Performance Analysis of Cognitive Coexistence Systems with Sensing Errors

Xiaohui Li and Xin Xue State Key Lab of ISN

Xidian University Xi' an, China

xhli@mail.xidian.edu.cn

Abstract-In this paper, we focus on the performance analysis of

the cognitive coexistence between Bluetooth and WLAN systems

with sensing errors. The packet transmission rate and packet

error probability are derived corresponding to the sensor

operating points (consisting of the false alarm probability and the

miss detection probability). Then, the optimization problem is

established as maximizing the throughput of cognitive user with

the constraint of the colliding probability with primary user. Simulation results illustrate that the proposed error analysis approach can obtain the optimal performance when considering

the sensing errors. Moreover, the influence on the throughput of

cognitive user caused by different sensor operating points is

investigated by simulation.

Keywords Cognitive Coexistence, Bluetooth, WLAN, Sensing Errors

I. INTRODUCTION

With the fast development of the wireless communication technology, interference between different systems has become the main handicap to improve the performance of the systems. In the unlicensed frequency band, interference is serious due to the lack of cooperation between different wireless systems. The concept of Cognitive Radio is proposed to alleviate the spectrum scarcity and interference problem in wireless communications.

Recently, there has been an explosion of research in cognitive radio. A large portion of this research has been in spectrum sensing and accessing. Qing Zhao et al have analyzed the dynamic spectrum access process under time slotted pattern[ll. Based on [1], an optimal algorithm [2] of spectrum access with sensing errors has been proposed. Moreover, a principle to separate the sensing and accessing parts has been presented. In [3], a Markov model is proposed based on the prediction of the data pattern of WLAN system. A hopping frequency protocol with perfect sensing in coexistence system between WLAN and Bluetooth based on the continuous time Markov model is investigated in [4]. In [5], the throughput of cognitive user is maximized by a Lyapunov optimizing algorithm. In [6], a multi-channel situation is considered and a linear algorithm is proposed. Some other contributions in this area are mentioned in [7, 8].

978-1-4577-9538-2/111$26.00 ©2011 IEEE 483

Guanghui Yu Department of Wireless Communications

ZTE Corporation Shenzhen, China

yu.guanghui@zte.com.cn

Most techniques described above are not directly applicable to the cognitive coexistence system with sensing errors. In this paper, a new error analysis approach based on Bayes Theorem is presented for the coexistence system, in which, the continuous time Markov model is applied to the primary user. In our method, un-slotted structure is used by the primary user. In other words, the system framework is more complicated than that of [2,5,6]. Different from [4], the error analysis model is established and the performance of the coexistence system is analyzed with sensing errors.

The remainder of this paper is organized as follows: In section II, the coexistence system is overviewed and the sensing errors are introduced. In section Ill, we establish the error analysis model by deriving the transmission rate and the collision probability considering sensing errors. In section IV, the optimization model is formulated and the optimal access strategy is derived under the error analysis model. The performances of the cognitive coexistence system are presented by simulations in section V, which illustrates the validity of our error analysis model in section Ill. Finally, the conclusions of the paper are given in section VI.

II. SYSTEM OVERVIEW

The cognitive coexistence system consists of Bluetooth and WLAN users, in which the Bluetooth users act as cognitive users as well as WLAN users act as primary users. Several Bluetooth channels interfere with a WLAN channel due to the bandwidth of WLAN is much wider than that of Bluetooth. For simplicity, only one-channel case [4] is considered in this paper.

The time behavior of WLAN user is modeled by a two-state IdlelBusy (1/0) continuous time Markov chain. The holding times in both Idle and Busy state are exponentially distributed

with parameters J1 for the idle state and A for the busy state.

For the cognitive user, a time slotted pattern is used, as shown in figure 1. The process of dynamic spectrum access (DSA) for cognitive user can be described as follows:

1. At the beginning of each slot, the cognitive user senses the channel and obtains the sensing outcome.

2. According to the sensing outcome, the cognitive user accesses the channel with probability f ( fJ) .

False Alan � Miss det.ect.ioll

���! Time slots : 0 : I : 2 : 3 : 4 : 5 : 6 : 7 : 8 :

time

� Primary user � Cognit.ive IISC"

o The sensing outcome is idle 0 The sensing outcome is busy

Figure I. the DSA process with sensing errors

Actually, the sensing outcome cannot be always true due to the existence of sensing errors caused by the noise and channel fading. From figure I, we can see that the false alarm and miss detection may mislead the cognitive user, which will generate the collision or lose the chance to transmit.

The errors consist of False alarm and Miss detection. Their probabilities are expressed as:

False alarm c(t) � Pr {0(t) = 0 I S(t) = I}

Miss detection <5 (t) � Pr { 0 (t) = II S (t) = O}

where S (t) = 1 means that the channel state is Idle at time t and 0(k)=odenotes that the sensing outcome is busy. We

denote the sensor operating point as (£,0) , which is

determined by the signal sample frequency, SNR and decision threshold[9] .

III. ANALYSIS ON ERRORS MODEL

As shown in Figure 1, when cognitive user accesses the channel (sends a packet) and the WLAN user keeps silent during the full slot, the packet will be transmitted successfully. A collision occurs when the packet of WLAN user is sent during the transition of the cognitive user's packet. Then, we define the packet rate of cognitive user and collision probability as:

r(k 10{k) = 0) � Pr{<t>{k) = I.{S{t) =1, 'dtE [kTs,{k + I)Ts)} 10{k) = o} (I)

d, (k 10{k) = 0) � Pr{<t>{k) = I,{ s{t) =O,3tE [kTs,{k +1)Ts)} I 0{k) =o} (2)

In Eq. (1) and Eq. (2), <I> (k) = 1 means that the cognitive

user will send a packet in the current slot. [kTs,(k+l)Ts) denotes the period during the kth slot.

With the Bayes Theorem, Eq. (I) and (2) can be further developed as:

r{kI0(k)=B) = Pr{ S(kTs) = 1}.Pr{<t>(k) = 110(k) = B}· Pr{0(k) = BI S(kTs) = I} . Pr{S(t) = I, 'dtE [kTs,(k + I)Ts) I S(kTs) =I}/ g (B)

(3)

484

d,{kI0{k)=0) = [Pr{S{kTs) = 1}.Pr{<t>{k) = II 0{k) = O}. Pr{0(k) = BI S(kTs) = I} . Pr{S(t) = O,3tE [kTs,{k + I)Ts)1 S{kTs) = I} +Pr{S(kTs) =O}.Pr{<t>{k) = II 0{k) = O}. Pr{0{k) = BI S(kTs) = O} . Pr{ S(t) =O,3tE [kTs,(k + I)Ts)1 S(kTs) =O}} g (B)

(4)

where, g (0) is the probability of the sensing outcome 0( k) = B, which can be defined as:

g( 0) �Pr{0(k) =O} = I:=oPr{e(k) =O,S(kTs) =s}

1�((1-C)+�<5) e(k)=l 2+.u .u -�(C+�(1-<5)) e(k)=O 2+.u .u

IV. FORMULATION AND SOLUTION

A. The optimazition model

(5)

For a cognitive coexistence system, we are committed to improving the date rate and alleviating the interference. So, the optimization problem can be formulated as:

max r (6)

where, a is the interference constraint. With Eq. (3) and Eq.

(4), the objective function r and constraint de can be

presented as:

r = L �=o r ( k , e ( k ) = 0) (7)

where

= I�=og (O)r(k I e(k) = 0) = vof (0)+ vJ (1)

de = �P(k,0{k) = 0) = �g( O)de(kl 0{k) = 0) = "0 ' f(O)+Kj' f{l) �a

f.1e -%15 Va = --- £, A+f.1

lKO =_l_( f.1 (l_e-J.Ts)c+A(I_<5)) A+f.1

Kj = _1_( f.1 (l_e-J.TS )(I-c) + A<5) A+f.1

B. The optimal accessing probability with sensing errors considered

(8)

(9)

(10)

From Eq. (7), when A and f.1 are determined, the packet

rate r of the cognitive user is decided by the false alarm

probability £ , accessing probability f (O ) andf ( I ) . From Eq.

(8), it can be discovered that I (0) and I (1) are determined

by the false alarm probability e , miss detection probability

8 and the interference constraint a . Therefore, the optimal

accessing strategy is to find a feasible probability pair I (0) and I (1) to maximize the packet rate of the cognitive user and

subject to the interference constraint.

Lemma 1 The optimal spectrum access strategy (1* (O},f* (1) ) must satisfy the constraint of Eq.(8) and

maximize (or minimize) the value of I ( 1) .

Proof It is obvious that Eq.(8) is necessary condition to obtain the

optimal value of I ( 0) and I (1) . Therefore, the original

optimization model can be simplified as an unconstraint problem shown as following:

From the monotonicity of Eq. (11), we can obtained:

max r� {if !i > '4J, maximize 1(1)

� Ko

if !i::; vo, minimize I(1) � �

(12)

From the Lemma 1, the optimal value of (1* (O},f* (I}) exists in the maximization or minimization of I ( 1 ) of the

feasible solutions. So once sensing errors (e, 8) are

determined, the optimal strategy to access can be divided into three steps.

Step 1: Calculate the accessing probability with the

constraint satisfied when I (1) is maximized.

1;(o) = (r-�)/KO 1; (0) = 0 (13)

1;(0) =0 Step 2: Calculate the accessing probability with the

constraint satisfied when I ( 0) is maximized. {KO < r 12 (l) = (r-Ko)/ � Ko =r 12{l) =0 Ko > r 12 (1) = 0

12(0) = 1 12(0) = 1 (14) 12 (0) = r/ Ko

485

Step 3: Compare the value of 1j and r2, when I (0) and

I (1) get different values in the Step 1 or Step 2. Choose the

larger one between 1j and r2 as the optimal solution.

{to (O),J* (1)) = (1; (0),1; (1))

(1* (0),1* (1)) = (12 (0),12 (1)) (15)

V. SIMULATIONS

A. System performance on different access algorithms. In our simulations, the scenarios with and without sensing

errors are considered to illustrate the performance of the proposed error analysis model and accessing strategy. The scenario without sensing errors is used to present the upper bound of throughput of the cognitive user. Characteristics of the scenarios simulated are shown in table 1. TABLE I. THE SCENARIOS WITH DIFFERENT CHARACTERISTICS

Sensing Consider Consider

the Scenarios errors the sensing

interference exist errors

constraint

CD No sensing error, Access when the NO NO channel idle

NO ® No sensing error, the optimal access NO YES algorithm

@ With sensing errors, access when the NO NO channel is idle

@ With sensing errors, consider the YES NO YES interference constraint

is) With sensing erros, the optimal accessing YES YES algorithm

From figure 2 and figure 3, we can see that when the sending rate of WLAN users is larger than 0.3, the collision probability is limited to 5% in scenario ®, but in scenario CD higher throughput is achieved. The packet collision rate in scenario CD is increasing as the channel gets busy, which indicates that even there is no sensing error, the cognitive user can't employ the algorithm in scenario CD due to the collision constraint. This case is peculiar to the cognitive coexistence system with time un-slotted pattern.

In figure 3, simulation results show that if the sensing errors are not considered, there will be serious interference to the coexistence system. Comparing the throughput and packet

error curves of scenarios ® and �, we can find that sensing errors have great influence on the system performance and cannot be neglected. That is if we ignore the sensing errors, the

interference constraint to the primary users can't be limited to a required level. While, the throughput of cognitive user decreased as the protection to the primary user is strengthened.

B. System performance at different sensing operation points Basing on the scenario �, simulation results of the optimal

accessing algorithm on different sensing operation points with the collision constraint a = 0.03 , are shown in figure 4.

0.8

� � 0.7

-g � 0.6

"0 i 0.5 g> 11 j 0.4

1 0.3

. £ 0.2

0.1

.......... No sensing error, access when the channel is idle

--e- No sensing error, the optimal access algorithm

� --.. - Sensing errors, access when the channel is idle

--9-- Sensing errors, consider the interference constraint

--e-- Sensing errors, the optimal access algorithm

I

the constrainllhreshold: a-O.05

the sensing operallon pomt E.O 1, 0 .0 1 a

o O:------:!O.L, --:'0.::-2 --:'0.::-3

-::'0.4-=----::';:----:'::----:'::----::'::---7::="'"

the packets sending rate of priamary user o_RfAmax

Figure 2 Throughput of cognitive user with the constraint de

In the simulations, the values of sensing errors are shown in the table below [9].

TABLE II. THE VALUE OF SENSING ERRORS USED IN THE SIMULATION

£ 0.05 0.10 0.20 0.30 0040

t5 0.2477 0.1819 0.1176 0.0820 0.0583

£ 0.60 0.70 0.80 0.90 1.00

t5 0.0282 0.0182 0.0104 0.0043 0

� No sensing error, access when the channle is idle I I I � No sensing error, the optimal access algorithm I I ....... ---.. ..

---i:T- With sensing errors, consider the interference constraint ��;� � __ � __ --e-- With sensing errors, the optimal access algorithm ,,'1 I I I ,/ I I I

0.50

0.0412

--�- With sensing errors, access when the channel IS Idle I ,......

.. I I � the inter1erence constrain! threshold: Jl I I I

1''" �T'�r-�-�;>/c

L

t>,

�

-m

� 0.10 _sensing - � - - � -/� ... 1t--:.-:�-.:-.:�-.: .. .: T - - I - --: --

:i!i erro� I JI ..... I I I I I � I \ I ,,# I I I , I I ,

I (fJ I � ...... I I I I I I Qj I ,f>r� I I I I I I i 0.05 'G-,�:�----.-

I I I I I I i! rll 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

the packets sending rate of primary user O'",RlRmax

Figure 3 Packets error rate with the constraint de

486

0.9,.-----,----,-------,---,------;,.---,

I

0.8 <=0.10_ �

single channel, with sensing errors, the interference constraint threshold a=0.03

� 0.7

� � 0.6

� '0 0.5 a. g, � 0.4

� rn 0.3

� � .: 0.2

0.1

I <=0.20�

_ � _ ___ L ____ � _____ L ____ � ____ _ £=0.30-> \ I

I I I I I £=0.40->'" \ I I I I ----,-\ - - - r- - --'-- - - - r----' - --- ­

£=0.50 --. \ 1 , , I \ \ I I I I £=0.60->- \-\ -'\:' - r- - -choose the sensing operation point dynamically-

I \ '''',,1 I I I £=O.70--t \\1\"\\ j,- I I 1 E=0.80->- ,.l � �\

""'-�� - - - - ..J _ __ _ _ L ____ .J ____ _ 1 \\ 't�\ \\ 1 1 1

E=0.90 � \\\.. \�,,\�,�\ : : : E=1.00 - ;>-�,\ '.;� - ,\:\i�� - -I - - - - - 1- - - - - "I - ----

: \ \ " '" ��S'��, : : : -, \ to" , 'r--... :��', \ , r -, 1 .A. "

I...... �� \\�,

� - "�t::::::!��:�_::! �:�

0.2 0.4 0.6 0.8 the packets sending rate of primary user o""AlAmax

1.0

Figure 4 Throughput of cognitive user on different sensing operation points

From the analyses above, conclusions can be drawn out that when the packets sending rate of WLAN users are very small, the throughput of the cognitive user can be improved obviously

with small false alarm ratio like £ � 0.1 O. As the packets sending rate of WLAN users grows, larger false alarm ratio can bring more decrement in the throughput. Furthermore, when the false alarm ratio £ is beyond some extent, the throughput

curve will declined sharply, like the curve when £=1.0 . Therefore, with the growing of the packets sending rate of the WLAN user, we should adjust the sensor operating point to maximize the throughput of the cognitive user.

VI. CONCLUSIONS

In this paper, with the WLAN systems based on continuous time Markov model, we study the spectrum access process in the single-channel mode where the sensing errors are considered for the cognitive coexistence between WLAN and Bluetooth system. Closed form expressions of the throughput and packet error rate of cognitive user are obtained. An optimal spectrum accessing strategy with fixed sensing errors is put forward. The advantage of this strategy is considering the influence caused by sensing errors on the accessing probability, which ensures that the interference constraint is satisfied. We simulate several access strategies in different scenarios and the results illustrate the advantage of the proposed optimal strategy. Besides, we analyze the influence on the throughput of cognitive user caused by the different sensor operating points, and how to choose the optimal sensor operating point dynamically will be studied in the future.

ACKNOWLEDGMENT

This work is supported by NSFC project(60702060), Fundamental Research Funds for the Central Universities of China (K505100100l6), State Special Project on mobile communications(IMT03003-005-03) and III Project(B08038).

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