Scheduling in a Cognitive Radio Network

Dong Huang, Cyril Leung, Zhiqi Shen and Chunyan Miao

School of Computer Engineering, Nanyang Technological University, Singapore

Email: {dhuang, ASCYMiao}@ntu.edu.sgDepartment of Electrical and Computer Engineering, University of British Columbia

Vancouver, Canada, Email: cleung@ece.ubc.caSchool of Electrical and Electronic Engineering, Nanyang Technological University, Singapore

Email: zqshen@ntu.edu.sg

AbstractIn this paper, we consider the channel access andpower allocation problem for secondary users in a time divisionmultiple access (TDMA) cognitive radio network. An algorithmis proposed to minimize the total transmit power while ensuringthat SU queue lengths are stable. Simulation results show thatthe proposed algorithm can achieve a good tradeoff between thepower consumption and the queue length.

I. INTRODUCTION

Dynamic power allocation is an effective method to transmit

data efciently over wireless channels and is important in

wireless communications due to the limited energy in wire-

less devices. Algorithms based on the concept of congestion

control have been successfully applied to the resource allo-

cation problem in wireless networks [1], [2], [3], [4]. These

algorithms optimize the network performance by fully utilizing

the network capacity and avoiding excessive congestion inside

the network. In addition, the network capacity region (i.e.,

the set of all feasible data rates) has been shown to be a

powerful technique for the resource allocation problem in

wireless networks [5], [6].

Cognitive radio (CR) is a promising technology for improv-

ing the spectrum utilization by allowing secondary users (SUs)

to access unoccupied licensed channels opportunistically. The

resource management in CR has been studied widely [7], [8],

[9], [10]. A decentralized cognitive MAC protocol based on

the theory of Partially Observable Markov Decision Process

(POMDP) is proposed in [7]. The goal of the proposed

cognitive MAC protocol is to optimize the performance of

secondary users while limiting the interference perceived by

primary users (PUs). The impacts of the transmission power

of SUs on the occurrence of spectrum opportunities and the

reliability of opportunity detection are investigated in [8]. In

order to maximize the throughput of SUs, an opportunistic

scheduling policy for cognitive radio networks is developed in

[9]. In [10], the rate adaptation problem in a cognitive radio

network is formulated as a general sum constrained switching

control Markovian dynamic game. Most of these works are

based on Markov Decision Process (MDP). Finding the opti-

mal policy may be computationally prohibitive. Suboptimal

algorithms with low complexity may be more suitable for

online implementation in wireless networks.

In this paper, we consider a Time Division Multiple Access

(TDMA) cognitive radio system model [10], where multiple

SUs compete to access an unlicensed channel at each time

slot. To provide a distinct tradeoff in power consumption and

queue length, we develop an algorithm for the access rule and

rate adaptation problem by introducing a control parameter. By

varying the control parameter value, we can achieve a good

tradeoff between the power consumption and the queue length.

The rest of the paper is structured as follows: The network

model and problem denition are presented in Section II.

In Section III, the achievable rates for a transmission policy

in which the SUs transmit with xed equal powers are rst

discussed. An algorithm with variable transmit power is then

proposed. Simulation results are presented in Section IV, and

conclusions are provided in Section V.

II. NETWORK MODEL AND PROBLEM DEFINITION

Consider a TDMA cognitive radio network with N SUlink pairs; the SUs share a common channel with PUs. SUs

are allowed to access the channel when they sense that the

channel is not being used by PUs. We assume that at most

one SU accesses the channel in each time slot, i.e. there are no

collisions among SUs. SUs can obtain historical PU channel

usage information from the primary user base station (PUBS).

SUs are able to exchange information, such as individual

SU link pair channel gains and individual SU queue lengths,

through a control channel. For brevity, we dene the set

N = {1, 2, . . . , N}. For SU n, the number of bits arrivingin time slot t is dn(t). We assume dn(t) are stationary andergodic with rate n, i.e., limT

1T

T1t=0 dn(t) = n. We

also assume that the number of arriving bits for all SUs

at every time slot is bounded and there exists a constant

dmax > 0 such that dn(t) dmax, n N. Let hn(t) bethe channel quality state of user n and it is assumed thathn(t) H = {H1, . . . , HM}, n N.

Let S(t) be the channel indicator variable. When the chan-nel is available, i.e., PU does not transmit, S(t) = 1; S(t) = 0otherwise. The channel availability is modeled as a two state

Markov chain, as shown in Fig. 1. Let q denote the probabilitythat the channel is not available, then q = /( + ). Themaximum allowable probability of collision with an SU given

that the PU transmits is .

Let Pn(t) [0, Pmax] be the transmit power of SU n in ___________________________________ 978-1-61284-307-0/11/$26.00 2011 IEEE

Fig. 1: Channel availability model.

time slot t. The corresponding bit rate is given by [11]

(Pn(t), hn(t)) = log2

(1 +

hn(t)Pn(t)

N0

), (1)

where N0 denotes the noise power and hn(t) is the channelgain. Let Xn(t) be the number of bits in the queue of SU nat the beginning of time slot t. Then,

Xn(t + 1)

= max [Xn(t) an(t)(Pn(t), hn(t))S(t), 0] + dn(t) (2)

subject to

Nn=1

an(t) 1, (3)

where an(t) {0, 1} is an allocation indicator variable. Whenthe channel is allocated to SU n at time slot t, an(t) = 1,otherwise, an(t) = 0. Constraint (3) states that at most oneSU can access the channel in any given time slot. The average

SU queue length is

X = limT

1

T

T1t=0

Nn=1

Xn(t). (4)

According to [12], the queue is stable if

limt

P(Xn(t) < x) = F (x), and limx

F (x) = 1. (5)

In this paper, we use Loynes theorem [13], which states that

when the arrival and service processes in a queueing system

are strictly stationary and ergodic, the queue is stable if and

only if the average arrival rate is strictly less than the average

service rate [14]. Let (t) be the collision indicator, where

(t) =

{1 if an SU transmits and S(t) = 0,

0 otherwise.(6)

Then the SU collision rate is

= limT

1

T

T1t=0

(t). (7)

Let the average SU transmit power be

P = limT

1

T

T1t=0

Nn=1

Pn(t) (8)

and the average bit rate for SU n be

n = limT

1

T

T1t=0

an(t) (Pn(t), hn(t))S(t), n N.

(9)

Our objective is to minimize the value of P

minP , (10)

subject to

n > n, n N (11)

P (collision|PU transmitting) . (12)

We assume the existence of a feasible solution space for the

problem in (10)-(12). In order to ensure that constraint (12)

is satised, we introduce a process Y (t), with Y (0) = 0,which evolves as follows: (1) If SUs do not transmit when

PU is transmitting, Y (t + 1) is lower than Y (t) by as longas Y (t) ; (2) if SUs transmit when PU is transmitting,Y (t + 1) is set higher than Y (t) by 1 when Y (t) and 1 when Y (t) < . Therefore, the dynamics of Y (t) canbe expressed as:

Y (t + 1) = max [Y (t) (1 S(t)), 0] + (t). (13)

When the system (13) is stable, i.e.,

q = limT

1

T

T1t=0

(1 S(t))

> limT

1

T

T1t=0

(t) = qP (collision|PU transmitting),

(14)

constraint (12) is satised. It can be seen that any feasible so-

lution to the constraints (11)-(12) should stabilize the systems

in (2) and (13).

Let Pdenote the optimal solution to the problem, where

= [1, 2, . . . , N ] is the data arrival rate vector. It isdifcult to solve the optimization problem in (10)-(12) due

to the fact that only partial channel state information (CSI)

is available to the SUs. Similar problems have been modeled

as partially observable Markov decision processes (POMDPs)

[7], [15]. However, nding an optimal solution for a general

POMDP problem can be computationally prohibitive. For

suboptimal algorithms with low complexity such as greedy

algorithm (i.e., an SU with the best channel quality in each

time slot has the highest priority to access the channel when

the channel is available) and longest queue algorithm (i.e.,

an SU with the longest queue length in each time slot has

the highest priority to access the channel when the channel is

available) cannot solve the problem effectively. For example,

an SU may not transmit any data when its channel quality is

always in Bad state.

In the following section, we study the impact of sensing

on the achievable rate region and the associated average

power consumption. The proposed access and power control

algorithm (APCA) is then discussed.

III. MAIN RESULTS

Note that sensing results at SUs have a signicant impact

on the optimal access rule. In this section, we rst study the

achievable rate region of (11)-(12) under a simple scenario

and transmission policy.

Scenario (S1): Sensing is conducted at SUs. The probability

of false alarm (PFA) is P (S(t) = 0|S(t) = 1) = and theprobability of miss detection (PMD) is P (S(t) = 1|S(t) =0) = , where S(t) denotes the sensing result at SUs at slott. S(t) = 1 when the channel is observed to be available, andS(t) = 0 otherwise.Transmission Policy (P1): When there is incoming data,

if S(t) = 1, a selected SU transmits data with probabilityP (SU transmitting|S(t) = 1) = > 0.

Lemma 1. Assume each SU transmits data at a xed power

P . The average data transmission rate of SU n is equal ton/(1 q) when the channel is available. Under Scenario S1and Transmission Policy P1, the maximum of for which con-straint (12) is satised is max = min(/, 1). The achievablerate region of constraints (11) and (12) is characterized by

Nn=1

nmax(1 )n

< 1. (15)

When is interior to , the system can be stabilized with

average power P =N

n=1[(1)(1q)+q]n

(1)nP .

Proof: For the constraint (12), it is required that the

inequality P (Transmitting|S(t) = 0) = P (Transmitting|S =1)P (S = 1|S(t) = 0) holds. If < , we get max = 1.If , we get / and derive max = /. Thus, weget max = min(/, 1).From transmission policy P1, we get

P (SU transmitting|S(t) = 0) = 0. Therefore,P (SU transmitting, S(t) = 1) = P (SU transmitting, S(t) =1, S(t) = 1) = P (SU transmitting|S(t) = 1)P (S(t) =1, S(t) = 1) = (1 q)(1 ). The average total number oftime slots needed for SU n in order to transmit n/(1 q)units of data is 1/((1q)(1)). The fraction of time that theserver is in busy state is equal to

Nn=1

n(1)n

and it should

be less than 1 for stability. Since P (SU transmitting, S(t) =0) = P (SU transmitting, S(t) = 1, S(t) = 0) =P (SU transmitting|S(t) = 1)P (S(t) = 1, S(t) = 0) = q,we get P (SU transmitting) = [(1 q)(1 ) + q]. Theactual average number of transmitting slots needed for SU nin order to transmit n/(1 q) units of data is

(1)(1q)+q(1)(1q) .

In this case, the fraction of time that the server is in busy

state is equal toN

n=1[(1)(1q)+q]n

(1)n. The associated

average power consumption isN

n=1[(1)(1q)+q]n

(1)nP .

Based on some assumptions (e.g., SUs transmit data with

xed power), Lemma 1 can not only provide the achievable

rate region for the problem in (10)-(12), but also give the av-

erage power consumption under scenario S1 and transmission

policy P1. If the assumption that SUs transmit data with xed

power is relaxed, its not easy to derive the corresponding

average power consumption. But when SUs transmit data

with dynamic power control, the average power consumption

should be less than or equal to that in the case of xed power

transmission.

In the following subsection, we assume that SUs transmit

under dynamic power control. We analyze the dynamics of

the systems in (2) and (13), and propose an APCA algorithm

based on Lyapunov optimization.

A. The Proposed Algorithm

Let V 0 be a xed control parameter. The proposedAPCA algorithm is based on solving the following optimiza-

tion problem

min f(Q(t),P(t), a(t))

= N

n=1

Xn(t) E [an(t)(Pn(t), hn(t))S(t)|Q(t)]

+ Y (t) E

[(1 S(t))

Nn=1

an(t)

]+ V E

[N

n=1

Pn(t)|Q(t)

],

(16)

with

Q(t) = [X1(t), X2(t), . . . , XN(t), Y (t)], (17)

where > 0 is a constant weighting factor, P(t) =[P1(t), . . . , PN (t)] denotes the power allocation vector anda(t) = [a1(t), . . . , aN (t)] is the channel allocation indicatorvector for time slot t. In each time slot, we need to determinethe values of an(t) and Pn(t) such that the objective functionis minimized. It can be seen that whether SUs access the

channel depends on not only the historical statistics of the

channel, but also on the current queue lengths.

SinceN

n=1 an(t) 1 and an(t) {0, 1} n N, we minimize the objective function in (16) by the

following steps: First, set an(t) = 1 and aj(t) =0, j N {n}. The corresponding objective func-tion is denoted by fn(Q(t),P(t), a(t)). In addition, weset an(t) = 0 n N. The corresponding objec-tive function is denoted by f0(Q(t),P(t), a(t)). Then wecompare fn(Q(t),P(t), a(t)), n = 0, 1, . . . , N . Assumefn(Q(t),P(t), a(t)) is the minimum. If n = 0, then we setan(t) = 1, and an(t) = 0, n N, otherwise. Specically, itcan be achieved by solving the following problem:

j = argminn

Un(t), (18)

where

Un(t) =

{n(t) if n(t) < 0

0 otherwise,

and

n(t) = minPn(t)

{Y (t)(1 S(t)) + V Pn(t)

Xn(t)S(t)(Pn(t), hn(t))}.

S(t) denotes the expectation of S(t) at time slot t. After theabove problem is solved, the access rule and power control

are as follows:

an(t) =

{1 if n = j and Un(t) < 0

0 otherwise,(19)

and

Pn(t) =

argminPn(t)

n(t) if an(t) = 1

0 otherwise.(20)

Based on the above discussion, we now use the following

theorem to illustrate how we derive the objective function in

(16) and characterize the performance of the APCA algorithm.

Specically, it provides an upper bound for the average queue

length and power consumption.

Theorem 1. Let be an achievable rate region of problem

(10)-(12). Assume is interior to . For any control pa-

rameter V > 0, the solution derived by the proposed APCAalgorithm can stabilize the system in (2) and (13) has the

following inequalities:

limT

sup1

T

T1t=0

E

[N

n=1

Xn(t) + Y (t)

]

B + V Pmaxmax

,

(21)

limT

sup1

T

T1t=0

E

[N

n=1

Pn(t)

]

B

V+ P, (22)

where B =(N + d2max + (

2 + 1)2)/2 and max is the

largest value such that (+ max) .

Proof: Suppose the state vector is dened as (17). In this

paper, we set = 5. The Lyapunov function can be denedas

L(Q(t)) =1

2Q(t)QT (t) =

1

2

[N

n=1

X2n(t) + 2Y 2(t)

],

(23)

where QT (t) denotes the transpose of Q(t). Assume H1is the best channel quality, then (Pn(t), hn(t)) =(Pmax, H1). Since (t) 1 and X

2n(t + 1) (Xn(t)

(Pn(t), hn(t)))2+d2n(t), the Lyapunov drift can be expressed

as

(Q(t)) =E [L(Q(t + 1)) L(Q(t))|Q(t)]

Nn=1

Xn(t) E[an(t)(Pn(t), hn(t))S(t)

dn(t)|Q(t)] + B

2Y (t) E [((1 S(t)) (t))|Q(t)] , (24)

where B =(N + d2max + (

2 + 1)2)/2. From (6), and

(19)-(20), we have

(t) =

Nn=1

an(t)1[n(Pn(t),h(t))>0](1 S(t))

=N

n=1

an(t)(1 S(t)),

where 1[] is an indicator function. 1[] = 1 when the condition[] is true, and 0 otherwise. Therefore, (24) can be changed to

(Q(t)) B +N

n=1

nXn(t) q2Y (t)

Nn=1

Xn(t) E [an(t)(Pn(t), hn(t))S(t)|Q(t)]

+ 2Y (t)

Nn=1

E [an(t)(1 S(t))|Q(t)] . (25)

Motivated by the Lyapunov optimization technique developed

in [4], we add V E[N

n=1 Pn(t)|Q(t)]with V > 0 to both

sides of (25), and obtain

(Q(t)) + V E

[N

n=1

Pn(t)|Q(t)

]

B +N

n=1

nXn(t) q2Y (t) + V E

[N

n=1

Pn(t)|Q(t)

]

N

n=1

Xn(t) E [an(t)(Pn(t), hn(t))S(t)|Q(t)]

+ 2Y (t)

Nn=1

E [an(t)(1 S(t))|Q(t)]

B(t)

Nn=1

Xn(t) E [an(t)(Pn(t), hn(t))S(t)|Q(t)]

+ 2Y (t)

Nn=1

E [an(t)(1 S(t))|Q(t)]

+ V E

[N

n=1

Pn(t)|Q(t)

], (26)

where B(t) = B +N

n=1 nXn(t) q2Y (t).

Since is interior to , there exist a strategy an(t), Pn (t)

such that

E

[N

n=1

Pn (t)

]= P +, (27)

E[an(t)(P

n (t), hn(t))S(t)

] n + , (28)

E[(t)

]+ q. (29)

Fig. 2: The Markov channel quality model.

Therefore, we get

(Q(t)) + V E

[N

n=1

Pn(t)|Q(t)

]

B +N

n=1

nXn(t) q2Y (t)

N

n=1

Xn(t) E[an(t)n(P

n (t), hn(t))|Q(t)

]

+ 2Y (t)N

n=1

E[an(t)(1 S(t))|Q(t)

]+ V P +

B

(N

n=1

Xn(t) + Y (t)

)+ V P +. (30)

Taking the expectation of (30) overQ(t) and summing it fromt = 0 to t = T 1 and divided by T , we get

L(Q(T )) L(Q(0))

T+ V

T1t=0

E

[N

n=1

Pn(t)

]

B + V P +

T

T1t=0

E

[N

n=1

Xn(t) + Y (t)

]. (31)

The above inequality always holds when + . Letmax be the largest value satisfying + max . Notethat

Nn=1 Pn(t) Pmax. By setting = 0 and = max,

inequalities (21) and (22) follow.

Theorem 1 indicates that the total average queue length

increases with V whereas the average power consumptionapproaches the minimum power as V increases. Therefore,adjusting the value of V allows a tradeoff between the queuelength and the power consumption.

IV. PERFORMANCE EVALUATION

In this section, we present computer simulation results to

illustrate the results in Section III. We consider a TDMA

cognitive radio system with N = 5 secondary link pairs. Thechannel state S(t) is characterized by a 0/1 Markov chain, asshown in Fig. 1, with = 0.7 and = 0.3. Data arrival ratefor every link is the same (i.e., 1 = 2 = = 5 = ). Thechannel quality for each secondary link pair is quantized into

three different states, namely {H1, H2, H3}, where H1 meansthe channel is in Good state, H2 is in Medium state andH3 is in Bad state. The channel quality model is the 3-state Markov chain shown in Fig. 2. The transition probability

0.05 0.1 0.15 0.2 0.250

5

10

15

20

25

30

Data Arrival Rate, (bits/slot)

Ave

rag

e S

U T

ran

sm

it P

ow

er,

P (

mW

)

V=0.1

V=1

V=5

V=20

Fig. 3: Average total SU power consumption versus arrival

data rate for different values of V .

matrix is

H =

0.4 0.4 0.20.3 0.5 0.2

0.2 0.5 0.3

.

Transitions between channel quality states for different link

pairs are assumed to be independent. We also set = 0.05,Pmax = 200 mW and N0 = 100 dBm. The simulation isconducted over T = 50000 time slots.The average total SU transmit power dened in (8) and the

average total SU queue length dened in (4) are plotted as

a function of the bit arrival rate, , in Figs. 3 and 4. FromFig. 3, it can be seen that for a given value of V , the averagetransmit power increases with the bit arrival rate due to the

increased transmission requirements. For a given bit arrival

rate, the average power decreases with the control parameter

V . It can be seen from Fig. 4 that the average queue lengthincreases with the bit arrival rate for a given value of V ; fora given value of , the average queue length increases withV . An appropriate value of V can be selected to achieve adesired tradeoff between the average transmit power and the

average queue length.

V. CONCLUSION

In this paper, the SU access and power allocation scheme

in a TDMA cognitive radio system was studied. An algo-

rithm was proposed which allows a tradeoff between power

consumption and queue length. The solution derived by the

algorithm can be a good solution when the control parameter

is chosen appropriately.

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