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Performance Modeling of Secondary Users in CRNs with Heterogeneous Channels

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Abstract

The goal of this paper is to model heterogeneous channel Access in Cognitive Radio Networks (CRNs). In CRNs, when licensed users, known as Primary Users (PUs), are idle, unlicensed users, known as Secondary Users (SUs) can use their assigned channels. In the model we consider in this paper, there are two types of licensed channels, where one type has a larger bandwidth, and hence a higher service rate for SUs. Therefore, SUs prefer to use such channels, if available, over channels in the second type which have a lower service rate. SUs may also switch from the second to the first type of channels when they become available, even if their current channels are still available. Moreover in our performance model, we model the SUs' sensing process, and its dependence on the system load, and number of sensing users. We use a Continuous Time Markov Chain (CTMC) modeling approach, and derive SUs' performance metrics, which include SUs admission and blocking probabilities, and their average waiting time in the system. We also develop a baseline model and compare its performance to our proposed model.
Performance Modeling of Secondary Users in
CRNs with Heterogeneous Channels
Sharhabeel H. Alnabelsi Ahmed E. Kamal
Dept. of Electrical and Computer Eng., Iowa State University, Ames, Iowa 50011, USA
E-mail:{alnabsh,kamal}@iastate.edu
Abstract—The goal of this paper is to model heterogeneous
channel Access in Cognitive Radio Networks (CRNs). In CRNs,
when licensed users, known as Primary Users (PUs), are idle,
unlicensed users, known as Secondary Users (SUs) can use their
assigned channels. In the model we consider in this paper,
there are two types of licensed channels, where one type has
a larger bandwidth, and hence a higher service rate for SUs.
Therefore, SUs prefer to use such channels, if available, over
channels in the second type which have a lower service rate. SUs
may also switch from the second to the first type of channels
when they become available, even if their current channels are
still available. Moreover in our performance model, we model
the SUs’ sensing process, and its dependence on the system
load, and number of sensing users. We use a Continuous Time
Markov Chain (CT M C ) modeling approach, and derive SUs’
performance metrics, which include SUs admission and blocking
probabilities, and their average waiting time in the system. We
also develop a baseline model in which SUs do not switch channels
between the two types, unless they are interrupted by PUs, and
compare its performance to our proposed model. Our numerical
analysis shows that our proposed model outperforms the baseline
model. We also, found that if sensing time is very small (1ms),
its effect on SUs performance is insignificant.
I. INT ROD UC TI ON
A. Background
Due to the temporal and spatial underutilization of licensed
spectrum bands, as well as the crowdedness of unlicensed
bands, a new spectrum access paradigm has been recently
proposed namely, Cognitive Radio (CR) [1]. CR enables users
to adjust their transceivers’ frequencies depending on the
availability of licensed frequency bands which are otherwise
unused by their licensees [2]. Thus, unlicensed wireless users,
called Secondary Users (SUs) can dynamically and oppor-
tunistically access unused licensed bands in order to improve
their throughput and service reliability. In this case, whenever
the licensed or the Primary Users (PUs) become active, SUs
must vacate their bands.
CRNs have many challenges such as spectrum sensing,
management, mobility, allocation and sharing [3], [4]. Usually,
SUs have QoS performance requirements, e.g., throughput and
maximum transmission delay. Evaluating these metrics is not
a trivial task, due to the CRNs dynamic nature, e.g., due to
PUs fluctuating activities which may interrupt SUs, and hence
may need to access the channel multiple times just to finish
one communication session. To evaluate these performance
metrics, a few models have been proposed in literature. In
[5], [6], a Markovian model is proposed to analyze spectrum
access with and without buffering for new and interrupted
SUs requests, which is used to evaluate SUs mean waiting
time, and the probabilities of blocking, interruption, forced
termination, and non-completion. Results show that buffer-
ing SUs requests reduces SUs’ blocking and non-completion
probabilities, with a very small increase of forced termination
probability. However, in all other models network channels
are assumed symmetric in terms of channels bandwidth. In
addition, SUs’ sensing overhead is not considered in those
models.
A quasi-birth and death Markov chain with continuous time
and state space model is proposed in [7], to improve SUs
performance by distributing their flows to multiple wireless
networks. Due to the high complexity for this model, an
approximation solution was proposed. They proposed two
admission control schemes for SU flows priority, and no
priority schemes. In both admission control schemes, if an
SU is admitted to a network, it will not leave it until finishing
its transmission as long as it is not interrupted by a PU arrival.
A Markov model for spectrum sharing between PUs and
SUs is proposed in [8], when SUs are interrupted, they are
suspended and wait to access another channel in a call level
queue. During SUs’ suspension, packets generated by SUs
are either delayed or discarded, therefore the queue becomes
two sub-queues, delay and discard queues. Three metrics are
evaluated: packet loss ratio, packet delay, and throughput.
Results show by increasing SU suspension queue length, both
packet loss ratio and throughput increase and packet delay
decreases. A queuing network model for spectrum sharing
between PUs and SUs is introduced in [9], where a closed
form solution for equilibrium system state was derived as a
generating function. The model studies PUs QoS degradation
due to unreliable SUs spectrum sensing where an SU keeps
on using the channel, although a PU has arrived to the same
channel. Besides, an SU moves from its channel to another
only when it is interrupted by a PU arrival. Channels are
assumed symmetric in terms of service rate for PUs and SUs
in [8], [9].
B. Motivation
This work is motivated by:
First, the fact that heterogeneous channels may be present
in the same locality, e.g., TV channels, cellular telephone
channels, wireless microphone channels, etc, which might
be used by SUs, if available. The bandwidth availability
in these channels is different. For instance, the licensed
spectrum of Wireless Microphones has 200 KHz band-
width, and that of Digital TV (ATSC) has 6 MHz band-
width. Therefore, this work is motivated by the possibility
of SUs switching channels opportunistically in order to
improve their performance.
Second, the fact that some of the PUs of those channels
characterized by long idle times, e.g., Digital TV chan-
nels, which may lead to a sustainable SU throughput,
which also reduces channels switching overhead.
Third, this work is also motivated by the need to consider
sensing time and its effect on channel utilization and
transmission delay. There are different technologies for
spectrum sensing such as energy and feature detection.
Energy detection sensing is frequent, and its typical
sensing time is less than 1 ms, while feature detection,
such as cyclostationary detection, is less frequent and
sensing time is around 24.2 ms for Digital TV [13].
We are therefore motivated to develop a modeling approach
that considers these three important issues and allows one
to evaluate the performance of SUs under these realistic
conditions.
C. Paper Contributions
The contributions of this paper are as follows:
1) We introduce a performance model for CRNs that models
heterogeneous channels, as well as the sensing process in
a manner that is dependent on the load. That is, the sens-
ing time increases if fewer channels become available,
and if fewer SUs are available to sense channels.
2) We introduce a strategy that gives preference to access
channels with potentially larger idle times and higher
bandwidth.
3) Through numerical results, we show that our proposed
strategy outperforms a baseline model that does not allow
switching between channels. In particular, our proposed
strategy reduces the mean waiting time for SUs in the
system.
4) Also, our numerical results show if sensing time is
very small (1ms), its effect on SUs performance is
insignificant.
D. Paper Organization
The rest of this paper is organized as follows. The model
and assumptions are explained in Section II. In Section III, our
proposed Continuous Time Markov Chains (CT M C) model
is presented. Performance metrics are derived in Section IV.
The baseline model is described in Section V, which is used
for comparison to our proposed model. Numerical results and
discussions are presented in Section VI. We conclude the paper
in Section VII.
II. MO DE L AN D ASS UM PT IO NS
We use a mixed queuing network to model the CRN system
where PUs are modeled as a closed chain of customers, while
SUs are modeled as an open chain. Table I shows the notation
and their description. Our proposed model contains two types
of channels, C1and C2, and a Virtual Queue (VQ), which
is used to accommodate SUs. It is assumed that channels in
C1have a higher bandwidth than channels in C2, and SUs,
therefore, prefer to use channels in C1. SUs may move from
the VQ to a channel in C1, if available, as their first preference.
TABLE I
TABL E OF NOTATIO NS ,WHERE i={1,2}.
Notation Description
CiNumber of channels in type i.
vNumber of SUs in the system: VQ, C1, and
C2.
βThe maximum size of the VQ buffer.
sA binary variable for sensing state, where
0 means no sensing is being conducted. 1,
otherwise.
piNumber of busy PUs in type ichannels.
ηSUs sensing rate.
Ψ(p1+p2,v)SUs sensing rate function.
pfProbability of false alarm.
λsSUs arrival rate.
λpiPUs arrival rate in type ichannels.
µsiSUs service rate in type ichannels.
µpiPUs service rate in type ichannels.
{v, p1, p2, s}A system state where v,p1,p2, and sare the
number of SUs in system, busy PUs in C1,
busy PUs in C2, and sensing state.
πv,p1,p2,s The probability of a steady state {v, p1, p2, s}.
pbProbability of SUs blocking, for C1and C2
overall.
paProbability of SUs admission, for C1and C2
overall.
LAverage number of SUs in the system: VQ,
C1, and C2.
WSUs average waiting time in the system: VQ,
C1, and C2, until finishing their packet trans-
mission.
Otherwise, they move to a channel in C2, if available. In
this model, whenever an SU detects an available channel in
C1, the SU starts using this channel, although the SU may
have been using a channel in C2. The purpose for doing so
is to improve the SUs performance. SUs detect out-of-band
channels availability by exchanging control information over
Common Control Channel (CCC) [10]. The maximum number
of SUs which can be in the system equals the VQ buffer size,
β. Therefore, if an SU is interrupted during its service by the
channel’s PU, the SU moves to the VQ, and starts to sense
for available channels in order to finish its own transmission,
and then leaves the system.
A. Assumptions
SUs exchange channels’ information, such as channel’s
availability using a CCC [11], which is assumed to be
always available.
Each channel has its own PU assigned to it.
The number of SUs in the network is unlimited, but a
maximum of βcan be in the system, either occupying
channels, or waiting for channels to become available.
Each channel is modeled as a server with no buffer.
There are two types of channels, type 1and type 2.
SUs assign a higher priority for using type 1channels over
type 2, due to the higher throughput of type 1channels.
Assume each SU has two transceivers, one for data trans-
mission, and the other for exchanging control packets with
other SUs over the CCC, and for conducting in band and
out-of-band sensing.
The Virtual Queue (VQ) is a concept to hold the newly
arrived and interrupted SUs, as well as SUs being served.
When an SU finishes its transmission, the SU leaves the
network. However, if an SU is interrupted, the SU moves
to the VQ and waits for an available channel in order to
complete its transmission.
When a PU or an SU finishes its transmission on a type 1
channel, e.g., channel k, then an SU being served on a type
2 channel, if any, moves to channel k, in order to improve
the SUs throughput.
SUs sensing time1is exponentially distributed with a rate
that is dependent on v,p1, and p2. Let Ψ(p1+p2,v)be this
sensing rate function, and it will be defined in the numer-
ical results Section, Section VI, equation (13). Practically,
Ψ(p1+p2,v)>> λs,λp1,λp2,µs1,µs2,µp1, and µp2.
Sensing is triggered when an SU arrives, given there is an
idle channel. Or, when a PU or an SU finishes transmission
and there is at least one SU waiting in the VQ.
We only model good sensing which results in finding an idle
channel that the SU can use. Modeling sensing which does
not result in accessing a channel, either because all channels
are busy, or because there are no waiting SUs, will have no
bearing on the system operation, and does not change the
model.
The probability of misdetection under sensing is assumed to
be very small, and is therefore negligible, in order to reduce
the model complexity. Misdetection is defined as detecting
the channel as idle, while the channel is occupied by a PU’s
transmission.
The probability of false alarm, pf, is considered in this
model, since it has much higher effect than the probability
of misdetection in our system model, and it is usually less
than 0.1, e.g., as in IEEE 802.22 CRNs standard [12]. False
alarm is defined as detecting the channel as busy by a PU’s
transmission, while in reality it is idle.
B. Parameters
C1and C2are the number of channels of types 1and 2,
respectively, and are also the number of PUs assigned to
these channels.
PUs assigned to type 1and type 2channels, have exponen-
tially distributed inter-arrival times with rates of λp1and
λp2, respectively, when they are idle.
PUs using type 1and type 2channels have service rates
of µp1and µp2, respectively, with exponential distributions,
when they are active.
βis the maximum size of the VQ2.
1In this paper, it is assumed that what we refer to as the sensing time,
includes both the channel sensing, and channel switching times.
2In our numerical results, βis set to a large value such that SUs pa1.
SUs arrival rates to the VQ is λswith Poisson distributions.
On type 1and type 2channels, the SUs service rates are
µs1and µs2, respectively, with an exponential distributions.
C. Variables
sis a binary variable, {0,1}, for sensing state, where 0
means no sensing is being conducted. While 1, otherwise.
vis the total number of SUs in the VQ, including those
being served by types 1and 2channels, while in this model
vis taken as finite, the virtual queue size, β, can also be
set to a very large number, hence approximating the infinite
number of SUs case, as will be shown in Section VI.
p1and p2are the numbers of PUs being served by type 1
and type 2channels, respectively.
For our model, we define the state space, call it ζ, as
(v, p1, p2, s), where: 0vβ,0p1C1,
0p2C2, and sis a binary variable, such that vmust
be 1, if s= 1, which means at least one SU must exist
to conduct sensing.
let πˆv, ˆp1,ˆp2,s be the stationary probability vector where v=
ˆv,p1= ˆp1,p2= ˆp2, and sis a binary variable such that if
s= 1, sensing is being conducted by SU(s). Otherwise; no
sensing.
It is to be noted that the assumption of memoryless
distributions, i.e., exponential distributions, has been made
in order to make the model mathematically tractable. This
is a standard assumption that is made in such complicated
models. It is to be also noted that the queuing network
is ergodic, because it is irreducible and has a finite state
space. The queueing network therefore has a unique steady
state (S.S.) distribution,
π.
III. MOD EL FO RM UL ATIO N
There are 5 cases of the global balance equations. Since
sensing is inconsequential when no channels are available, it
is assumed that sensing is terminated when a PU arrives to
occupy its channel and no other channels are available. It is
also assumed that at most one decision can be made based on
sensing at the same time.
In order to model the system exactly, a greater number of
state variables need to be included, which will significantly
increase the system complexity. Therefore, we introduce two
relaxations which result on bounds on system performance.
These are an optimistic bound and a pessimistic bound. The
definition of these two models are as follows:
For the optimistic bound analysis, if sensing is con-
ducted, then we assume it is on a channel in type 2(lower
SUs service rate), i.e., all available channels in type 1are
being used.
For the pessimistic bound analysis, if sensing is con-
ducted, then we assume it is on a channel in type 1(higher
SUs service rate), i.e., all available channels in type 2are
being used.
Throughout this section, we consider the optimistic bound
performance, while formulating the global balance equations.
With minor modifications of these global balance equations,
we can also model the pessimistic bound performance.
Case 1: If v < (C1p1), then all active SUs are using
channels in C1. Hence, the global balance equations are
equations (1) and (2).
πv,p1,p2,1[λs+s1+p1µp1+p2µp2+ (C1p1)λp1+
(C2p2)λp2+ Ψ(p1+p2,v)(1 pf)]
=πv1,p1,p2,0[λs]v1+πv1,p1,p2,1
[λs]v2+πv+1,p1,p2,1[(v+ 1)µs1] + πv,p1+1,p2,1
[(p1+ 1)µp1]v1+πv,p1,p2+1,1[(p2+ 1)µp2]v1
+πv,p1,p21,1[(C2p2+ 1)λp2]v1
+v
C1p1+ 1πv,p11,p2,0[(C1p1+ 1)λp1]
+C1p1+ 1 v
C1p1+ 1 πv,p11,p2,1[(C1p1+ 1)λp1]v1.
(1)
Sensing is considered for all channels, with channels in C1
given a higher priority when sensed by SUs. In equation (1),
vxis an indicator function which equals 1if the condition,
vx, holds. Otherwise, it is 0. The LHS of equation (1),
is the probability flux of leaving state (v, p1, p2,1) due to: an
SU arrival with rate λs, an SU in C1finishes its transmission
with rate s1, a PU in C1or C2finishing its transmission
with rates p1µp1and p2µp2, respectively, a PU arrived to C1
or C2with rates (C1p1)λp1or (C2p2)λp2, respectively,
and end of sensing with rate of Ψ(p1+p2,v)(1 pf).
The RHS of equation 1, is probability flux of entering state
(v, p1, p2,1). This is due to: an SU arrived while the system in
states (v1, p1, p2,0) and (v1, p1, p2,1). An SU finishing its
transmission while the system in state (v+ 1, p1, p2,1) with
rate (v+ 1)µs1, a PU completing service while the system
is in state (v, p1+ 1, p2,1) or (v, p1, p2+ 1,1), with rates
(p1+ 1)µp1or (p2+ 1)µp2, respectively, a PU arriving to
C2with rate (C2p2+ 1)λp2, while the system in state
in state (v, p1, p21,1), a PU arriving to C1while in state
(v, p11, p2,0), and interrupting an SU which is using its
channel, thus sensing by the SU is triggered with probability
v
C1p1+1 , and a PU arriving to its channel which is not being
used by an SU, with probability C1p1+1v
C1p1+1 , while the system
is in state (v, p11, p2,1), given there has been sensing. In
the rest of the paper, only the new transition states will be
explained, due to space limitation.
In equation (2), the LHS is similar to that in equation (1),
but there is no sensing. In the RHS, the second term to the
last, the system transits from state (v, p11, p2,0) to state
(v, p1, p2,0), due to a PU arrival to its channel in C1where
no SU exits, with a probability of C1p1+1v
C1p1+1 , given there was
no sensing.
Case 2: If (C1p1)v < (C1p1) + (C2p2),
then the global balance equations are (3) and (4). In this case,
if PU being served within C1finishes its transmission, SUs
sensing is triggered. Also, these equations implicitly model
the SUs preference to be served by C1channels rather than
C2channels. Thus, when a PU in C1finishes its transmission,
say at channel k, sensing is triggered, and then an SU moves
to channel k.
πv,p1,p2,0[λs+s1+p1µp1+p2µp2+ (C1p1)λp1+ (C2
p2)λp2] = πv,p1,p2,1Ψ(p1+p2,v)(1 pf)v1
+πv+1,p1,p2,0[(v+ 1)µs1] + πv,p1+1,p2,0[(p1+ 1)µp1]
+πv,p1,p2+1,0[(p2+ 1)µp2]
+C1p1+ 1 v
C1p1+ 1 πv,p11,p2,0[(C1p1+ 1)λp1]
+πv,p1,p21,0[(C2p2+ 1)λp2].
(2)
In equation (3) in the last term on the RHS, a PU arrives
to its channel in C2, where no SU is using it, with probability
C2p2+1(vC1p1)
C2p2+1 , given sensing was not being conducted.
Thus, system transits to state (v, p1, p2,0) (LHS). In equation
(4), the system transits to state (v, p1, p2,1) in LHS, from
different states, for example: from state (v, p1, p21,0) with
a probability of vC1p1
C2p2+1 , when a PU arrives to C2and
interrupts an SU that is using its channel. Thus, the PU arrival
causes sensing to start. The same thing occurs in the second
term to last, in state (v, p1, p21,1) with the same probability.
However, in this case an SU which was already engaged in
sensing will just continue to sense. However, in the last term
a PU arrives to its channel in C2, where no SU is using it,
with probability C2p2+1(vC1p1)
C2p2+1 , given sensing was being
conducted.
Case 3: If v= (C1p1) + (C2p2), then the global
balance equations are equations (5) and (6). In equation (5)
the last term in RHS, shows sensing is triggered by a PU
interruption of an SU which was served by the PU’s channel,
with probability C2p2
C2p2+1 , given there is still one free channel
in C2. However, in equation (6), the last term on the RHS
corresponds to a PU arriving to a channel where no SU was
being served, with probability of 1
C2p2+1 , and hence, sensing
is not triggered.
Case 4: If (C1p1) + (C2p2)< v < β, then, equations
(7) and (8) are the global balance equations. Recall that for
the optimistic bound analysis, if sensing is conducted, then it
is at a channel in C2, i.e., all available channels in C1are
being used.
πv,p1,p2,0[λs+ (C1p1)µs1+ (vC2+p2)µs2+p1µp1
+p2µp2+ (C1p1)λp1+ (C2p2)λp2]
=πv,p1,p2,1Ψ(p1+p2,v)(1 pf)v1
+πv+1,p1,p2,0[(v+ 1 C1+p1)µs2] + πv,p1,p2+1,0
[(p2+ 1)µp2] + C2p2+ 1 (vC1+p1)
C2p2+ 1
πv,p1,p21,0[(C2p2+ 1)λp2].
(3)
πv,p1,p2,1[λs+ (C1p1)µs1+ (vC1+p11
(vC1+p1)1)µs2+p1µp1+p2µp2+ (C1p1)λp1+ (C2
p2)λp2+ Ψ(p1+p2,v)(1 pf)] = πv1,p1,p2,0[λs]v1
+πv1,p1,p2,1[λs]v2+πv+1,p1,p2,0[(C1p1)µs1]
+πv+1,p1,p2,1[(C1p1)µs1] + πv+1,p1,p2,1
[(v+ 1 C1+p11)µs2] + πv,p1+1,p2,0[(p1+ 1)µp1]
+πv,p1+1,p2,1[(p1+ 1)µp1]v1+πv,p1,p2+1,1
[(p2+ 1)µp2]v1+πv,p11,p2,1[(C1p1+ 1)λp1]v1
+πv,p11,p2,0[(C1p1+ 1)λp1] + vC1+p1
C2p2+ 1
πv,p1,p21,0[(C2p2+ 1)λp2] + vC1+p1
C2p2+ 1 πv,p1,p21,1
[(C2p2+ 1)λp2]v1+C2p2+ 1 (vC1+p1)
C2p2+ 1
πv,p1,p21,1[(C2p2+ 1)λp2]v1.
(4)
πv,p1,p2,1[λs+ (C1p1)µs1+ (C2p21)µs2C2p2̸=0
+p1µp1+p2µp2+ (C1p1)λp1+ (C2p2)λp2+
Ψ(p1+p2,v)(1 pf)]
=πv1,p1,p2,0[λs]v1+πv1,p1,p2,1[λs]v2
+πv+1,p1,p2,0[(C1p1)µs1] + πv+1,p1,p2,0[(C2p2)µs2]
+πv+1,p1,p2,1[(C1p1)µs1]
+πv+1,p1,p2,1(C2p21(C2p2)1)µs2
+πv,p1+1,p2,0[(p1+ 1)µp1] + πv,p1,p2+1,0[(p2+ 1)µp2]
+πv,p1+1,p2,1[(p1+ 1)µp1]v1+πv,p1,p2+1,1
[(p2+ 1)µp2]v1+πv,p11,p2,0[(C1p1+ 1)λp1]
+πv,p11,p2,1[(C1p1+ 1)λp1]v1
+πv,p1,p21,1[(C2p2+ 1)λp2]v1
+C2p2
C2p2+ 1πv,p1,p21,0[(C2p2+ 1)λp2].
(5)
πv,p1,p2,0[λs+ (C1p1)µs1+ (C2p2)µs2+p1µp1
+p2µp2+ (C1p1)λp1+ (C2p2)λp2]
=πv,p1,p2,1Ψ(p1+p2,v)(1 pf)v1
+1
C2p2+ 1πv,p1,p21,0[(C2p2+ 1)λp2].
(6)
In equations (7) and (9), the last term in RHS corresponds
to a PU arriving to a channel where an SU is sensing it,
which occurs with probability of 1
C2p2+1 , hence sensing is
terminated. However, in Equation (8) the last term in RHS,
shows that the sensing has not been terminated , since the PU
arrives to a channel where sensing is not being conducted,
with probability of C2p2
C2p2+1 . However, the PU arrival causes
an SU interruption, where the SU goes back to the VQ, and
waits for a channel to become available. Recall that we assume
sensing is always conducted at a channel in type 2.
Case 5: In this case v=β. As a result, equations (9) and
(10) are the global balance equations.
πv,p1,p2,0[λs+ (C1p1)µs1+ (C2p2)µs2+p1µp1
+p2µp2+ (C1p1)λp1+ (C2p2)λp2]
=πv,p1,p2,1Ψ(p1+p2,v)(1 pf)v1
+πv1,p1,p2,0[λs] + πv,p11,p2,0[(C1p1+ 1)λp1]
+πv,p1,p21,0[(C2p2+ 1)λp2]
+1
C2p2+ 1πv,p1,p21,1[(C2p2+ 1)λp2]v1.
(7)
πv,p1,p2,1[λs+ (C1p1)µs1+ (C2p21
(C2p2)̸=0)µs2+p1µp1+p2µp2+ (C1p1)λp1
+ (C2p2)λp2+ Ψ(p1+p2,v)(1 pf)]
=πv1,p1,p2,1[λs]v2+πv+1,p1,p2,1[(C1p1)µs1]
+πv+1,p1,p2,1(C2p21(C2p2)1))µs2
+πv+1,p1,p2,0[(C1p1)µs1] + πv+1,p1,p2,0
[(C2p2)µs2] + πv,p1+1,p2,1[(p1+ 1)µp1]v1
+πv,p1,p2+1,1[(p2+ 1)µp2]v1
+πv,p1+1,p2,0[(p1+ 1)µp1] + πv,p1,p2+1,0
[(p2+ 1)µp2] + πv,p11,p2,1[(C1p1+ 1)λp1]v1
+C2p2
C2p2+ 1πv,p1,p21,1[(C2p2+ 1)λp2]v1.
(8)
πβ,p1,p2,0[(C1p1)µs1+ (C2p2)µs2+p1µp1+
p2µp2+ (C1p1)λp1+ (C2p2)λp2]
=πβ1,p1,p2,0[λs]β1+πβ,p1,p2,1
Ψ(p1+p2,v)(1 pf)β1+πβ,p11,p2,0
[(C1p1+ 1)λp1] + πβ,p1,p21,0[(C2p2+ 1)λp2]
+1
C2p2+ 1πβ,p1,p21,1[(C2p2+ 1)λp2]β1.
(9)
πβ,p1,p2,1[(C1p1)µs1+ (C2p21(C2p2)̸=0)µs2
+p1µp1+p2µp2+ (C1p1)λp1+ (C2p2)λp2+
Ψ(p1+p2,v)(1 pf)]
=πβ1,p1,p2,1[λs]β2+πβ,p1+1,p2,1[(p1+ 1)µp1]
β1+πβ,p1,p2+1,1[(p2+ 1)µp2]β1
+πβ,p1+1,p2,0[(p1+ 1)µp1] + πβ,p1,p2+1,0
[(p2+ 1)µp2] + πβ,p11,p2,1[(C1p1+ 1)λp1]β1
+C2p2
C2p2+ 1πβ,p1,p21,1[(C2p2+ 1)λp2]β1.
(10)
IV. PER FO RM AN CE ME TR IC S
In this section, we introduce several performance metrics
which can be used to evaluate CRN performance. These
include the probabilities of admission and blocking of SUs,
average number of SUs in the system during the network
operation, and average waiting time for SUs in the system
until completing service. We solved the steady state probability
distribution,
π, by solving the equation
π Q = 0, where Q
is the transition rate matrix that can be constructed using the
global balance equations (1)(10).
However, the number of linearly independent global balance
equation is (m1). Therefore, use the fact that the summation
of all probabilities in the steady state distribution equals 1. As
a results, we have mlinearly independent solvable equations.
Let us introduce the following definitions:
Definition IV.1 Probability of blocking of SUs (pb): It is the
probability that a new SU request for transmission is blocked
due to the lack of space in the VQ.
Definition IV.2 Probability of admission for SUs (pa): It is
the probability that a new SU request for transmission is
admitted.
Definition IV.3 The average number of SUs in the system (L),
which includes those being served by channels of types 1and
2, and also those waiting for a channel to become available.
Definition IV.4 Average waiting time (W) of SUs, which
is measured from the instant of arrival, until finishing its
transmission.
The following equations are used to evaluate the perfor-
mance metrics of our proposed model.
1) The probability of blocking for SUs (pb) is given by
equation (11).
pb=
C1
p1=0
C2
p2=0
1
s=0
{v=β},
(v,p1,p2,s)ζ
πv,p1,p2,s.(11)
2) The probability of SU admission, (pa), equals to 1pb.
3) The average number of SUs in the system (L), is given
by equation (12).
L=
C1
p1=0
C2
p2=0
1
s=0β
v=1,
(v,p1,p2,s)ζ
v×πv,p1,p2,s.(12)
4) To find the average waiting time W, we appeal to Little’s
Theorem, where Lis given by equation (12), and Wis
expressed as W=L
pa×λs.
V. BASELINE MODEL
In this section, we introduce and model another system.
This is a system similar to our proposed model, but with no
channel switching to type 1 channels (if available) by SUs
which are being served in type 2 channels, unless there are no
longer available channels on type 2. We developed this system
and use it as a baseline model to establish the advantages of
our proposed approach. For example, if an SU arrives and
selects a channel, say from set C2, the SU keeps using this
channel, until finishing its transmission, as long as this channel
is available. However, if the SU is interrupted, and sense there
are no available channels on type 2 to use it, and there is
an available channel on type 1, therefore the SU switches to
this channel. Otherwise, when no channel is available in both
types 1 and 2, the SU is buffered in the VQ, until a channel
becomes available. Due to space limitation in this paper, we
did not write the global balance equations for the baseline
model. The performance metrics for the baseline model are
similar to our model, in Section IV. Similarly, those equations
with minor modifications are used to evaluate the baseline
model performance metrics, and due to space limitation in
this report, we did not rewrite these equations.
VI. NUMERICAL RE SU LTS
This section presents the numerical results for SUs average
waiting time, with respect to SUs arrival rate to the system, λs.
Also, we study the effect of SUs sensing rate on the system
performance.
The sensing rate is dependent on both the number of unused
channels, and on the number of SUs performing the sensing
process. It was proven in [14] that the expected time to detect
an unused channel is inversely proportional to the number
of unused channels, which means that the sensing rate is
proportional to this number. Moreover, if the total number
of channels very large, and is evenly divided among the SUs
sensing for available channels (out-of-band sensing), then the
rate of detecting an empty channel is the sum of the individual
SUs sensing rates. We therefore express the sensing rate, as
a function of p1,p2, and v,Ψ(p1+p2,v), as shown in equation
(13), where ηis the sensing rate when there is only a single
SU sensing, and there is only one available channel.
Ψ(p1+p2,v)=ηˆ
Nˆ
I. (13)
ˆ
Nis the number of SUs in the system which are not being
served by channels (waiting/interrupted) or want to improve
their performance by switching to a channel in type 1, and
therefore conduct out-of-band sensing. ˆ
Iis number of idle
channels in type 1and 2channels which are not being used by
SUs or PUs. Based on the global balance equations (1)(10),
if v(C1p1),ˆ
N= 0 (No SUs are interested in sensing,
since all current SUs are being served by type 1channels). If
(C1p1)< v (C1p1+C2p2), then ˆ
N=v(C1p1).
Otherwise, ˆ
N=v(C1p1+C2p2). If v(C1p1+
C2p2), then ˆ
I= (C1p1+C2p2)v. Otherwise,
ˆ
I= 1. According to equation (13) the sensing rate increases
(the sensing time decreases) when more SUs are active and
sensing the channels. The sensing rate decreases (the sensing
time increases) when more PUs are active, and therefore there
are fewer available channels, and it takes longer to search for
and sense those channels.
In order to evaluate our proposed model, we consider two
different scenarios as follows, it is worth mentioning that in
both scenarios, SUs service rates in type 1and 2channels are
different.
Scenario 1parameters, µs1= 60,µs2= 15,λp1=λp2=
5,µp1=µp2= 10,η= 250,C1=C2= 4,pf= 0.09,
and β= 40.
Scenario 2parameters, µs1= 80,µs2= 20,λp1= 5,
λp2= 25,µp1= 15,µp2= 80,η= 380,C1=C2= 3,
pf= 0.05, and β= 50. This scenario, is different from
the first one, where PUs arrival and service rates are not
equal in both channel types. Also, PUs service time in type
1channels is greater than those in type 2, to capture the
heterogeneity nature, such as in TV channels and cellular
phones channels.
A. Average waiting time of SUs:
We show how the SUs’ average waiting time, W, changes
with respect to SUs arrival rate, λs.It is worth mentioning
the probability of SUs admission, pa, in our model and
the baseline model for all numerical results in this section
SUs average waiting time (sec)
SUs arrival rate ( s)
Our model, OB
Baseline model, OB
Our model, PB
Baseline model, PB
Fig. 1. Scenario 1, SUs Wtime with respect to
their arrival rate, λs.
SUs average waiting time (sec)
SUs arrival rate ( s)
Our model, OB
Baseline model, OB
Our Model, PB
Baseline model, PB
Fig. 2. Scenario 2, SUs Wtime with respect to
their arrival rate, λs.
SUs average waiting time (sec)
sensing rate ( )
Scenario 1, PB
Scenario 2, OB
Fig. 3. SUs Wtime, with respect to their sensing
rate, η, for scenarios 1and 2for PB and OB,
respectively, where λsis fixed and set to 100.
is almost 1. In our results, βis set to a value, e.g., in
scenario 2β= 50, such that pais almost 1. We have varied
βsize up to 100 in both Scenarios studies, however, this
do not change the numerical results, e.g., W. Therefore,
we approximate the infinite number of SUs case in our
results. Figure 1 which corresponds to scenario 1, shows that
Wincreases by increasing SUs arrival rate, λs. Our model
outperforms the baseline model in both the Optimistic Bound
(OB) and Pessimistic Bound (PB) analysis, because our model
reduces Wfor SUs in the system. For example, for the OB
analysis, and when λs= 20,100, and 150, our model reduces
Wby up to 12.44%,20.68%, and 11.99%, respectively, with
respect to the baseline model. One observation, when λs=
100,Wreduction is higher than when λs= 150. Therefore,
our model Wreduction percentage over the baseline model
reaches its maximum value, when λsincreased to some value,
and then this percentage decreases.
Also, Figure 2, which corresponds to scenario 2system
parameters, shows that Wincreases by increasing λs. This
figure, shows although the PUs behavior is different between
the two types of channels, our model outperforms the baseline
model in the OB and PB analysis. For example, for the PB
analysis, and when λs= 50, our model reduces Wby up to
16.23% with respect to the baseline model. Please notice that
sensing rate, equation (13), is higher than the SUs and PUs
arrival and service rates in these cases studies.
B. Sensing Rate:
We consider the Pessimistic and the Optimistic bounds
analysis for scenarios 1and 2, respectively, in our model to
study the effect of sensing rate, η, on SUs performance. The
system parameters correspond to scenarios 1and 2parameters,
except that in both scenarios λsis fixed and is set to 100, while
the sensing rate is varied on the X axis. Figure 3 shows that
the SUs’ average waiting time, W, decreases by increasing η.
The smallest value for sensing rate in this figure is 50, i.e., an
average sensing time of 20 ms, which is about the sensing time
using feature detection [13]. However, for the energy detection
method, the sensing time is 1ms [13], or η1000. Clearly,
when the energy detection method is used instead of feature
detection, the SUs performance is better and Wdecreases.
This figure also shows that if ηis increased beyond 1000,
its effect on SUs performance is insignificant for both cases
studies scenarios, e.g., in scenario 1for the PB, when ηis
increased from 50 to 1000,Wis reduced by up to 34.56%,
however, when ηis increased from 1000 to 2000,Wis only
reduced by up to 3.42%. Since our model discards SU arrivals
occurring while channels are being sensed, Win Figure 3 is
underestimated.
VII. CONCLUSIONS
In this paper we proposed a model for heterogeneous
channel access in Cognitive Radio Networks (CRNs). In this
model, there are two types of licensed channels, where one
type has a larger bandwidth. SUs may use the first type if
it is available, or if it becomes available. We also model the
SUs’ sensing process and study its effect on performance, such
that sensing rate is dependent on both the number of unused
channels, and on the number of SUs performing the sensing
process. We used a mixed queuing network model to model
the CRN system, and developed the global balance equations
for a CT M C . We derived SUs’ performance metrics, such as
SUs admission and blocking probabilities, and their average
waiting time in the system. We compare our proposed system
to a baseline model, which is the same as our proposed model,
except that SUs in type 2 channel can not improve their
throughput by switching to channels in type 1, if available,
unless they are interrupted at their current type 2 channels.
Numerical results show that our proposed model outperforms
the baseline model. We also found that if sensing time is very
small (1 ms), its effect on SUs performance is insignificant.
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SECON’07.
... Latency of the data processing technique and algorithm of user i ψ Scalability factor [5]. ...
... On the other hand, for a network architecture with components on different data generation and transmission hierarchy (e.g. a centralized or multi-structured clustered network), one representative component from each hierarchy would be required in order to model the entire network's SA. Hence, the proposed approach is also applicable for heterogeneous network analysis [7]. ...
... Therefore, if an SU is interrupted during its service by the channel's PU, the SU moves to the VQ, and starts to sense for available channels in order to finish its own transmission, and then leaves the system. Our work in this chapter is accepted in [41]. ...
Thesis
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Today’s wireless networks are characterized by a fixed spectrum assignment policy. However, a large portion of the assigned spectrum is used sporadically and geographical variations in the utilization of assigned spectrum ranges from 15% to 85% with a high variance in time. The limited available spectrum and the inefficiency in the spectrum usage necessitate a new communication paradigm to exploit the existing wireless spectrum opportunistically. This new networking paradigm is referred to as NeXt Generation (xG) Networks as well as Dynamic Spectrum Access (DSA) and cognitive radio networks. The term xG networks is used throughout the paper. The novel functionalities and current research challenges of the xG networks are explained in detail. More specifically, a brief overview of the cognitive radio technology is provided and the xG network architecture is introduced. Moreover, the xG network functions such as spectrum management, spectrum mobility and spectrum sharing are explained in detail. The influence of these functions on the performance of the upper layer protocols such as routing and transport are investigated and open research issues in these areas are also outlined. Finally, the cross-layer design challenges in xG networks are discussed.
Conference Paper
Cognitive radio wireless networks is an emerging communication paradigm to effectively address spectrum scarcity challenge. Spectrum sharing enables the secondary unlicensed system to dynamically access the licensed frequency bands in the primary system without any modification to the devices, terminals, services and networks in the primary system. In this paper, we propose and analyze new dynamic spectrum access schemes in the absence or presence of buffering mechanism for the cognitive secondary subscriber (SU). A Markov approach is developed to analyze the proposed spectrum sharing policies with generalized bandwidth size in both primary system and secondary system. Performance metrics for SU are developed with respect to blocking probability, interrupted probability, forced termination probability, non-completion probability and waiting time. Numerical examples are presented to explore the impact of key systems parameters like the traffic load on the performance metrics. Comparison results indicate that the buffer is able to significantly reduce the SU blocking probability and non-completion probability with very minor increased forced termination probability. The analytic model has been verified by extensive simulation.