN throughput for
each service class and short-term fairness of channel
access opportunities is computed. The results show that
the approximate WLAN model agrees with the optimal
WLAN model and that the models achieve the desired
throughput ratio 1:0.5. The results also show that the
aggregate throughput of the classes does not depend on
the number of stations when using our WLAN models,
while with 802.11e the aggregate throughput decreases
with an increase in the number of stations.
5.1.4 Linear Bargaining Set
In this section, we use the simulator to compute the aggregate throughputs (X1 , X2 ) for the classes at different
weights (w1 , w2 ), and show that the aggregate throughputs on the X1 -X2 plane are well approximated by
the linear expression (1). Consider a multi-rate 802.11b
11
Approximate
Line
Analytical
Simulator
1
1
0
1
2
X1 (Mbps)
(a)
3
0
1
Points in the Bargaining Set
Brute Force − Analytical
Brute Force − Simulator
CCRN − Analytical
CCRN − Simulator
Disagreement Point
2
X1 (Mbps)
(b)
Fig. 6: Comparison of the optimal aggregate throughput of
class1 and class2 with the approximated linear equation under
(a) time fairness, and (b) throughput fairness constraints.
5.2
5.2.1 CCRN Solution Validation
Consider a CCRN network with 8 primary and 8 secondary users in a IEEE 802.11n WLAN. For simplicity,
symmetric bit rates are assumed on the uplink and
downlink of each user. In each service class (classp and
classs ), the users use a unique bit rate from the set {13,
26, 39, 52, 78, 104, 117, 130} Mbps. For the disagreement
point, (Xpd , Xsd ), the initial aggregate throughput of the
primary network is set to 15 Mbps. The initial aggregate
throughput of the secondary network is calculated using
both the optimal and the approximate WLAN model in
Section 3.1.1. For the operating point obtained in line
4 of Algorithm 1, the aggregate throughput of the primary and secondary networks are calculated analytically
using (6) and shown in Fig. 7. Also, to replicate the
real-time behavior of the CCRN, the operating point
in line 4 of Algorithm 1 is used as the input to the
discrete event simulator. The aggregate throughput of
the primary and secondary networks at the end of 200
seconds of simulation time is shown in Fig. 7.
CCRN Scheme
In Section 5.2.1, we verify the optimality of the operating point obtained using our approach in Algorithm 1
with the operating point obtained using the exhaustive
search (brute-force) method. Through the experiment we
show that the optimality of the Nash solution obtained
using our approach in Algorithm 1 is largely unaffected
despite the approximations used in the approximate
WLAN model, closed-form expression for the linear
bargaining set, and the pseudo-polynomial algorithm
for finding the user distribution. Section 5.2.2 quantifies
the resulting improvement in the throughputs of the
primary and secondary networks under the proposed
CCRN scheme.
For the experiments, we assume primary and secondary users are equipped with 2 antennas supporting
two spatial streams. The AP of the secondary network
is equipped with 4 antennas and uses 2 of them per
cell (or WLAN). The transmission power for a user is
17 dBm and for the AP is 20 dBm. The users and the
AP use the following 802.11n PHY settings in 5 GHz
band: bandwidth 20 MHz, Long Guard Interval (800 ns),
MAC Service Data Unit Aggregation (A-MSDU) scheme,
aggregation size of 5 frames per A-MSDU with 1500
Points in the Bargaining Set
Brute Force − Analytical
Brute Force − Simulator
CCRN − Analytical
CCRN − Simulator
Disagreement Point
details at
baragining point
90
details at
baragining point
90
73.7
Xs (Mbps)
X2 (Mbps)
2
2
X2 (Mbps)
Approximate
Line
Analytical
Simulator
3
bytes payload data per frame, and supported physical
bit rates of {13, 26, 39, 52, 78, 104, 117, 130} Mbps [27].
The discrete event simulator is modified to support the
802.11n PHY settings.
80
72.9
73.1
33.1
33.9
70
Xs (Mbps)
WLAN with 8 stations each in class1 and class2 . In
each service class, exactly two users use the same bit
rate from the supported set of {1, 2, 5.5, 11} Mbps.
For simplicity, symmetric bit rates are assumed on the
uplink and downlink of a user and the downlink to
uplink traffic ratio is set to wd = 3. Consider 30 different
logarithmically spaced values between 0.1 and 10 for the
1
weight ratio r = w
w2 . For each r, the contention window
for the AP and the stations are computed using the
approximate WLAN model. The aggregate throughput
of the classes calculated using (7) and from the simulator
are plotted in Fig. 6. With the bit rates of all the links
known, the constant coefficients in (40) and (53) are
calculated and the corresponding straight line expression
in X1 and X2 is shown in Fig. 6. As shown in Fig. 6,
the realistic aggregate throughput of the classes obtained
from the simulator is well approximated by the straight
line in (40) and (53) (within < 5% margin of error).
80
72.7
70
32.9
33.5
60
60
20
30
40
50
20
30
40
Xp (Mbps)
Xp (Mbps)
(a)
(b)
50
Fig. 7: Graphical representation of the bargaining problem
along with the Nash solution when (a) the optimal WLAN
model and, (b) the approximate WLAN model in Section 3
are used to calculate the channel access probabilities for the
users (line 3 of Algorithm 1 and 2).
The exhaustive search approach necessitates iterating
through all possible distributions of primary and secondary users in the two cells. For each user distribution,
the aggregate throughput of the primary and secondary
networks, (Xp , Xs ), are calculated for the target ratio r
that satisfies the cell fairness constraint C1. The aggregate
throughput of the networks that maximizes the Nash
product, (Xp − Xpd )(Xs − Xsd ), ∀ Xp ≥ Xpd , Xs ≥ Xsd , is
the bargaining point. The target ratio r that maintains
the constraint C1 between the cells can be obtained
using (54) and (55):
r=
(1 + wd )(n1s − n2s ) + κ(αs1 − αs2 )
.
(1 + wd )(n2p − n1p ) + κ(αp2 − αp1 )
(69)
12
Inputs: Same inputs as for Algorithm 1.
1: for each combination of users in cell1 and ce112 , hC1 , C2 i,
do
2:
3:
4:
5:
6:
7:
8:
9:
10:
calculate r using (69) for the inputs {C1 , C2 , Rp , Rs };
find the corresponding optimal access probabilities for
the users in each cell, hP1b , P2b i, using either the optimal
or the approximate WLAN model in Section 3.
find the optimal aggregate throughput of primary and
secondary users, (Xp , Xs ), using (6).
if Nash product is maximized then
hC1b , P1b i=hC1 , P1 i, hC2b , P2b i=hC2 , P2 i;
Xpb =Xp , Xsb =Xs ;
end if
end for
return hC1b , P1b i, hC2b , P2b i;
. operating point.
5.2.2 Performance Evaluation of CCRN Scheme
To gain insight in the expected performance of the
proposed CCRN solution, we evaluate the resulting improvement in throughputs of the primary and secondary
networks while varying the number of primary users,
as well as the initial throughput of the primary users
(before cooperation). The applicable bit rate for each
uplink-downlink pair is derived based on the RSSI,
which in turn is calculated according to the log distance
path loss model with shadow fading (Model D) defined
by the Task Group n (TGn) [28]. Under this model, a user
must be within 80 meters (on the average) from the AP to
receive the minimum bit rate of 13 Mbps on their uplink
and downlink. Consider a circular coverage region with
the AP at the center and radius of the coverage set R set
to 80 meters. Assume all the users in the coverage area
receive at least the minimum bit rate on their uplink and
downlink. Two types of user placements are considered
in the coverage area:
(i) uniform: users are randomly positioned uniformly
within the circular coverage area (probability densi1
2r
ties are: r ∼ R
2 , 0 ≤ r ≤ R, and θ ∼ 2π , θ ∈ (0, 2π]).
6. Note that there are significant gains in execution time when the
approximate WLAN model is used in Algorithm 1 over the optimal
WLAN model when the number of users is large (n > 20).
Primary Network
Secondary Network
200
160
120
80
40
0
2
5
8
11 14 17 20
np
(a)
Percentage throughput improvement
Algorithm 2 Brute Force Approach
(ii) clustered: similar to uniform but half of the user
population is within the inner circle of radius R2
(probability densities are: r ∼ R1 , r ∈ [0, R], and
1
, θ ∈ (0, 2π]).
θ ∼ 2π
Percentage throughput improvement
The steps in the brute-force approach are detailed in Algorithm 2 and the algorithm is run for the primary and
secondary network under study in Fig. 7. As shown
in Fig. 7, the aggregate throughput of the networks,
(Xp ,Xs ), calculated for all user distributions in the two
cells forms the bargaining set and has a straight line
appearance ((59) is the corresponding straight line equation). The operating point in line 10 of Algorithm 2 is
used in the simulator and the aggregate throughput of
the primary and secondary networks at the end of 200
seconds of simulation time is shown in Fig. 7 along with
the analytically obtained bargaining solution in line 7
of Algorithm 2. Fig. 7 shows that the loss in optimality
by using our approach (Algorithm 1) over the brute-force
approach (Algorithm 2) is negligible6 .
Primary Network
Secondary Network
200
160
120
80
40
0
2
5
8
11 14 17 20
np
(b)
Fig. 8: Percentage improvement in the aggregate throughput
of the primary and secondary users while varying the number
of primary users and holding the number of secondary users
constant (ns =10) for (a) uniform, and (b) clustered placements.
Using the simulator, we show the average and 90%
confidence intervals in the throughput improvement of
the networks after performing 1000 simulation runs for
the uniform and clustered user placement types. We
assume an aggregate throughput of 15 Mbps for the primary users when served by its BS (before cooperation).
This is consistent with the average throughput of LTE
macrocells (instead of the peak rates). The downlink to
uplink traffic ratio is set to wd = 3.
In this section we present the results for time fairness.
The results for throughput fairness are very similar
only with a slightly lower value for the improvement
as throughput fairness trades some cell capacity for
increased fairness. Due to space limitations and the
similarity of the results we do not present the throughput
fairness results. The improvement in throughput for both
the primary and secondary users when the number of
cellular (primary) users np changes from 2 to 20 while
the number of secondary users ns is held constant at 10
users is shown in Fig. 8. The percentage of improvement is considerably higher for the cellular users, as
they start with a relatively low aggregate throughput of
15 Mbps. On average, the cellular users approximately
double their throughput (on the average by 100%) under the uniform placement type while their throughput
improves by 150% on the average under the clustered
placement type. The comparatively higher throughput
improvement in the clustered placement is due to the
presence of more primary users in close proximity to the
AP (and therefore having superior bit rates). While not
as spectacular as for the primary users, the secondary
(WLAN) users also increase their throughput by approximately 40% under both placement types. The 90%
confidence intervals show that the primary users experience a higher variability in the improvement because
13
Primary Network
Secondary Network
120
80
40
0
15
20
25
Xdp
30
35
40
(Mbps)
(a)
Percentage throughput improvement
Percentage throughput improvement
their bit rate after the agreement depends considerably
on the quality of their link to the AP. In contrast, for
the secondary users, if they have a good link to the
AP before agreement, they will maintain that good link
after the agreement (the converse is also true). Finally,
the throughput improvement is relatively insensitive to
the number of primary users. In fact the improvement
is insensitive to the number of primary and secondary
users. The explanation for this fact is that the bargaining
point is chosen as a function of the aggregate throughput
for both the primary and the secondary users. Those aggregate throughputs are, however, almost independent
of the number of users. Fig. 9 shows the percentage
Primary Network
Secondary Network
160
120
80
40
0
15
20
25
30
Xdp (Mbps)
35
40
(b)
Fig. 9: Percentage improvement in the throughputs of the primary and secondary users while varying the initial aggregate
throughput of the primary users for (a) uniform, and (b)
clustered placements.
of improvement as a function of the initial aggregate
throughput of the primary users. For this graph ten
primary users and ten secondary users were considered,
although, as mentioned before, the results are insensitive
to the number of users. From Fig. 9 it is clear that as
the initial aggregate throughput of the cellular users
increases, the improvement resulting from cooperation
becomes smaller and smaller, until, at about 40 Mbps
under uniform placement type, the networks decide to
operate at the disagreement point, i.e., they choose not
to cooperate. The lack of an agreement (due to reduced
throughput after cooperation) can only happen if the primary users are better served by the cellular base station
than by the access point. While this may happen for
a particular combination of technologies (e.g., a legacy
802.11b AP for WLAN and LTE advanced for the cellular
network with a relatively close base station), in general
WLAN data rates are often higher than cellular data
rates due to the reduced cell size and higher signal to
noise ratio for WLANs.
6
RELATED WORK
Resource allocation and spectrum trading are treated as
two separate problems in the spectrum sharing model
of cognitive radios [29]. Optimal resource allocation of
frequency channels, channel access time, transmission
power, throughput etc. between primary and secondary
users hold the key to efficient spectrum sharing. Spectrum trading is the economic aspect of spectrum sharing,
where secondary users pay for the leased channel. Existing literature used a combination of game theory, market
theory and price theory to model the problems in optimal resource allocation and economic interactions [29].
CCRNs combine the spectrum sharing scheme with the
physical layer cooperative communication technique in
which one or more relay terminals are recruited to assist
in the communication when the direct link suffers from
severe signal fading [6].
The CCRN scheme in [5] uses Stakelberg games for optimal resource sharing between the primary link (Stakelberg leader) and the secondary ad hoc network (Stakelberg follower). The primary link optimizes its strategy
(lease time and amount of cooperation in terms of distributed space-time coding) to maximize its transmission
rate, being aware that its decision will influence the
strategy adopted by the secondary network, namely the
transmission power expended for relaying the primary
traffic. The work in [7] extends [5] to include a revenue/payment mechanism and a Stakelberg game is
adopted to solve the joint problem of resource allocation and spectrum trading. The restriction of only one
primary link in the system model of [5], [7] is addressed
in [8], which extends the work in [7] to two co-located
infrastructure based primary and secondary networks.
The work in [5], [7], [8] employs a three phase TDMA
based scheme for cooperation, where the primary traffic
is broadcasted in phase 1, one or more secondary users
are recruited to relay the traffic to the destination in
phase 2 and the secondary users access the leased channel using TDMA in phase 3. The work in [13] proposes a
CCRN scheme based on Stakelberg games for secondary
users that employ slotted Aloha access method in phase
3. The work in [10] extends [5] to equip secondary users
with multiple input multiple output (MIMO) antennas.
Since MIMO allows concurrent transmission of multiple independent data streams, the need for phase 3 is
eliminated where now the secondary users cooperatively
relay the primary traffic in phases 1 and 2 while obtaining spectrum access opportunities for their own traffic.
While [10] leverages the degrees of freedom (DoFs)
offered in the spatial domain, [12] exploits the DoFs
provided by the orthogonal dimensions in quadrature
phase shift keying (QPSK). The secondary users employ
in-phase binary phase shift keying (I-BPSK) to relay
the primary traffic and use the quadrature BPSK (QBPSK) to transmit their own traffic. A two-phase FDMA
scheme is proposed in [9], where the primary users grant
secondary users exclusive access to a portion of their
spectrum in exchange for cooperation. To the best of our
knowledge, the current work is the first to propose a
CCRN scheme for WLANs employing contention based
access schemes such as IEEE 802.11 DCF.
14
7
C ONCLUSION
In this paper, we have investigated and proposed an
implementation of the CCRN framework for IEEE 802.11
WLANs. In the proposed CCRN scheme, the mobile
operator leases a channel from the licensed spectrum
band to a privately owned WiFi AP, and in return, the
mobile operator leverages the AP as cooperative relays
to offload its Internet traffic. The cooperation between
the primary (cellular) and secondary (WLAN) networks
is analyzed using a two-player bargaining game where
the utility function for the players are their respective
aggregate network throughputs. We show that under
fairness and optimal throughput constraints, the bargaining set for the bargaining game is a straight line
whose slope only depends on the bit rates of the users.
Calculating the Nash bargaining solution for a linear bargaining set is trivial, and the proposed CCRN algorithm
determines the corresponding distribution of the users
in the two WLAN and the service weights for the users
at the Nash solution. The proposed computationally
inexpensive WLAN model then calculates the contention
window for each user that results in the operating point
of the system close to the Nash solution. The simulation
results verify the optimality of the operating point as
well as quantify the benefits of employing the CCRN
scheme in WLANs.
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Mani Bharathi Pandian is currently a Ph.D.
candidate in the Department of Electrical and
Computer Engineering at North Carolina State
University under the supervision of Dr. Mihail
Sichitiu and Dr. Huaiyu Dai. He received an M.S.
degree from the same department in 2011. His
research focuses on cooperative cognitive radio
networking in wireless local area networks.
Mihail L. Sichitiu was born in Bucharest, Romania. He received a B.E. and an M.S. in Electrical
Engineering from the Polytechnic University of
Bucharest in 1995 and 1996 respectively. In
May 2001, he received a Ph.D. degree in Electrical Engineering from the University of Notre
Dame. He is currently employed as an associate
professor in the Department of Electrical and
Computer Engineering at North Carolina State
University. His primary research interest is in
Wireless Networking with emphasis on ad hoc
networking and wireless local area networks.
Huaiyu Dai (M’03, SM’09) received the B.E.
and M.S. degrees in electrical engineering from
Tsinghua University, Beijing, China, in 1996 and
1998, respectively, and the Ph.D. degree in
electrical engineering from Princeton University,
Princeton, NJ in 2002. Currently he is an Associate Professor of Electrical and Computer
Engineering at NC State University, Raleigh.
His research interests are in the general areas
of communication systems and networks, advanced signal processing for digital communications, and communication theory and information theory.