making the best of limited resources: optimized differential sensing in cognitive pans

Computer Networks 54 (2010) 605–617

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Computer Networks

journal homepage: www.elsevier .com/ locate/comnet

Making the best of limited resources: Optimized differential sensingin cognitive PANs q

Jelena Mišic *, Vojislav B. MišicRyerson University, School of Computer Science, 245 Church Street, Toronto, ON, Canada M5B 2k3

a r t i c l e i n f o

Article history:Available online 19 August 2009

Keywords:Opportunistic spectrum accessCooperative spectrum sensingAdaptive sensingWireless personal area networks

1389-1286/$ - see front matter � 2010 Elsevier B.Vdoi:10.1016/j.comnet.2009.08.009

q The paper is a substantially revised and expande‘‘Making the Best of Limited Resources: DifferentialPANs” that has been presented at the MSWiMVancouver, BC, Canada.

* Corresponding author. Tel.: +1 416 979 5000x75064.

E-mail addresses: [email protected] (J. Mišson.ca (V.B. Mišic).

a b s t r a c t

Cognitive radio technology necessitates accurate and timely sensing of primary users’activity on the chosen set of channels. The simplest selection procedure is a simple randomchoice of channels to be sensed, but the impact of sensing errors with respect to primaryuser activity or inactivity differs considerably. In order to improve sensing accuracy andincrease the likelihood of finding channels which are free from primary user activity, theselection procedure is modified by assigning different sensing probabilities to active andinactive channels. The paper presents a probabilistic analysis of this policy and investigatesthe range of values in which the modulation of sensing probability is capable of maintain-ing an accurate view of the status of the working channel set. We also present a modifica-tion of the probability modulation algorithm that adapts the weighting factor to changes inperceived duty cycle of primary users’ activity, and show that it achieves minimum sensingerror in a wide range of the values of that duty cycle.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction Random selection of channels with equal probability

Cognitive communications technology [1] is predomi-nantly envisaged for use in the area of local and wide rangenetworks [3,7], but it can provide benefits for wireless per-sonal area networks (WPANs) as well [5]. Co-existence ofseveral WPANs in the same physical area may be achievedby combining opportunistic spectrum access with fre-quency hopping [9], similar to Bluetooth [2] except thatthe hopping sequence of a PAN with cognitive access (cog-nitive PAN or CPAN) should dynamically adapt to the activ-ity patterns of primary users. Those patterns must beobtained by sensing, which should be performed repeti-tively and cooperatively [16,18], and in such a manner asto minimize the sensing error.

. All rights reserved.

d version of the paperSensing in Cognitive

’2008 conference in

404; fax: +1 416 979

ic), [email protected]

(hereafter referred to as uniform random sensing) ensuresthat all channels are sensed with equal frequency and,thus, with equal error in the statistical sense [13]. This er-ror may be reduced by increasing the ratio of sensed chan-nels vs. total channels, either by increasing the number ofchannels to be sensed in each cycle or, if that is not possi-ble, by reducing the total number of working channels.

However, sensing error can be reduced in another man-ner. Namely, not all errors affect the operation of a CPAN inthe same way: a channel that becomes inactive while con-sidered active is but a missed opportunity, whereas a chan-nel that becomes active during CPAN operation may causeinterference and, in extreme cases, complete failure ofcommunication in the CPAN. Therefore, the onset of pri-mary user activity on an inactive channel is more criticalfor the CPAN operation, and should be sensed with smallererror than the preceding (or succeeding) end of suchactivity.

Smaller error for inactive channels requires shortersensing intervals, which may be accomplished by assigninggreater weight to idle channels than to active channels inthe process of selecting which channels to sense. The

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606 J. Mišic, V.B. Mišic / Computer Networks 54 (2010) 605–617

performance of this technique, hereafter referred to asprobability modulation, is modeled and analyzed througha queueing theoretic approach. The probability modulationapproach is shown to be capable of reducing the error inboth magnitude and duration, compared to that of uniformrandom sensing.

Since a closer investigation of the performance of thistechnique has revealed the existence of an optimum valueof the weight factor – optimum in the sense that it mini-mizes the sensing error expressed as the number of chan-nels with erroneous information and the delay in detectingchanges in channel activity – we have looked into the pos-sibility of adapting the weight factor to the dynamics ofprimary users’ activity. A simple yet effective adaptivealgorithm is presented that minimizes sensing error in awide range of values of the duty cycle of primary users’activity.

The paper is organized as follows: Section 2 gives moredetails about the operation of a frequency hopping cogni-tive personal area network and the sensing process in par-ticular, together with a detailed description of the channelsensing policies under consideration. Section 3 presentsthe probabilistic model of the sensing activity, whileSection 3.3 models probabilities of incorrect channelinformation. Section 4 presents and discusses perfor-mance of these policies. Section 5 presents the design ofthe adaptive version of the probability modulation algo-rithm and demonstrates its performance. Finally, Section6 concludes the paper and highlights some avenues forfuture research.

2. CPAN operation and sensing

Let us now describe the operation of a cognitive PAN inmore detail. Consider a generic piconet that consists of adedicated coordinator and a number of nodes. All commu-nications within the piconet are performed under the con-trol of the piconet coordinator, which is responsible foradministrative tasks such as starting the piconet, admittingnodes to join the piconet, and monitoring and controllingthe operation of the piconet.

We assume that the available time is partitioned intoslots or superframes of fixed size. Each superframe ismarked by a beacon frame emitted by the coordinator,and each superframe uses a different RF channel from theworking frequency band. The sequence of channels (i.e.,the hopping sequence) should be random, insofar as tech-nically possible, but also adaptive, in the sense that anychannel currently occupied by a primary user ought to beavoided. To that end, the piconet coordinator must main-tain an accurate and timely channel map, i.e., the map ofprimary user activity on each of the N working channels,which is accomplished by instructing a certain number ofsecondary users to sense and report back the status of Xdistinct channels in each superframe. Upon receiving thisinformation, the coordinator updates the channel map, se-lects the best channel for a subsequent frequency hop, andannounces it in the beacon frame.

The sensing activity may be performed in parallel withthe regular data communications, provided that the super-

frame is further subdivided in to a number of specializedsub-frames, similar to the HRMA protocol described in[17] or the more recent IEEE 802.15.3 MAC protocol [8].During the reservation sub-frame, any device that wantsto transmit a packet (or packets) to another device will re-quest a dedicated time slot. The coordinator will grant (orreject) this request, taking into account the amount ofavailable resources, the traffic in the piconet, and other cri-teria such as fairness, performance, and the like; this infor-mation is sent to the interested parties during theallocation sub-frame, together with the sensing instruc-tions. Actual packet transmissions take place in data ex-change slots, during which the sensing nodes performsensing and report back their findings in a separate slotthat immediately precedes the next beacon frame. Thestructure of the superframe and various activities in theCPAN are schematically depicted in Fig. 1, while Fig. 2shows how the results of sensing affect frequency hoppingof a CPAN; in both cases, we assumed that the RF band hasN = 5 working channels, and that X = 3 channels are sensedin each sensing cycle.

Ideally, the channel map should accurately reflect thestate of the channels at any given time. However, the sens-ing process incurs errors due to the following. First, sensingis performed in discrete intervals and any change in thestate of a channel can be detected only upon the next sens-ing event. Therefore, state changes in the channel map arealways delayed with respect to the actual changes. Second,a sensing cycle may include some but not all channels, i.e.,N > X, which means that the information for those channelsthat were not sensed in the last cycle is by default obsolete.

As a result, the information in the channel map is onlypartially correct at any given time. The magnitude of thiserror will determine the success rate of CPAN transmis-sions and, ultimately, its quality of service. The error maybe expressed through the mean number of channels withincorrect information and the delay in detecting changesin channel status. Error reduction may be accomplishedby increasing the number of sensors or by reducing thenumber of working channels, whichever is moreconvenient.

The number of sensed channels X should ideally beequal to, or larger than, the number of channels N in theworking set, so that the channel map may be kept accurate.As sensing is performed in discrete intervals, any change inthe state of a channel can be detected only upon the nextsensing event; therefore, state changes in the channelmap are always delayed with respect to the actual changes.

When there are more channels than sensing nodes, i.e.,N > X, not every channel can be sensed in every sensing cy-cle, and the information in the channel map is only par-tially correct at any given time. The magnitude of thiserror will determine the success rate of CPAN transmis-sions and, ultimately, its quality of service. The error maybe expressed through the mean number of channels withincorrect information and the delay in detecting changesin channel status. Error reduction may be accomplishedby increasing the number of sensors (i.e., the number ofchannels which are sensed in each cycle) or by reducingthe number of working channels, whichever is moreconvenient.

channel 1 channel 5channel 2

beacon frame: new working channel(#5) announced, all devices switch

channel 4

primary user active

s3

s3

channel 3

reservation slot: some nodesrequest bandwidth allocationallocation slot: some nodesgiven data slots, others told tosense channels #1, #2, #4

primary user active

s2s1

reporting slot: sensingnodes report back

sensesensesense

s2s1

all

beacon frame, new workingchannel announced

superframe

data exchange slots:

nodes given slotstransmit and receivedata;

at the same time,sensing nodes switchto sense theirdesignated channels

time

Fig. 1. Activities during a CPAN superframe.

1

2

4

5

3

RF channel

primary useractivity

sensingevents

time

CPAN

CPAN

CPAN

CPAN

CPAN

CPAN

CPAN

CPAN

CPAN CPANactivity

Fig. 2. CPAN frequency hopping.

J. Mišic, V.B. Mišic / Computer Networks 54 (2010) 605–617 607

Not all errors have the same impact, though. A missedinactive channel is just a missed opportunity which isnot too critical as long as there are other inactive channelsavailable; a missed activity on a channel, on the otherhand, can harm the CPAN operation if that channel hasbeen selected for data transmission. In order to reducethe probability of errors of the latter kind, the delay indetecting the beginning of primary user activity (i.e., theend of a spectral opportunity) should be lower than thecorresponding delay in detecting its end (i.e., the beginningof a spectral opportunity). This may be accomplished by

sensing inactive channels more frequently than the activeones. Note that, in this context, ‘inactive’ refers to channelswhich are marked as inactive in the channel map, sincethis is the only information available to a CPAN piconetand its coordinator.

Preferential treatment of inactive channels may beaccomplished by modulating the sensing probability, i.e.,by choosing the probability that an inactive channel is se-lected for sensing to be exactly w times higher than thecorresponding probability for an active channel. By adjust-ing the value of w, hereafter referred to as the weight factor


(for idle channels), we can reduce or increase the meansensing interval within certain limits and, thus, reducethe sensing error for inactive channels. The correspondingerror for active channels will be changed in inverse propor-tion. Pseudocode for this algorithm is shown in Algorithm1.

Algorithm 1. Differential sensing via probability modula-tion algorithm.

We note that a number of papers deal with sensing is-
sues in cognitive networks [16,11,18]. However, most ofthem discuss sensing from the perspective of the physical(PHY) layer of the protocol stack, and thus take ‘coopera-tion’ to mean the combination of sensing results from sev-eral sensing nodes in order to improve the confidence inthose results, rather than in the sense used in this paper.A recent paper discusses the so-called differential sensing[13] which is shown to achieve a reduction in sensing er-ror; however, this technique uses static partitioning only,and the results are thus not directly comparable to thosepresented here.
3. Analytical model of sensing with probabilitymodulation

Let us now present a probabilistic model of the sensingprocess. Let the working spectrum band be partitioned intoN narrowband RF channels (which we will refer to as theworking channel set), and let each primary user be activeon a distinct channel from that group. (The common con-trol channel is excluded from this group.) Let us also de-note relevant variables in the active and inactive (free)periods of the channel state with subscripts a and f, respec-tively, while subscripts r and o refer to real and observedvalues of the network parameters, respectively. In the anal-ysis that follows, we assume that active and inactive timeson each channel follow probability distributions withcumulative density functions Ta;rðxÞ and Tf ;rðxÞ, and meanvalues of Ta;r and Tf ;r , respectively. Actual mean value ofthe cycle time will be denoted as Tcyc;r ¼ Ta;r þ Tf ;r .

Sensing is performed in a frequency hopping mannerwith the normalized sensing period of Ts (for convenience,we set Ts ¼ 1). Assuming that Ts � Ta;r ; Tf ;r , the probability

distributions of active and inactive times of primary usersmay be taken to be discrete, and their state changes can oc-cur at the boundaries of the sensing period Ts. Let us de-note the Probability Generating Functions (PGFs) foractive and idle times of primary user activity as

Ta;rðzÞ ¼X1k¼0

paðkÞzk

Tf ;rðzÞ ¼X1k¼0

pf ðkÞzk

ð1Þ

For example, if Ta;r and Tf ;r are geometrically distributedwith parameters a and b, respectively, then paðkÞ ¼að1� aÞk�1 and pf ðkÞ ¼ bð1� bÞk�1.

3.1. Sensing periods and residual sensing times

Let the mean observed durations of active and inactiveperiod be Ta;o and Tf ;o, respectively. The probability that achannel is inactive, as observed via the channel map, ispf ;o ¼ Tf ;o=ðTa;o þ Tf ;oÞ, while the observed probability thatchannel is occupied by the primary user is pa;o ¼ 1� pf ;o.The mean observed numbers of inactive and active chan-nels are Nf ;o ¼ pf ;oN and Na;o ¼ pa;oN ¼ N � Nf ;o, respec-tively. The probability that a channel is actually inactiveis pf ;r ¼ Tf ;r=ðTa;r þ Tf ;rÞ – pf ;o; by the same token, pa;r – pa;o.

Fig. 3 shows the relationship of actual and observed(in)activity period on a given channel, together with theassociated detection delays.

To model the probability modulation policy, let usintroduce additional w� 1 virtual channels for each inac-tive channel, to give a pool with a total ofNw ¼ wNf ;o þ Na;o ¼ N þ ðw� 1ÞNf ;o channels with equalpriority. The probability of selecting a channel from thispool is pf ¼ wNf ;o=Nw and pa ¼ Na;o=Nw for inactive and ac-tive channels, respectively. The number of inactive and ac-tive channels to be sensed in one cycle are

Xf ¼XminðNf ;o ;XÞ

k¼1

X

k

� �kpk

f ð1� pf ÞX�k

Xa ¼XminðNa;o ;XÞ

k¼1

X

k

� �kpk

að1� paÞX�k

ð2Þ

Since the number of sensors should not exceed the numberof channels in each group, e.g., Xf 6 Nf ;o, inactive channelswill be given priority until all of them are selected for sens-ing. (No channel is assigned to two or more sensing nodesin any given sensing cycle.) The sensing probabilitiesbecome

pf ¼Xf

Nf ;o; Xf < Nf ;o

1; Xf P Nf ;o

8<:

pa ¼Xa

Na;o; Xa < Na;o

1; Xa P Na;o

( ð3Þ

The last line is given for completeness only since, undernormal circumstances, X < N, and pa should not reach 1.

The time between two consecutive sensing events has ageometric distribution. As probabilities of selecting inac-

timeRa

sensing instants

Ta,r

Ta,oTf,r

Tf,oRa

RfRf

channel x

channel y

realactivity

observedactivity

sensingevents

Fig. 3. Discrete channel sensing causes detection delays.


tive and active channels differ, so do the appropriate PGFs,which are

Bf ðzÞ ¼P1i¼1

pf ð1� pf Þi�1zi ¼P1j¼1

bf ;jzj; Xf < Nf ;o

z; Xf P Nf ;o

8><>:

BaðzÞ ¼P1i¼1

pað1� paÞi�1zi ¼P1j¼1

ba;jzj; Xa < Na;o

z; Xa P Na;o

8><>:

ð4Þ

for inactive and active channels, respectively. The meanvalues of these times are bf ¼ limz!1@Bf ðzÞ=@z ¼ B0f ð1Þ, forinactive channels, and ba ¼ limz!1@BaðzÞ=@z ¼ B0að1Þ, for ac-tive ones.

The time between the actual change of channel stateand the moment when it is detected through sensing canbe found as follows. The sensing process for a single chan-nel may be considered as a discrete-time renewal processwhere sensing events correspond to renewal points, whilethe renewal time corresponds to the period between twoconsecutive sensing events [6]. In terms of renewal theory,the time between the channel state change and the nextsensing event is denoted as the residual life (time) or for-ward recurrence time; note that the channel state changecan occur anywhere between two sensing points (whichtake place on the basic sensing slot boundary). This resid-ual time defines the time period in which the where infor-mation about the channel state might differ from theactual channel state. Let us consider a transition from inac-tive to active state, and a random edge j of the sensing slotwithin a sensing period. The probability that the next sens-ing event will occur exactly k basic sensing slots later isbf ;jþk=bf . By summing over all basic sensing slots withinthe sensing period, the probability that the residual sens-ing time is k basic sensing slots is obtained [15] as

Rf ;k ¼X1j¼1

bf ;jþk

bf

¼X1

j¼kþ1

bf ;j

bf

ð5Þ

Note that the first subscript of Rf ;k denotes that the channelis inactive, whereas the second one corresponds to the in-dex within the sequence. Then, the PGF for the residualsensing time and its mean values are

Rf ðzÞ ¼X1k¼0

Rf ;kzk ¼ 1� Bf ðzÞbf ð1� zÞ

Rf ¼ B00f ð1Þ=ð2B0f ð1ÞÞð6Þ

where B00f ð1Þ ¼ limz!1@2Bf ðzÞ@z2 . In a similar fashion, the PGF for

the distribution of the residual sensing time for active-to-inactive transitions and its mean value are obtained as

RaðzÞ ¼X1k¼0

Ra;kzk ¼ 1� BaðzÞbað1� zÞ

Ra ¼ B00að1Þ=ð2B0að1ÞÞð7Þ

3.2. Observed durations of inactive and active periods

Let us now find the probability distribution of the ob-served duration of active and inactive period of a channel.As noted above, the observed durations of inactive and ac-tive channel periods will be affected by delays in detectingthe channel state changes; if the residual sensing time islarger than the period under observation (inactive or ac-tive), an entire (in)activity period may be skipped. Giventhe PGFs for residual sensing times, the probability thatan entire period is skipped is

rf ¼X1k¼2

Ra;k

Xk�1

n¼1

pf ðnÞ ¼X1n¼1

pf ðnÞX1

k¼nþ1

Ra;k ð8Þ

ra ¼X1k¼2

Rf ;k

Xk�1

n¼1

paðnÞ ¼X1n¼1

paðnÞX1

k¼nþ1

Rf ;k ð9Þ

where the second form in both equations has been ob-tained from the first by exchanging the order of summa-tion of series.

The probability distributions of the duration of inactiveand active periods, conditioned on the event that they arenot skipped in sensing (which means that at least onesensing event had occurred during the given inactive or ac-tive period), are

Hf ðzÞð1� rf Þ ¼X1n¼1

pf ðnÞznXn

k¼0

Ra;k

HaðzÞð1� raÞ ¼X1n¼1

paðnÞznXn

k¼0

Rf ;k

ð10Þ


From expressions (8) and (9) it follows that 1� rf ¼P1n¼1pf ðnÞ

Pnk¼0Ra;k and 1� ra ¼

P1n¼1paðnÞ

Pnk¼0Rf ;k. There-

fore, Hf ð1Þ ¼ 1 and Hað1Þ ¼ 1, which shows that Hf ðzÞand HaðzÞ are indeed probability generating functions.

Finally, we can derive the expressions for the probabil-ity distribution of observed values of inactive and activeperiods on the channel. The PGF for the duration of inactiveperiod is

Tf ;oðzÞ ¼ HiðzÞðð1� raÞ þ ð1� psaÞrazTcyc;r

þ ð1� psaÞðrazTcyc;r Þ2 þ � � �þÞ Rf ðzÞRaðzÞ

ð11Þ

After summing the infinite series we obtain

Tf ;oðzÞ ¼Hf ðzÞð1� raÞ

1� razTcyc;r

Rf ðzÞRaðzÞ

ð12Þ

Since Hf ð1Þ ¼ 1, it follows that Tf ;oð1Þ ¼ 1, which showsthat Tf ;oðzÞ is indeed the probability generating functionand its mean value is

Tf ;o ¼ T 0f ;oð1Þ ð13Þ

In a similar way, we obtain

mean sensing period when active

2040

6080

100

channels246810

weight

05

101520253035

(a) Mean sensing interval for active channels

d

mean sensing period when idle

2040

6080

100

channels 246810 weight

02468

10

(c) Mean sensing interval for idle channels

012345

Fig. 4. Mean sensing interval expressed in unit sensing intervals. On the left, resuunder fixed N ¼ 50, variable duty cycle c.

Ta;oðzÞ ¼HaðzÞð1� rf Þ

1� rf zTcyc;r

RaðzÞRf ðzÞ

ð14Þ

with mean value of Ta;o ¼ T 0a;oð1Þ.Eqs. (3), (6)–(10), (12) and (14), allow us to find the val-

ues of pf ;o; pf ;r ; pa;o; pa;r ;pf ;pa; Tf ;o; Ta;o, and Rf ;Ra. Further-more, mean detection delays are ð1� rf ÞRa andð1� raÞRf , for detection of inactive and active channelstate, respectively.

3.3. Probability of incorrect information about channelactivity

All sensing points within a single active period of a pri-mary user will find the channel active, and this informationwill be recorded in the channel map. Once the primary userends its activity, this information becomes incorrect; it willbecome correct again upon the next sensing point whichoccurs, on the average, Ra basic sensing slots after the firststate transition of the primary channel. If the probabilitythat the primary user will have a single transition from ac-tive to inactive state between two successive sensingevents is Pð1Þa ¼

P1n¼0Ra;n

P1k¼nþ1pf ðkÞ, the joint PGF for the

duration of residual sensing time and inactive time of theprimary user may be expressed as

mean sensing period when active

0.20.4

0.60.8

uty cycle2 4 6 8 10

weight

05

1015202530

(b) Mean sensing interval for active channels

mean sensing period when idle

0.20.4

0.60.8

duty cycle2 4 6 8 10weight(d) Mean sensing interval for idle channels

lts under fixed c ¼ 0:5, variable number of channels N; on the right, results


Gaðz; yÞð1Þ ¼1

Pð1Þa

X1n¼0

Ra;nznX1

k¼nþ1

pf ðkÞyk ð15Þ

and the time interval during which the channel state infor-mation in the channel map is incorrectly considered active is

La ¼ Pð1Þa limz!1

limy!1

@Gð1Þa ðz; yÞ@z

þ � ð16Þ

where the error � reflects the possibility of incorrect infor-mation caused by multiple state transitions. The differencemay easily be obtained but the detailed derivation, whichcan be found in [12], is not shown here due to limited space.

The probability that the channel is incorrectly observedto be in the active (inactive) state is /a ¼ La=Ta;o and/f ¼ Lf =Tf ;o, respectively, with the complementary proba-bilities (of correct observed state) of /0a ¼ 1� /a and/0f ¼ 1� /f , respectively.

Given that the primary user is inactive or active withthe probabilities pf ;r ¼ Tf ;r=ðTa;r þ Tf ;rÞ and pa;r ¼ 1� pf ;r ,respectively, the number of channels with obsolete infor-mation can be characterized with the PGF of

Eðw; z; yÞ ¼XN

k¼0

Xk

i¼0

XN�k

j¼0

Nk

� �pk

a;rð1� pa;rÞN�kwk

� ki

� �/i

að1� /aÞk�izi N � k

j

� �/j

f ð1� /f ÞN�k�jyj

ð17Þ

mean detection delay (beginning of activity)

2040

6080

100


0123456

(a) Mean detection delay for beginning of activity on a channel (

mean detection delay (end of activity)

2040

6080

100


02468

10

(c) Mean detection delay for end of activity on a channel

Fig. 5. Sensing error expressed through the delay in detecting a change in channeright, results under fixed N ¼ 50.

Mean number of channels for which the information ofbeing in the active or inactive state (obtained earlier) is ob-solete, is Ea ¼ @Eð1;1;1Þ

@z and Ef ¼ @Eð1;1;1Þ@y , for active and inactive

channels, respectively. Finally, mean number of observedactive and inactive channels can, then, be obtained asNa;o ¼ pa;oN and Na;i ¼ pf ;oN, respectively.

4. Performance evaluation

Let us now investigate the practical meaning of the for-mulae derived above. To that end, let us assume that thedistribution of active and inactive periods of primary useractivity is geometric, i.e., Ta;rðzÞ ¼

P1k¼1að1� aÞk�1zk and

Tf ;rðzÞ ¼P1

k¼0bð1� bÞk�1zk, with parameters a ¼ 1=Ta;r

and b ¼ 1=Tf ;r . With these values, we have solved the equa-tions shown above to calculate a number of performancemeasures, including the mean sensing interval, mean num-ber of channels with incorrect (obsolete) information inthe channel map, and mean duration (lifetime) of thatinformation, for both inactive and active channels. Our cal-culations were done using Maple 11 from Maplesoft, Inc.[10], truncating the infinite series for various PGFs after500 members. All time variables are expressed in units ofbasic sensing period Ts. The default parameter values wereX ¼ 10 channels sensed in each sensing cycle, out of thetotal of N ¼ 50 channels with mean activity/inactivityperiods of Ton ¼ Toff ¼ 50 basic sensing periods (which

mean detection delay (beginning of activity)

0.20.4

0.60.8duty cycle 2

46

810

weight

00.5

11.5

22.5

33.5

b) Mean detection delay for beginning of activity on a channel

mean detection delay (end of activity)

0.20.4

0.60.8duty cycle 2

46

810

weight

02468

101214

(d) Mean detection delay for end of activity on a channel

l status (analytical results). On the left, results under fixed c ¼ 0:5; on the


translates into mean activity period of 100 basic sensingperiods and duty cycle of c ¼ 0:5). Two experiments wereperformed in which the independent variables were thenumber of channels and duty cycle, respectively, togetherwith the weight factor w.

Performance of the sensing process is perhaps best rep-resented in the diagrams of Fig. 4 which show the meansensing interval for active and idle channels in upper andlower row, respectively. In all diagrams, the modulationweight values were 0.9, 1.0, 2.0, 4.0, 8.0, and 10.0, withthe value of 1.0 corresponding to uniform random sensing.For the diagrams on the left, the duty cycle of primarysources was kept fixed at c ¼ 0:5 while the channel countwas varied between N ¼ 10 and 100; diagrams on the rightwere obtained with duty cycle varied between c ¼ 0:1 and0.9, while the number of channels was constant at N ¼ 50.(Different orientation of the axes was introduced for im-proved visibility.)

As can be seen, the mean sensing intervals exhibit an al-most linear increase with the number of channels, andmonotonic but not quite linear increase with the duty cycleof active sources, provided the weight factor w is largerthan one. But most importantly, differential sensingthrough probability modulation does decrease the meansensing interval for idle channels, at the expense ofincreasing the corresponding value for active channels;this was indeed our primary objective when applying thistechnique.

mean detection delay (beginning of activity) [simulation]

2040

6080

100


0123456

(a) Mean detection delay for beginning of activity on a channel (b

mean detection delay (end of activity) [simulation]

2040

6080

100


02468

10

(c) Mean detection delay for end of activity on a channel

Fig. 6. Sensing error expressed through the delay in detecting a change in channeright, results under fixed N ¼ 50.

The performance of the sensing process is further pre-sented in the diagrams of Figs. 5 and 7, which show themain measures of the accuracy of the sensing process:the mean delay in detecting changes in primary user activ-ity and the mean number of channels for which the infor-mation in the channel map is incorrect. Both sets ofdiagrams were obtained with the same set of independentvariables as above.

First set of diagrams, Fig. 5, shows the mean delay indetecting the end of primary user activity on a channel(upper row) and the mean delay in detecting the beginningof primary user activity (lower row). Second set of dia-grams, Fig. 7, shows the mean number of active channelsmistakenly thought to be idle (upper row), and the meannumber of idle channels mistakenly thought to be active(lower row).

As could be expected, all errors increase when the num-ber of working channels increases; the change is mono-tonic but not linear. This pattern can be countered byincreasing X, the number of channels sensed in each sens-ing cycle or, if that is not possible, by reducing the numberof working channels N. The diagrams in Figs. 7a and c, 5cand a, vividly demonstrate the feasibility of the latterapproach.

When the weight factor w is increased, the errors wehave tried to minimize indeed decrease: the mean detec-tion delay for the beginning of channel activity, Fig. 5aand b, and the number of idle channels thought to be

mean detection delay (beginning of activity) [simulation]

0.20.4

0.60.8duty cycle 2

46

810

weight

00.5

11.5

22.5

33.5

) Mean detection delay for beginning of activity on a channel

mean detection delay (end of activity) [simulation]

0.20.4

0.60.8duty cycle 2

46

810

weight

02468

101214

(d) Mean detection delay for end of activity on a channel

l status (simulation results). On the left, results under fixed c ¼ 0:5; on the


active, Fig. 7c and d. The price to pay for this improvementin one component of the error is an increase in the othererror, i.e., the delay in detecting the end of channel activityand the number of active channels thought to be inactive.

In order to assess the validity of the analytical frame-work, we have built a simulator of a cognitive CPAN thatuses the probability modulation algorithm. The simulatorwas built using the object-oriented Petri Net simulationengine Artifex by RSoft Design, Inc. [14]. The main perfor-mance indicators of the sensing process, the mean delay indetecting changes in primary user activity and the meannumber of channels for which the information in the chan-nel map is incorrect, but obtained through simulation thistime, are shown in Figs. 6 and 8. As can be seen, the agree-ment between analytical and simulation results is quitegood, which confirms the validity of the analytical frame-works. Similar degree of agreement was obtained for otherperformance indicators such as mean sensing interval, butwe do not show it here due to space limitations.

An interesting observation may be made from diagramsobtained with variable duty cycle of primary sources inFigs. 5b, and 7d. Namely, at low values of the weight factorw, both type of errors have highest values near the middleof the range, i.e., around c ¼ 0:5, but decrease towards the

error in mean number of active channels

2040

6080

100


0

5

10

15

(a) Mean number of active channels mistaken to be inactive

0

2

4

6

8

error in mean number of idle channels

2040

6080

100


01234567

(c) Mean number of inactive channels mistaken to be active.

0.

0.

1.

1.

Fig. 7. Sensing error expressed through the number of channels for which the inresults under fixed c ¼ 0:5; on the right, results under fixed N ¼ 50.

edges on both sides. This effect, however, tends to disap-pear when the weight factor w is increased. A similar phe-nomenon is barely visible in the diagrams of Figs. 5d and7b, where it is essentially masked by the increase of errorswith the weight factor w.

5. Optimizing the weight factor

A far more interesting observation can be made fromthe diagrams of Fig. 9, where the top row shows meandetection delay for any change in primary user activity,while the bottom row shows the mean number of channelsfor which the information in the channel map is erroneous,regardless of whether they are actually active or idle. Care-ful examination of Fig. 9b and d reveals that it might bepossible to minimize the detection delay or the numberof channels with erroneous information. On account ofthis, we have numerically found the values of the weightfactor w which, given the number of channels N and dutycycle c, result in minimum values of the mean detectiondelay and in the mean number of channels with erroneousinformation. These values are shown in Fig. 10; as can beseen, the values of w that minimize the values of the two

error in mean number of active channels

0.20.4

0.60.8duty cycle 2

46

810

weight(b) Mean number of active channels mistaken to be inactive

error in mean number of idle channels

0.20.4

0.60.8duty cycle 2

46

810

weight

0

4

8

2

6

(d) Mean number of inactive channels mistaken to be active

formation in the channel map is incorrect (analytical results). On the left,

error in mean number of active channels [simulation]

2040

6080

100


0

5

10

15

(a) Mean number of active channels mistaken to be inactive

error in mean number of active channels [simulation]

0.20.4

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weight

0

2

4

6

8

(b) Mean number of active channels mistaken to be inactive

error in mean number of idle channels [simulation]

2040

6080

100


01234567

(c) Mean number of inactive channels mistaken to be active

error in mean number of idle channels [simulation]

0.20.4

0.60.8duty cycle 2

46

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weight

0

0.4

0.8

1.2

1.6

(d) Mean number of inactive channels mistaken to be active

Fig. 8. Sensing error expressed through the number of channels for which the information in the channel map is incorrect (simulation results). On the left,results under fixed c ¼ 0:5; on the right, results under fixed N ¼ 50.


variables of interest are close, but not identical, to eachother.

However, a number of obstacles remain when imple-menting the optimized algorithm. First, to make the prob-ability modulation algorithm adaptive with respect to themain parameters of the cognitive CPAN – namely, thenumber of channels and the duty cycle of active sources– and thus improve its performance, the value of theweight factor w which is used in Algorithm 1 would haveto reflect the duty cycle of primary user activity. But the ac-tual values of the parameters such as activity period andduty cycle are not known to the CPAN, which can only inferthem through sensing of primary users’ activity on theworking channel set.

In order to assess the magnitude of the discrepancy be-tween the duty cycle values observed through the channelmap and the corresponding true values, we have per-formed measurements using the simulator. The ratio ofduty cycles, represented as a function of actual duty cyclec and weight factor w, is shown in Fig. 11.

As can be seen, the observed value of duty cycle is rea-sonably close to the actual value, except in the far corner ofthe diagram which corresponds to low values of the dutycycle and high values of the weight factor. Since the opti-mum weight factor for both minimum delay and minimumerror is around one for duty cycle values of 0.6 and below,as can be seen from the diagrams in Fig. 10, this discrep-

ancy may safely be ignored, and observed value of the dutycycle can be used to determine the optimum value of theweight factor.

However, the observed value of the duty cycle used inthe last diagram is only the statistical mean value; in sim-ulation, as well as in real life, this could be obtained only asa long-term average which is not feasible. The instanta-neous value, which could be readily obtained from ob-served durations of activity and inactivity periods, wouldexhibit large fluctuations due to the random character ofprimary user activity. These fluctuations have to be re-duced, or smoothed, before being used to calculate the de-sired value of the weight factor w. A commonly usedsmoothing algorithm is the exponential weighted movingaverage (EWMA) [4], where the value of an average XðeÞ

after collecting i samples of a variable x is obtained as

XðeÞi ¼ SF � XðeÞi�1 þ ð1� SFÞ � xi ð18Þ

where SF denotes the EWMA smoothing constant whichtakes values between 0 and 1. (We do not use more com-mon label a so as to avoid confusion with the previouslydefined reciprocal of the mean duration of activity period.)

However, initial experiments have shown that expo-nential smoothing of duty cycle values is not sufficient,and that the remaining variability is still too high for usefulresults to be obtained. Therefore, we have performed

mean detection delay

2040

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0123456

(a) Mean detection delay for change of activity on a channel


0.20.4

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weight

0

2

4

6

8

(b) Mean detection delay for change of activity on a channel

error in mean number of channels

2040

6080

100


0

5

10

15

20

(c) Mean number of channels for which incorrectinformation is recorded in the channel map

error in mean number of channels

0.20.4

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weight

02468

10

(d) Mean number of channels for which incorrectinformation is recorded in the channel map

Fig. 9. Total sensing error. On the left, results under fixed c ¼ 0:5; on the right, results under fixed N ¼ 50.

weight that results in minimum delay

0.20.4

0.60.8

duty cycle2040

6080

100

channels

02468

10

(a) Optimum weight to minimize the total delay

weight that results in minimum error

0.20.4

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duty cycle2040

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channels

02468

10

(b) Optimum weight to minimize the total error

Fig. 10. Optimum weight values that lead to best performance in terms of the number of channels with erroneous information and mean detection delay.


smoothing in two stages, as recommended in [4]. First, weused a plain moving window average where the averagevalue is simply the arithmetic mean of the last n values:

XðwÞi ¼ 1n

Xi

j¼i�n

xj ð19Þ

Second, we applied exponential smoothing to these aver-ages. The EWMA obtained in this manner is, then, used

to update the value of the weight factor w according tothe dependency shown in Fig. 10a; this is done in regularintervals of tu basic sensing periods.

Overall, this approach has been found to give satisfac-tory results, and the performance of the algorithm, usingthe moving window size n ¼ 10, smoothing constantSF ¼ 0:9, and update interval tu ¼ 5000, is shown inFig. 12. As can be seen, the values for both the detec-tion delay and the number of channels with erroneous

duty cycle: observed vs. actual

0.20.4

0.60.8duty cycle 2

46

810

weight

00.5

11.5

22.5

Fig. 11. Ratio of mean observed duty cycle vs. actual duty cycle as afunction of actual duty cycle c and weight factor w.


information are virtually identical to the minimum valuesobtained when the weight factor c has a fixed value.Moreover, the performance is not very sensitive to thevalues of n, a, and tu. As an example, the diagrams in

mean detection delay (in unit sensing intervals)

duty cycle

adaptive weight

0

1

2

3

4

0 0.2 0.4 0.6 0.8 1

minimum value obtainedwith a fixed weight

(a) Mean detection delay

0

1

2

3

4

Fig. 12. Comparing the performance of adaptive (soli


0.2 0.4 0.6 0.8duty cycle4000

800012000

16000

weight update interval

00.5

11.5

22.5

33.5

(a) Mean detection delay

0

1

2

Fig. 13. Performance of the adaptive weight algorithm as a f

Fig. 13 show the dependency of the mean error on the ac-tual duty cycle c and the update interval tu; it can be seenthat the mean error is virtually independent of the updateinterval.

6. Conclusion

In this paper, we have presented a simple algorithmthat assigns different relative probability of channel sens-ing to idle and active channels in order to reduce sensingerror in cognitive CPANs. We have presented an analyticalframework that allows accurate analysis of the perfor-mance of this algorithm, and we have shown that it is in-deed effective in reducing the sensing error. We havealso presented a simple modification that allows for adap-tive determination of the said probability, and we haveshown that it is capable of indeed achieving minimumsensing error for a wide range of parameter values, in par-ticular, the duty cycle of primary users’ activity.

Our results confirm that accurate channel sensing isfeasible even when the number of sensing nodes is well be-low the number of available channels, and that modulation

mean errror in the number of channels

duty cycle0 0.2 0.4 0.6 0.8 1

adaptive weight

minimum value obtainedwith a fixed weight

(b) Mean number of channels with erroneous information

d gray line) vs. fixed weight algorithm (circles).

mean number of channels with erroneous information

0.2 0.4 0.6 0.8duty cycle4000

800012000

16000

weight update interval

0.51

.52

.53

(b) Mean number of channels with erroneous information

unction of duty cycle c and weight update interval tu .


of sensing probability may help reduce the sensing errorwith respect to inactive channels to almost any desired va-lue; the price to pay for this is the decrease in accuracywith respect to active channels.

In future work, we plan to address imperfect transmis-sion of sensing results, together with other issues relatedto the design, analysis, and performance optimization offrequency hopping CPANs.

References

[1] I.F. Akyildiz, W.-Y. Lee, M.C. Vuran, S. Mohanty, Next generation/dynamic spectrum access/cognitive radio wireless networks: asurvey, Computer Networks 50 (2006) 2127–2159.

[2] Bluetooth SIG, Core Specification of the Bluetooth System. Version2.0 + EDR, November, 2004.

[3] C.-T. Chou, N. Sai Shankar, H. Kim, K.G. Shin, What and how much togain by spectrum agility?, IEEE Journal on Special Areas inCommunications – Wireless Series 25 (3) (2007) 576–588

[4] S. Delurgio, Forecasting – Principles, and Application, McGraw-Hill/Irwin, New York, 1998.

[5] S. Geirhofer, L. Tong, B.M. Sadler, Cognitive medium access: Aprotocol for enhancing coexistence in WLAN bands, in: ProceedingsGlobal Telecommunications Conference GLOBECOM’07, Washington,DC, November 2007.

[6] D.P. Heyman, M.J. Sobel, Stochastic Models in Operations Research,Stochastic Processes and Operating Characteristics, vol. I, McGraw-Hill, New York, 1982.

[7] W. Hu, E. Sofer, IEEE 802.22 wireless RAN standard PHY and MACproposal, Technical Proposal Submitted to IEEE 802.22 WG, 22-05-0098-00-0000, IEEE 802.22 WG, 2005.

[8] IEEE, Wireless MAC and PHY specifications for high rate WPAN, IEEEStd 802.15.3, IEEE, New York, NY, 2003.

[9] P.K. Lee, Joint frequency hopping and adaptive spectrumexploitation, in: IEEE Military Communications ConferenceMILCOM2001, vol. 1, October 2001, pp. 566–570.

[10] Maplesoft, Inc. Maple 11, Waterloo, ON, Canada, 2007.[11] S. Mishra, A. Sahai, R. Brodersen, Cooperative sensing among

cognitive radios, in: Proceedings of IEEE International Conferenceon Communications ICC 2006, vol. 4, Istanbul, Turkey, June 2006, pp.1658–1663.

[12] J. Mišic, V.B. Mišic, The impact of inaccurate sensing information incognitive wireless personal area networks, in: IEEE CogNet 2008,Beijing, China, May 2008.

[13] J. Mišic, V.B. Mišic, Performance of cooperative sensing at the MAClevel: error minimization through differential sensing, IEEETransactions on Vehicular Technology 58 (5) (2009) 2457–2470.

[14] RSoft Design, Artifex v.4.4.2, RSoft Design Group, Inc., San Jose, CA,2003.

[15] H. Takagi, Queueing Analysis, Vacation and Priority Systems, vol. 1,North-Holland, Amsterdam, The Netherlands, 1991.

[16] D. Cabric, S.M. Mishra, D. Willkomm, R. Brodersen, A. Wolisz, Acognitive radio approach for usage of virtual unlicensed spectrum,in: Proceedings of 14th IST Mobile Wireless CommunicationsSummit, Dresden, Germany, June 2005.

[17] Z. Yang, J. Garcia-Luna-Aceves, Hop-reservation multiple access(HRMA) for ad-hoc networks, in: 18th Annual Joint Conference of theIEEE Computer and Communications Societies INFOCOM’99, vol. 1,New York, NY, March 1999, pp. 194–201.

[18] J. Zhao, H. Zheng, G.-H. Yang, Spectrum sharing through distributedcoordination in dynamic spectrum access networks, WirelessCommunications and Mobile Computing 7 (9) (2007) 1061–1075.

Jelena Mišic received her PhD degree inComputer Engineering from University ofBelgrade, Serbia, in 1993. She is currentlyProfessor of Computer Science at RyersonUniversity in Toronto, Ontario, Canada. Hercurrent research interests include wirelessnetworks and security in wireless networks.She is a Senior Member of IEEE and Member ofACM.

Vojislav B. Mišic received his PhD in Com-puter Science from University of Belgrade,Serbia, in 1993. He is currently Professor ofComputer Science at Ryerson University inToronto, Ontario, Canada. His research inter-ests include modeling and performance eval-uation of wireless networks, and systems andsoftware engineering. He is a Senior Memberof IEEE, and member of ACM and AIS.

making the best of limited resources: optimized differential sensing in cognitive pans

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