cognitive ultra wideband radio spectrum sensing window length optimization algorithm

Zeng et al. EURASIP Journal onWireless Communications andNetworking 2014, 2014:18http://jwcn.eurasipjournals.com/content/2014/1/18

RESEARCH Open Access

Cognitive ultra wideband radio spectrumsensing window length optimization algorithmLiaoyuan Zeng1*, Sean McGrath2 and Guanghui Liu1

Abstract

A critical objective of cognitive radio (CR) system is to enhance the spectrum efficiency, and one of the key factors thatcan determine the spectrum efficiency is the system spectrum sensing performance with respect to sensing windowlength. For non-coherent detection-based sensing technique, the length of the sensing window required to meet thedetection criteria is inversely proportional to the detected signal-to-noise ratio (SNR) of the primary users (PUs). Thisfact may result in an inadequate use of the white or gray space for the conventional CR system whose transmissionand sensing window length are both fixed because a high detected PUs SNR can lead to an excessive long fixedsensing window which occupies the potential CR transmission opportunities while a low received PUs SNR can resultin an insufficient sensing window length which degrades the CR detection criteria. In this paper, to improve thespectrum efficiency compared with the fixed sensing/transmission window length-based CR system, we propose anadaptive spectrum sensing window length optimization algorithm. We design the algorithm based on the ultrawideband (UWB) system which is an ideal candidate for the implementation of the CR technology. Based on theanalysis of the CR-UWB’s spectrum sensing technique in terms of the factors such as spectrum efficiency, spectrumsensing length, PUs SNR, detection criteria etc., we formulate the optimization problem into a convex problem, whichenables the proposed algorithm to find the optimal trade-off with low computational complexity between thesensing window length and the desired detection probabilities for the CR-UWB system. Compared with theconventional fixed length spectrum sensing techniques, the proposed algorithm is verified to be able to adapt thelength of the CR-UWB’s transmission window according to the PUs SNR to optimize the use of the available spectrumwhile guaranteeing the PUs from being interfered.

Keywords: Cognitive radio; Ultra wideband; Spectrum sensing

IntroductionFor cognitive radio (CR) [1], ultra wideband (UWB) can beused as an implementation technology [2]. UWB operatesin 3.1 to 10.6 GHz with an extremely low power spectrumdensity (PSD) of -41.3 dBm/MHz [3], which facilitates theunderlay spectrum sharing technique to co-exist with theprimary users (PUs) that operate within the UWB’s widespectrum band [4]. Figure 1 illustrates the band overlapbetween the UWB system and the incumbent wirelesssystems such as wireless LAN [5]. Generally, to protectthe PUs from being harmfully interfered, the CR-UWB’s

*Correspondence: [email protected] of Electronic Engineering, University of Electronic Science andTechnology of China, 2006 Xiyuan Ave., Chengdu 611731, ChinaFull list of author information is available at the end of the article

transmit power can be decreased to a level that is signifi-cantly lower than theUWB’s regular PSD,which can resultin considerably low spectral efficiency.By using orthogonal frequency division multiplexing

(OFDM) [6], as shown in Figure 2, the UWB system canadaptively adjust the transmit power of the OFDM sub-carriers according to the spectrum sensing results withinthe interested spectrum segments [7]. Figure 2 shows theband allocation scheme in the OFDM-based UWB sys-tem. The UWB’s operating band is divided into bandgroups (BGs), each of which contains two or three sub-bands (SBs), and each SB consists of a series of mutu-ally orthogonal subcarriers, which facilitates the designof dynamic spectrum access (DSA)-based methods. Thespectral efficiency of the overlapped spectrum is critical tothe overall spectral efficiency of the CR-UWB system and

© 2014 Zeng et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative CommonsAttribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproductionin any medium, provided the original work is properly cited.

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Zeng et al. EURASIP Journal onWireless Communications and Networking 2014, 2014:18 of 9http://jwcn.eurasipjournals.com/content/2014/1/18

Figure 1 Band overlapping between wireless systems.

is dependent on the performance of the spectrum sensingalgorithm [8].In general cases, the characteristics of the PUs’ signal

are unknown to the CR-UWB. Thus, the non-coherentdetection-based energy detection (ED) technique canbe chosen to verify the availability of the overlappedspectrum [9]. In addition, ED’s use of the Fourier trans-form (FT) function can be inherent from the OFDM-based UWB system [10]. According to the features ofthe ED [11], to determine the PUs’ presence success-fully, the length of the CR-UWB’s spectrum sensing win-dow shall be above a certain threshold which is roughlyinversely proportional to the PUs signal’s signal-to-noiseratio (SNR) received at the CR-UWB and dependent onthe thresholds of the probability of false alarm (PFA) andprobability of detection (PD).For a CR-UWB system in which the duration of spec-

trum access is usually fixed [12], the length of the CR-UWB’s spectrum sensing window determines the lengthof the transmission window. An excessive sensing window

fulfilling the PUs’ protection requirement can producea shortened transmission window which will limit CR-UWB’s use of the overlapped spectrum. Figure 3 showsa pattern of time resource allocation for the use of theavailable spectrum, i.e., the length fixed transmissionopportunity (TXOP), in the CR-UWB system. Obviously,a high ratio between the transmission window length andthe sensing window length is preferred [13]. Neverthe-less, when PUs operate in a low-SNR regime, i.e., theSNR detected at the CR-UWB’s receiver is extremely low,the time required to successfully detect the PUs can beexcessively long, which can lead to a considerably shorttransmission window and may result in an unacceptablespectral efficiency.In this paper, we propose a spectrum sensing optimiza-

tion algorithm in low-SNR regime, aiming at improvingthe spectral efficiency by finding the trade-off optimalityof the spectrum sensing window length and the spec-trum sensing performance. Followed by an optimized wayof effective use of the available spectrum, the proposed

Figure 2 Band allocation of multiband OFDM-based UWB system.

Zeng et al. EURASIP Journal onWireless Communications andNetworking 2014, 2014:18 of 9http://jwcn.eurasipjournals.com/content/2014/1/18

Figure 3 Time allocation in CR-UWB.

algorithm can maximize the proportion between theCR-UWB’s transmission window length to the dura-tion of the spectrum access while guaranteeing the PUs’operation.The remainder of the paper is organized as follows. The

‘Literature review’ section gives a brief overview of thecurrent spectrum sensing window optimization methods.The next section presents the spectrum sensing modeland the formulation of the spectrum sensing window opti-mization problem. Then, the proposed sensing windowoptimization algorithm is demonstrated. Furthermore,the performance of the proposed algorithm is verifiedthrough numerical simulation which is in the section ofnumerical results. Finally, we give a conclusion to thepaper in the final section.

Literature reviewCR technology can be used in many areas [5,14,15].Specifically, Stotas and Nallanathan and Peh et al. laid thefundamental work for dealing with the spectrum sens-ing window optimization problem in [16,17], respectively.The Lagrange dual optimization method was used byStotas and Nallanathan in [16] to optimize the power dis-tribution mechanism and the spectrum sensing schemeby tuning the sensing window length adaptively to opti-mize the throughput of the CR system. In Stotas andNallanathan’s algorithm, the iterations required for identi-fying the multiple Lagrange multipliers’ values are consid-erable. In [18], Zou et al. used the Taylor approximation tofind the relationship of the PFA and PD. The authors thenminimized the CR’s overall outage probability throughoptimizing the sensing window length using linear pro-gramming technique [19]. However, the performance ofZou’s algorithm in low PU SNR regime will be degradedconsiderably because the required sensing window lengthwould be excessive.

SystemmodelIn the work, we assume that there exists a heterogenousnetwork consisting of a single user CR-UWB network anda multiuser PU network, as shown in Figure 4. The sin-gle CR-UWB network contains one CR communicationlink, and the CR-UWB’s infrastructure is in distributed

manner, i.e., ad hocmanner. The CR-UWB network over-laps with the PU network, in which the multiple PUsoperate in the same band of the CR-UWB and within therange of being interfered by the CR-UWBs. We assumethe use of the overlay spectrum sharing scheme [5], whichindicates that the CR-UWB can access to the overlappedspectrum if and only if the CR-UWB’s ED result showsthat the PUs are temporarily absent. We also assume thatan ideal notch filter is used in the CR-UWB system, hencethe impact of the sideband interference can be ignored[20].

CR-UWB transceiverFigure 5 depicts the architecture of CR-UWB transceiver.It shows that the spectrum sensing function is locatedin the cognitive engine block which lies posterior to thefast Fourier transform (FFT) engine of the CR-UWB’sreceiver side. The sensing results can be forwarded intothe cognitive algorithm block for the CR-UWB systemto dynamically use a radio resource allocation algorithmaccording to the sensing output.Furthermore, for spectrum sensing in low-SNR regime,

the low noise amplifier (LNA) and the automatic gain con-trol (AGC) at the CR-UWB receiver side are enhancedcompared with the conventional UWB transceiver [21].Since the power of PUs’ signals are much higher thanthat of the UWB user, which will lead to unlinear dis-tortion in LNA, the original LNA is changed to anLNA whose dynamic range is wide enough to handlethe power range of primary users’ signals. Furthermore,due to the low transmit power of the CR-UWB, theAGC that is set for measuring the peer CR users’ sig-nals cannot detect the PUs signals. Hence, the AGC isadjusted according to the number of bits available inthe analog-to-digital converter (ADC), so that the CR-UWB receiver can detect a wide variety of PUs powerlevels.

Spectrum sensingmethodOur objective is to find the minimum value of the sens-ing window length in order to enhance the spectrumefficiency of the overlapped spectrum, in such a waythat the time length for the effective data transmission


Figure 4 Illustration of a CR-UWB network with multiple PUs.

is maximized. Meanwhile, the value of the sensing win-dow length needs to be large enough for the CR-UWB’sED to successfully determine the availability of theoverlapped spectrum. An ED is implemented by averagingthe squared magnitude of the K-point FFT of the receivedsignal over the sensing period T which is proportional tothe number of received signal samples. Given a fixed pointFFT, the increase of the sensing period will improve theestimate of the signal energy [22]. The test statistic for anED can be given by [23]

T(y) = 1N

N∑n=1

|y(n)|2, (1)

where N denotes the number of received signal samples,and y(n) = x(n) + u(n), n ∈[ 1,N] , represents the dis-crete received signal at the CR user. Furthermore, u(n)represents the noise and is a Gaussian independent andidentically distributed (i.i.d.) random process with meanzero and variance E[ |u(n)|2]= σ 2

u . The PU’s signal x(n)

Figure 5 CR-UWB transceiver.


is an i.i.d. random process with mean zero and varianceE[ |u(n)|2]= σ 2

x , and the parameter γp = σ 2x /σ 2

u denotesthe received SNR of the PU.The sensing result is determined by comparing T(y)

with the threshold, as{H1, T(y) > ε(N)

H0, T(y) < ε(N),(2)

where ε(N) represents the threshold, H1 denotes thehypothesis that the primary user is present, whereas H0shows the hypothesis that the primary user is absent.In an ED, the PD is the probability of detecting under the

hypothesis H1 and is determined by the received signal’sSNR, the threshold, and the number of signal samples [24].Thus,

Pd = P(T(y) > ε(N)|H1)

= P(T(y)/σ 2

u − N − γp√2(2γp + N)

>ε(N)/σ 2

u − N − γp√2(2γp + N)

|H1

)

≈ Q(

ε(N)/σ 2u − N − γp√

2(2γp + N)

).

(3)

For PF which denotes the probability of detecting that thelicensed user under the hypothesisH0, the expression canbe given as [24]

Pf = P(T(y) > ε(N)|H0)

= P(T(y)/σ 2

u − N√2N

>ε(N)/σ 2

u − N√2N

|H0

)

≈ Q(

ε(N)/σ 2u − N√2N

).

(4)

Hence, for a given target Pd and Pf , the minimum N isdetermined by manipulating Equations 3 and 4, as

N ≈ 2γ 2p

[Q−1(Pf ) − Q−1(Pd)

]2 . (5)

Note that the complexity of ED is proportional toO( 1γ 2p

).By observing Equation 5, Q−1(Pd) and Q−1(Pf ) are

expressed as

Q−1(Pd) = ε(N)/σ 2u − N − γp√

2(2γp + N), (6)

Q−1(Pf ) = ε(N)/σ 2u − N√2N

. (7)

Thus, Pd and Pf are related to each other by

Pd = Q(Q−1(Pf )

√2N − γp√

2(2γp + N)

), (8)

Pf = Q(Q−1(Pd)

√2(2γp + N) + γp√

2N

). (9)

Problem formulationIn the work, wemodel the spectrum sensing window opti-mization problem as a convex optimization problem. Thedecision variable is the CR-UWB’s sensing window length,and the main constraints consist of the thresholds of CR-UWB’s PD and PFA. Hence, the problem of optimizing thespectrum sensing window length is expressed as:

P1 τs = argmaxτs βS(1 − Pf )(1 − P(H1)) (10)

subject to

Pf = Q(Q−1(Pd)

√2(2γp + τsfs) + γp√

2τsfs

)≥ P̄f ,

where S represents the spectral efficiency when the CR-UWB has full access to the overlapped spectrum whereno PU is surrounded, β denotes the ratio between the CR-UWB’s transmission window length and the fixed dura-tion of the CR-UWB’s access to the overlapped spectrum,as

β = (Top − τs)

Top, (11)

whereTop is the pre-defined length of the spectrum accesswindow [12]. The constraint presents the threshold PAFof the CR-UWB’s energy detector. The parameter τs rep-resents the sensing window length which is determined bythe PU’s SNR, UWB’s sampling frequency, and the targetPFA; Pf and P̄f represents the actual PFA and the tar-get PFA, respectively, Pd represents the real-time PD, andP(H1) shows the probability that a PU activates withinTop.We assume that the probability that a PU is activated

during Top follows a Poisson process and is expressed as[25]

P(H1) = p(x; λt) = e−λt(λt)x

x! , (12)

where x denotes the expected number of occurrences ofPU’s activations during the period of t which in our systemmodel t = Top.The objective function in Equation 10 shows that

the spectrum efficiency of the overlapped spectrum isdetermined by multiplying S by the ratio of the CR-UWB’s transmission window length to the total operatingwindow length when the PU is not activated (i.e., 1 −P(H1)), and the CR-UWB’s energy detector successfullydetermines the absence of the PU within the overlappedspectrum (i.e., 1-Pf ).For the constraints expressed in P1, γp represents the

received PU signals SNR at the CR-UWB receiver, and fs


denotes the UWB’s sampling rate. Furthermore, Q(x) isthe one-dimensional Gaussian Q-function, as [26]

Q(x) =∫ ∞

x

1√2π

exp(

−y2

2

)dy, (13)

For a certain threshold P̄f , the corresponding thresh-old sensing window length ¯taus can be determined bymanipulating Equation 5, as

τs ≥ 2γ 2p fs

(Q−1(P̄f ) − Q−1(P̄d))2, (14)

where P̄d denotes the target PD which can be calculatedthrough the use of the receiver operating characteristic(ROC) curves [11], and it shows that the value of the CR-UWB’s spectrum sensing window length should not beless than the threshold in order to ensure a successfuldetection of the availability of the overlapped spectrum.The threshold is determined by the value of P̄f , P̄d, thereceived PU signals SNR γp, and the CR-UWB system’ssampling rate fs.By observing that both S and P(H1) are independent of

τs, we can transform the optimization problem shown inP1 into P2 which is simpler to tackle as

P2 τs = argmaxτs β

[1 − Q

(Q−1(Pd)

√2(2γp + N) + γp√

2N

)],

(15)

subject to

Pf = Q(Q−1(Pd)

√2(2γp + τsfs) + γp√2τs fs

)≥ P̄f ,

where N = τsfs represents the number of spectrumsensing samples of CR-UWB’s energy detector,Figure 6 shows the time for spectrum sensing deduces

exponentially when the received SNR γp increases. Atlow γp (<15dB), the sensing time length is longer whenthe target value of Pf is reduced. For example, forthe target Pf = 0.10, Pd = 0.90, and Pf = 0.01, Pd =0.99, the time for spectrum sensing τs is 250 and 820 μs(1μs = 10−6s), respectively.When the value of γp increasesto a higher level, such as over 12 dB, the sensing timedifference between the two target values of Pf becomesminor.In Figure 7, it shows that the value of α increases expo-

nentially with the increase of the received SNR γp. Whenγp is low (< −17.6 dB) for Pf = 0.01, Pd = 0.99, over50% of the transmission opportunity is used for spectrumsensing. Thus, the cognitive UWB system can reach ahigher spectrum efficiency if the UWB system totally usethe TXOP for transmission on the non-overlapped spec-trum (i.e., the remaining 64 subcarriers) than performingthe spectrum sensing first in order to use the 128 subcar-riers for transmission. When the value of γp continues to

Figure 6 Sensing window length vs. PUs SNR.

increase, the fraction of time differences for UWB’s datatransmission under the two target values of Pf becomesminor.

Sensing window length optimizationTo show the impact of the variation of the spectrum sens-ing window length on the CR-UWB’s spectral efficiencyand that there exists an optimal trade-off between thesensing window length and the target PD and PFA, wecompute the spectral efficiency of the CR-UWB in theoverlapped spectrum as a function of the spectrum sens-ing window length which is measured in microseconds, asshown in Figure 8.At the CR-UWB’s receiver, when the PUs’ signal stren-

gth lies in the low-SNR regime, we observe that the spec-tral efficiency of the CR-UWB grows exponentially with

Figure 7 Transmission window length ratio vs. PUs SNR.


50 100 150 200 250 300 350 400 4500

0.5

1

1.5

2

2.5

Spectrum Sensing Window Length (microseconds)

CR

−U

WB

Spe

ctra

l Effi

cien

cy (

bps/

Hz) Pd = 0.9 SNRp = −19 dB

Pd = 0.99 SNRp = −19 dBPd = 0.9 SNRp = −22 dBPd = 0.99 SNRp = −22 dB

Figure 8 Spectrum efficiency vs. sensing window length.

the increase of τs and reaches a peak level when the spec-trum sensing window is tuned to a certain value. As thevalue of τs grows beyond the optimal value, the CR-UWB’sspectral efficiency decreases monotonically because thetransmission window size, Top − τs, is shortened. Figure 8numerically verifies that there exist an optimal τs underspecific target P̄d, P̄f , and γp values.To compute the optimal spectrum sensing window

length for CR-UWB spectral efficiency enhancementunder the constrains of P̄f and P̄d, we use linear program-ming to calculate the optimized value of τs by computingthe root for fr(τs) = dFr(τs)

dτs= 0, where

fr(τs) = − 1Ttxop

−[Q′(τs)− 1

T(Q(f (τs))+Q′(f (τs)))

]= 0,

(16)

where f (τs) represents a function of τs and can beexpressed as

f (τs) = Q−1(Pd)√2(2γp + τs fs) + γp√

2τs fs(17)

and the f (τs)′s first order differentiation is

f ′(τs) = Q−1(Pd)fs2√

(2γp + τs fs)τs fs

−√2fs(Q−1(Pd)

√(4γp + 2τs fs) + γp)

4(τs fs)3/2(18)

Nevertheless, computing the optimal τs in closed form iscomplex. Hence, line search method is used to approxi-mately find the optimal spectrum sensing window length.Figure 9 illustrates the flow diagram of the sensing timeoptimization algorithm. By initiating the values of P̄f , fsand Top, the target value of P̄d can be identified, whichin turn can determine the required τ̄s that is needed for

Figure 9 Flow diagram of sensing window length optimization.


−30 −25 −20 −15 −10 −5 00

0.5

1

1.5

2

2.5

3

3.5

Average received SNR (dB) of the PUs

CR

−U

WB

Spe

ctra

l Effi

cien

cy (

bps/

Hz)

Sensing Window Length OptimizedSensing Window Length Fixed

Figure 10 Spectral efficiency vs. SNRp.

successfully detecting the availability of the specific spec-trum, under a certain detected value of γp. Using linesearch method, the optimal window length value of τscan be found, which can maximize the spectrum effi-ciency while guaranteeing the operation of the PUs. Then,by successfully accessing the wireless medium throughthe use of the Carrier sense multiple access with colli-sion avoidance (CSMA/CA)-basedMAC scheme [12], theCR-UWB station starts using sensing the spectrum usingthe optimal τs. Finally, the sensing results are used bythe CR-UWB’s transmission function which is shown inFigure 5, to dynamically allocate the radio resource fordata transmission, until the transmission period is over.

Numerical simulationTo validate our algorithm performance in terms of spec-tral efficiency enhancement, we combine the proposedsensing window length optimization algorithm with thewater-filling based transmission scheme proposed in [7].In our work, the numerical simulation is implementedwithin a channel model that is previously specified in theUWB system [3]. The detected spectrum hole is used by awater filling-based algorithm [7] where the parameter set-tings can be referred to. Furthermore, for the PUs, λ is setto 1,000 per second to represent the random occupance ofthe PUs in the overlapped spectrum, and the target PF isset to 0.01.We compare the spectral efficiency achieved by the

fixed sensing window length-based spectrum sensingmethod with the proposed sensing window length opti-mization algorithm, as shown in Figure 10. It is seenthat the proposed algorithm can obviously enhance theCR-UWB’s spectral efficiency, especially when the PUsoperate in low SNR regime. For instance, the correspond-ing spectral efficiency achieved by the traditional sensing

method approaches zero when the value of γp decreasesbelow -19 dB, while the CR-UWBs spectral efficiencyachieved by the proposed sensing algorithm is profoundlyhigher. The spectral efficiency performance of the pro-posed algorithm is acceptable even when the PUs SNRdecreases below -25 dB. Furthermore, with the increase ofthe value of γp, the two-lines gap shrinks in an exponentialmanner. As a comparison, when the PUs operate in nor-mal or high-SNR regime (e.g., -10 dB), the gap becomesminor because a large value of γp can lead to a minor τsfor a pre-defined threshold of P̄f and P̄d .

ConclusionTo improve the overall spectral efficiency of the OFDMUWB-based CR system when the corresponding PUs’operating power is extremely low, we proposed a novelspectrum sensing window optimization algorithm for theED-based CR-UWB system to find the optimal trade-off between the detection probability and the length ofthe spectrum sensing window. We showed that our algo-rithm can identify the optimal length of the sensing win-dow length through numerical method constrained bythe target PD and PFA and then significantly prolong thetransmission windowwhen the duration of the CR-UWB’saccess to the overlapped spectrum is fixed. By integratingthe spectral sensing window optimization algorithm withthe existing spectrum management algorithm, the over-all spectral efficiency of the CR-UWB was verified to besignificantly increased compared with the traditional win-dow length fixed sensing algorithm, especially in PU’slow-SNR regime.

Competing interestsThe authors declare that they have no competing interests.

AcknowledgementsSupported by Wireless Access Research Centre at University of Limerick, ChinaPostdoctoral Science Foundation (Y02006023601254) and the FundamentalResearch Funds for the Central Universities (ZYGX2013J011).

Author details1School of Electronic Engineering, University of Electronic Science andTechnology of China, 2006 Xiyuan Ave., Chengdu 611731, China. 2Departmentof Electronic and Computer Engineering, University of Limerick, Limerick,Ireland.

Received: 27 September 2013 Accepted: 6 January 2014Published: 28 January 2014

References

1. J Mitola III, Cognitive radio for flexible mobile multimediacommunications, in Proceedings of the IEEE International Workshop onMobile Multimedia Communications, San Diego, 15-17 Nov 1999

2. D Porcino, H Walter, Ultra-wideband radio technology: potential andchallenges ahead. IEEE Commun. Mag. 41, 66–74 (2003)

3. L Yang, GB Giannakis, Ultra-wideband communications: an idea whosetime has come. IEEE Signal Process. Mag. 21, 26–54 (2004)

4. IF Akyildiz, WY Lee, MC Vuran, Next generation/dynamic spectrumaccess/cognitive radio wireless networks: a survey. Comput. Netw.50, 2127–2159 (2006)


5. E Hossain, V Bhargava, Cognitive Wireless Communication Networks(Springer, New York, 2007)

6. GH Liu, W Zhu, Compensation of phase noise in ofdm systems using anici reduction scheme. IEEE Trans. Broadcasting. 50(4), 399–407 (2004)

7. LY Zeng, Grath McS, E Cano, Rate maximization for multiband ofdm ultrawideband systems using adaptive power and bit loading algorithm, inProceedings of the 9th Advanced International Conference onTelecommunications, Venice, 24-28 May 2009

8. Spectrum Policy Task Force, Report of the spectrum efficiency workinggroup. Technical report, Federal Communications Commission SpectrumPolicy Task Force, Washington, D.C., November 2002

9. H Urkowitz, Energy detection of unkown deterministic signals. Proc. IEEE.55(4), 523–531 (1967)

10. FF Digham, MS Alouini, MK Simon, On the energy detection of unknownsignals over fading channels. IEEE Trans. Commun. 55, 21–24 (2007)

11. T Yucek, H Arslan, A survey of spectrum sensing algorithms for cognitiveradio applications. IEEE Commun. Surv. Tutorials. 1(11), 116–130 (2009)

12. WiMedia Alliance, Multiband ofdm physical layer specification. Technicalreport, WiMedia Alliance, 2009

13. LY Zeng, Grath McS, E Cano, Rate maximization for Multiband OFDM UltraWideband systems using adaptive power and bit loading algorithm, inProceedings of the 5th International Conference on AdvancedTelecommunications and Systems, Venice, 24–28 May 2009, pp. 369–374

14. B Fette, Cognitive Radio Technology (Elsevier, Burlington, 2009)15. HL Li, KH Ngan, A co-saliency model of image pairs. IEEE Trans. Image

Process. 20(12), 3365–3375 (2011)16. S Stotas, A Nallanathan, Optimal sensing time and power allocation in

multiband cognitive radio networks. IEEE Trans. Commun.59, 226–235 (2011)

17. ECY Peh, YC Liang, YL Guan, Optimization of cooperative sensing incognitive radio networks: a sensing-throughput tradeoff view. IEEE Trans.Vehicular Technol. 58, 5294–5299 (2009)

18. Y Zou, YD Yao, B Zheng, Outage probability analysis of cognitivetransmissions: impact of spectrum sensing overhead. IEEE Trans. WirelessCommun. 9, 2676–2688 (2010)

19. DP Palomar, JM Cioffi, AL Miguel, Joint tx-rx beamforming design formulticarrier mimo channels: A unified framework for convexoptimization. IEEE Trans. Signal Process. 51, 2381–2401 (2003)

20. C Snow, L Lampe, R Schober, Performance analysis and enhancement ofmultiband ofdm for uwb communications. IEEE Trans. Wireless Commun.6(6), 2182–2192 (2007)

21. SM Mishra, Brink Ten S, R Mahadevappa, RW Brodersen, Cognitivetechnology for ultra-wideband/wimax coexistence, in Proceedings of IEEEInternational Symposium on Dynamic Spectrum Access Networks,Dublin,17–20 Apr 2007, pp. 179–186

22. D Cabric, A Tkachenko, RW Brodersen, Spectrum sensing measurementsof pilot, energy, and collaborative detection, in Proceedings of IEEEMilitaryCommunication Conference,Washington, D.C., 23–25 Oct 2006, pp. 1–7

23. YC Liang, Y Zeng, ECY Peh, AT Hoang, Sensing-throughput tradeoff forcognitive radio networks. IEEE Trans. Wireless Commun. 7(4), 1326–1337(2008)

24. A Sahai, N Hoven, R Tandra, Some fundamental limits on cognitive radio,in Proceedings of Allerton Conference on Communication, Control, andComputing,Monticello, 29 Sept.–1 Oct. 2004, pp. 1–11

25. S Huang, X Liu, Z Ding, Opportunistic spectrum access in cognitive radionetworks, in Proceedings of the 27th Conference on ComputerCommunications, Phoenix, 13-18 April 2008

26. K Vogel, H Risken, Determination of quasiprobability distributions in termsof probability distributions for the rotated quadrature phase. Phys. Rev.40, 2847–2849 (1989)

doi:10.1186/1687-1499-2014-18Cite this article as: Zeng et al.: Cognitive ultra wideband radio spectrumsensing window length optimization algorithm. EURASIP Journal onWirelessCommunications and Networking 2014 2014:18.

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cognitive ultra wideband radio spectrum sensing window length optimization algorithm

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