A Sequential Test Based Cooperative Spectrum Sensing Scheme for Cognitive Radios

8/6/2019 A Sequential Test Based Cooperative Spectrum Sensing Scheme for Cognitive Radios

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A Sequential Test Based Cooperative Spectrum Sensing Scheme for Cognitive RadiosYeelin Shei and Yu T. SuDepartment of Communications Engineering

National Chiao Tung University1001 Dar-Shei Rd., Hsinchu, 30056, TAIWAN, +886-3-573-1820E-mail: [email protected]

Abstract-Fast and accurate spectrum sensing is crucial inrealizing a reliable cognitive network. Cooperative spectrumsensing can help reducing the mean detection time and increasingthe agility of the sensing process. However, when the numberof cognitive users is large, the bandwidth need for the controlchannel that are used to report the secondary user nodes' resultsto the fusion center may become excessively large. this paper,we apply the sequential probabili ty rat io test (SPRT) controlthe average number of the reporting bits. It is shown that theproposed technique not only reduces the mean detection time andbandwidth but also outperforms its non-sequential counterpart.We derive the relationships amongst the global performance, missprobabllity and false alarm probability and show how to controlthe average number of reports by thresholding the distributedcognitive users.

I. INTRODUCTION

Cognitive radio (CR) technique has been proposed to exploitthe spectrum holes-the frequency bands which are not usedat some time or space-for license-exempt usages [3]. Thespectrum below 3 GHz has become increasing crowded butreport [1] has shown that the utilization of licensed spectrumranges from 15% to 85% only. Inspired by the CR conceptand the fact that the some TV channels are unused in manyrural areas, IEEE has approved the establishment of a workinggroup to develop a CR-based wireless standard utilizing thespectrum between 54 MHz and 862 MHz [2].The realization of a CR-based wireless network depends,among other things, on the assumptions that network users areable to accurately sense the existence of spectrum holes and aproper coordination protocol among the unlicensed users is inplace. The sensing result is used to indicate the absence o)or presence of a primary user in the band of concern.It is desired that the sensing method gives high detectionprobability, that is, the probability that the sensing output iswhen the spectrum is in use, which is a measure on how wellthe primary user are protected. On the other hand, the falsealarm probability, i.e., the probability that the sensing resultis HI when the spectrum is not used, must be low enoughto ensure efficient usage of the spectrum for a false alarmwill prevent a secondary user (SU) from using the licensedband even though the spectrum is available. Another criticalconcern about the sensing method used is the average timeneeded to make a spectrum decision. As the availability of agiven band is non-deterministic, it is important for a SU toseize the transmission opportunity as soon as possible.It has been shown [4,5] that cooperative spectrum sensing

978-1-4244-2644-7/08/$25.00 2008 IEEE

improves the detection and false alarm probability performance [6] and enhances the agility [7]. A cooperative sensingscheme is usually conducted in two successive-sensing andreporting-stages. In the first stage, every cognitive user performs sensing independently using some detection method thatrequires a fixed observation interval to make a local decisionwhich is then sent to the common receiver called fusion center(FC) in the second stage through a control channel. The fusioncenter then make a final decision as to if 0) or ( isaccepted.To reduce the control channel's bandwidth requirement, acognitive user needs to quantize its decision before sendingit to the FC. Quantization of local observation in distributeddetection has attracted much research interest [8-12]. Althoughquantization error and signal-to-noise ratio (SNR) loss areintroduced [9], three-bit quantization is enough to recover most

of the performance loss [10]. [11], i t is shown that a decisionrule based on one-bit quantization can be asymptoticallyoptimal as the number of cooperative users and hence thatof the reporting bits approaches infinity. In general, the morereporting bits the FC collects, the more reliable the decisionis. Similarly, the reliability of the sensor-to-center report is anincreasing function of the sensor's observation duration.Conservation of the reporting (control) channel bandwidthand reduction of the average observation time can be accomplished if a sequential test instead of a fixed sample sizetest is used for the former can make a sensing decision assoon as it collects sufficient evidence (observations). Thispaper proposes a cooperative sensing scheme that employssequential tests in both sensor nodes and the FC. We restrictour investigation to the case of one bit quantization reporting.The sequential test we used is the so-called probabili ty ratiotest (SPRT) [13]. SPRT is an optimal test that minimizes theaverage required sample size among all tests which achievethe same detection and false-alarm probabilities performance,if the samples (observations) are independent. [12] suggestsa non-sequential approach which requires that each cognitiveuser reports to the FC only if its decision is reliable. Althoughthe required control channel bandwidth can be reduced, it isdifficult to determine the reliability thresholds that meet theperformance requirement. We present a systematic method toderive the detector parameter values that are guaranteed toyield the designed performance.The rest of the paper is organized as follows. SectionII, the system model is introduced and the major propertiesof the SPRT is briefly reviewed. In Section III we present


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key equations that relate various parameters of the proposedsequential distributed sensing method. Simulation results areprovided in Section IV, followed by conclusion in Section V.II. SYSTEM DESCRIPTION AN D B A S I C S E Q UE N T IA L T E S T SThe setup of this system is based on the IEEE 802.22WRAN scenario. The system model we consideration is shownin Fig. 1, which includes a primary user, an FC, and cognitivepremiss equipments (CPEs) as SUs. The SUs are randomly

distributed within the coverage radius of the FC.

(3)

(4)

p(Yk!H IT p(YkIHI)p(YkIHo) k=1 p(YkIHo)p(YkIHl) If p(YkIHl)p(YkIHo) k=1 p(YkIHo)A(Yk)A(Yk- 1)

types of detection errors, namely, the false alarm probability,and the miss probability, Let Yk be the observationat time k and Yk [Yl, Y2, .. . ,Yk]T be the column vectorconsisting of i.i.d. observations. Then the likelihood ratio

(LR) of the kth observation isA(Yk) p(YkIHI)p(YkIHo)

and that for Yk is

30

20

10The decision rule for the SPRT with thresholds "lo and "l1,denoted by T(170, T}I) is given by

-1 0

-2 0

-3 0

A(Yk) 2:: T}IA(Yk) :::; "lo

"l1 A(Yk) 2:: "loacceptaccept otaking another observation (5)

Fig. 1. A CR network that consists of a primary user terminal and severalSU terminals with one as the fusion center (common receiver).

The received power Pi at the ith SU terminal and thecorresponding SN R ri are respectively given byPi d ~ L P , 1 , ,Mz

(8)

(7)

log ( l ~ a ) + (3) log C ~ t J )E[L(YIH

1-{3 {3"l1 "lo( 1-Theorem 2: The average sample size of 171) is

( l - O ' ) I O g ( l ~ a ) + o I O g C ~ t J )E[KIHoJ = E[L(yIHo)]

The following properties of the SPRT are well-known [13].Theorem 1: Let P p a , (3 be the false-alarm anddetection probabilities associated with the SPRT T("lo, "l1),

then the two thresholds 770, "l1 satisfy

where K is the stopping time and

1-{3 {3"l1 :::; - - , "loa -aIf at the stopping time (i.e., the time when a decision toaccept or o is made), the LR is exactly equal to thecorresponding threshold, which happens if we have continuousobservation and the LR is a continuous process, the above twoinequalities become equalities.

L(YKIHi ) log [A(YKIHi )] , L(yIHi ) log [A(yIHAgain, if the log-likelihood ratio (LLR) is a continuous process, we have

For discrete observations, these two equations are only approximations but in many cases they are excellent approximations.

(2)i"Yi 10log 2' 1" , ,M(j

-1 0

and

where is the transmit power of the primary user, i is thedistance between the primary user and the i th SU, O'.L is thepath loss factor, is a scaling factor, is the noise powerand is the total number of SUs.Approaches to solve a binary hypothesis test are generallycategorized into fixed sample size tests and sequential or variable sample size tests. For the former class, one of two possibleactions is taken-accept or reject the null hypothesis Ho-after afixed number of samples are observed. In a sequential test, thenumber of samples needed to make a decision is not predetermined but depends on the values of the received samples. As itcan stop testing whenever the actual received samples providesufficient evidence for accepting or rejecting a hypothesis, theobservation time needed to make a decision is random. TheSPRT is a special class of sequential tests that offer an optimalproperty when the samples are identical and independentlydistributed (i.i.d.). I t is a Neyman-Pearson type test whosethresholds are functions of the required performance. Morespecifically, the two thresholds, "lo, "l1, are determined by two


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Fig. 2. Block diagram of the detector used a secondary user.

i ) == { log ( l ~ P f ) = 7702, = 0 (14)log (11;= ) 7712, i 1The FC computes its LLR by summing the LLR of each ditransmitted from the SUs and then compares with the twothresholds determined by the designed global false-alarm andmiss probabilities and This fusion method is similar

(15)

(16)

p log p (1 - p ) log 1 _ p

where is the LR of the FC at the stopping time, andis the corresponding number of sensing bits received from theSUs. Invoking the approximation that the the FC's LR is equalto one of the thresholds at the stopping time, we obtain

to the combination of the Chair-Varshney method [15] and theSPRT.Substituting (14) into (10) and (11), we obtain

log (1 ~ : M ) + log (1 ~ ~ )18)As and where == i ==I} are set by the FC , the FC obtain and from(15) and (16) ,and assign them to SUs. In particular, if ==

and == the thresholds for the FC's SPRT are== while those for the SUs' SPRT are "702 == -1}12.The overall distributed sensing method is shown in Fig. 3.Each cooperative SU obtains its observation (sample), computes the LR or LLR and compares it with the predeterminedthresholds. If the LR value exceeds one of the threshold, thecorresponding decision is reported to the FC, otherwise, nosensing bit is transmitted. The process continues until the FCnotifies the SUs to stop. The FC collects sensing bits from thecooperative SUs. The sensing process stops when the LR orLLR computed by the FC exceeds one of the correspondingthresholds.

Recall that our design parameter (thresholds) values arederived based on the assumption that the stopping LR or LLRvalues at both the FC and the SU terminals are equal to oneof the thresholds. In reality, these values would most likelyexceed one of the thresholds. If we define the excess as thedifference between the stopping LR value and the threshold,then the excess at the FC will result in larger K ' s and thatat the SU terminals leads to smaller K

>'71or


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V. CONCLUSIONAn SPRT-based cooperative spectrum sensing scheme foruse in CR networks has been proposed and analyzed. The

where r 1 is smallest integer greater than or equal to andthe excess of the LLR is given by~ ~ ~ ~ ; ) r/02, if 0 is accepted (23)( ~ ~ 1- ~ ~ ; ) 7]12, if o is rejected

(22)if o is acceptedif o is rejected"'Of "1== "102 02 ,"112 7]12

IV. SIMULATION RESULTSSimulation results of the proposed SPRT-based sensingscheme in the CR network shown in Fig. 1 are reported inthis section. The parameters values used are as follows.SUs are randomly distributed within the 5 km radius of theFC. The secondary BS is 59.7 km away from the primary

user. During the sensing period, each SU keeps sampling itsenergy detector output at a rate of W samples per second andreporting its LR value, if necessary, to the FC until it is toldby the FC to stop sensing. The path loss exponent factor Q ,in (1) is set to be 3.5, and are set at a value such thatthe primary user's SNR at the secondary BS is -2 dB. TheSUs' thresholds are determined by == == 0.01, and

== It is also assumed that each SU can estimate itsreceived SNR perfectly.Fig. 4 shows the relation between the theoretical andK derived by analysis and those estimated by simulationwith 20 SUs. The discrepancy is due to our zero-excess (overtwo thresholds) assumption. Fig. 5 plots the total sensing time

as a function or Under the same environment, theaverage sensing time for a distributed detection strategy withfix-sample-size energy detection at the SU sites and the "AND"fusion [16] at FC is == 94.448. If the "OR" fusion is usedinstead, the sensing time becomes == 67.794. Obviously,our approach achieves significant improvement on the meansensing time performance. However, these curves do exhibitsome discontinuities. (21) shows that the average sensingtime is a function of andBut it is that results in the discontinuities. This is because the FC may receive more thanone reporting sensing bits at the stopping time and if theLLR exceeds one of the thresholds, since == and

== by design, we have == and 7]02 == -1712,

Fig. 6 plots and for different and_ " '02 " '02 "'02K 'So It is found that there is a discontinuity in the excesswhenever the integer part of changes. Fig. 7 plots the four" '02terms in the denominator of with 20 SUs. We find thatremains constant, is small and insensitiveto the threshold while i ] is a decreasing functionof the threshold but as a function of is notcontinuous but exhibit a saw-like shape.

ith CR user node

==+ + +(21)

Fig. 3. Flow chart of the proposed SPRT-based distributed spectrum sensingmethod

C. Sensing Time AnalysisThe complete distributed sensing process consists of twoSPRT stages. If there are SUs in this system joining thecooperative sensing process, M samples are available at eachsampling epoch. The conditional average LR of one M -sampleblock observation is then given by the sum

== Lwhere j ] is the conditional average LR of onesample associated with the ith SU's observation From(8), we have

== (20)where is the total sensing time and is the stoppingLR under includes four parts:

the LR threshold used by the FC.the excess LR at the FC.the excess LR at a SU node.L non-excess stopping LR value at a SU node.According to equation (8) and (20), it can be proved, aftersome algebraic manipulations, that


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,, 0 110111...... 110111110111021-11011102

20

18

1614o12

"iii10;CW 8

10 12 14 16 18 20E[Kfil

-....

~ , o G : i : . . :::M.,

. ~ " G ' : : : . '

....~ , . "

~ i

/ . . . . ~ .o L - - _ L . - . - - _ l . . . . - - - - - - I l . . . . - - - - - - I L . . . . - . I I L . . . . . . . . . I _ - - - - - l . - - - = : . . . : . . t . . a ~ - - - L - - J2 8 10 12 14 16 18 20

Fig. 4. R used in simulation. Fig. 6. Behaviors of 1 and 1- for different26

20610 12 14

12 :.

.2 10o 8

6"T....J 4

' 4 2 K., . ",

2 48 10 12 14 16 18 20

.."eao ... . . . . . .' , . . . . . . . . . . lit ..

2

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[2 0Q)E 18C>c:

. 16 .14

Fig. 5. Normalized sensing time as a function of Fig. 7. The average LR of the four terms in (28) for different

scheme has the advantage of minimizing the control channelbandwidth and the total sensing time while rendering little orno compromise in performance. In fact, the proposed schemeis capable of controlling the average number of sensing bitssent to the FC with any given false alarm and miss probabilitiesperformance requirement.

ACKNOWLEDGEMENTThis work is supported in part by the NCTUIITRI JointResearch Center under Contract G1-97006.

REFERENCES[1] Federal Communications Commission, "Spectrum Policy Task Force,"Rep. ET Docket no. 02-135, Nov. 2002.[2] C. Cordeiro, et al. "IEEE 802.22: An introduction to the first worldwidewireless standard based on cognitive radios," Commun., vol.l , pp. 3847, Apr. 2006 .[3] S. Haykin, "Cognitive radio: brain-empowered wireless communications,"

IEEE Select. Areas Commun., vol. 23, pp. 201-220, Feb. 2005.[4] A. Ghasemi and E. S. Sousa , "Collaborative spectrum sensing foropportunistic access in fading environments," in Proc. 1st IEEE Symp.New Frontiers in Dynamic Spectrum Access Networks, Baltimore, USA,Nov. 8-11, 2005, pp. 131-136.[5] G. Ganesan and Y. Li, "Cooperative spectrum sensing in cognitive radionetworks," in Proc. DySPAN, Nov. 2005, pp. 137-143.

[6] G. Ganesan and Y. G. Li, "Agility improvement through cooperationdiversity in cognitive radio," in Proc. IEEE GlobeCom, St. Louis, USA,Nov. 28-Dec. 2, 2005, pp. 2505-2509.[7] E. Peh and Y. C. Liang, "Optimization for cooperative sensing in cognitiveradio networks," in Proc. IEEE WCNC, Hong Kong, Mar. 11-15, 2007,

pp.27-32.[8] A. Sahai, et ale "Some fundamental limits on cognitive radio," in Proc.Allerton Conf., Monticello, USA, Oct. 2004.[9] W. A. Hashlamoun and P. K. Varshney, "Near-optimum quantization forsignal detection," IEEE Trans. Commun., vol. 44, pp. 294-297, Mar. 1996.[10] R. S. Blum, "Distributed detection for diversity reception of fadingsignals in noise," IEEE Trans. Inform. Theory, pp. 158-164, Jan. 1999.[11] J. F. Chamberland and V. V. Veeravalli, "Decentralized detection insensor networks," IEEE Trans. Signal Proces., Vol. 51, Issue 2,pp. 407416, Feb. 2003.[12] C. Sun, W. Zhang, and K. B. Letaief, "Cooperative spectrum sensing forcognitive radios under bandwidth constraints," in Proc. IEEE Int. WirelessCommun. Networking Conf., Hong Kong, Mar. 11-15,2007, pp. 1-5.[13] A. Wald, "Sequential tests of statistical hypothesis," Annals Math.Statistics, vol. 16, no. 2, pp. 117-186, Jun. 1945.[14] F. F. Digham, et al., "On the energy detection of unknown signals overfading channels," in Proc. ICC, Anchorage, USA, May 11-15,2003, pp.

3575-3579.[15] Z. Chair and P.K. Varshney, "Optimal data fusion in multiple sensordetection systems," IEEE Trans. Aerospace, Elect. Syst., pp. 98-101, Jan.1986.[16] P. K. Varshney, Distributed detection and data fusion, Springer-Verlag,New York, 1997.

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A Sequential Test Based Cooperative Spectrum Sensing Scheme for Cognitive Radios