Interference Mitigation between Ultra-Wideband Sensor Network and Other Legal Systems

Hindawi Publishing CorporationEURASIP Journal on Wireless Communications and NetworkingVolume 2010, Article ID 290306, 15 pagesdoi:10.1155/2010/290306

Research Article

Interference Mitigation between Ultra-Wideband Sensor Networkand Other Legal Systems

Bin Li, Zheng Zhou, Weixia Zou, Feng Zhao, Zhuo Li, and Dejian Li

Wireless Network Laboratory, Key Laboratory of Universal Wireless Communications, Beijing University of Posts and Telecommunica-tions, Ministry of Education (MOE), Beijing 100876, China

Correspondence should be addressed to Bin Li, [email protected]

Received 1 December 2009; Revised 26 January 2010; Accepted 11 March 2010

Academic Editor: Qilian Liang

Copyright © 2010 Bin Li et al. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Ultra-wideband impulse radio (UWB-IR) sensor network has intensive military and commercial applications. However, theinterference between UWB and other existed networks should be casually investigated. In this paper, we consider interferencemitigation in UWB sensors in the context of cognitive radio (CR). Firstly, we suggest a general state transition model to characterizethe working states evolution of legal networks, also referred to as primary users (PU). Spectrum sensing, used to identify thestate of PU, is formulated as detection of a corresponding state sequence. Maximum posterior probability (MAP) criterion isadopted to perform spectrum sensing. By exploring potential gain of state transitions, detection probability for nearby networksis improved significantly. Subsequently, based on the radius basis function neural network (RBF), we present a novel spectrumsculptor to design UWB waveforms. Attributed to the excellent reconfiguration of RBF, our scheme can produce UWB waveformstracing available spectrums. The designed waveforms can entirely utilize multiple unoccupied bands to maintain uninterruptedcommunications. Also, sufficient spectral attenuation can be generated in specific bands to mitigate mutual interference betweenUWB sensors and other networks. Besides, orthogonal waveforms can be easily derived, which either improves transmissionperformance or provides a flexible accessing strategy for UWB sensors.

1. Introduction

Although the traditional Doppler radars have been com-monly applied in perimeter monitoring systems, they willfail to detect the target and create coverage shadows whenthe protected area has obstacles or in a foliage. Additionally,a large object moving outside of the range of interest cancreate false alarms because of the limited range resolutionof narrow-band radars, which cannot distinguish a nearbysmall target from another larger longer-range one. With acapability of excellent range resolution and penetration, onthe other hand, UWB sensor radars have attached extensiveinvestigations in recent years [1].

The emitted UWB signal occupies a tremendous band-width typically of several Gigahertz (GHz). Its fractionalbandwidth is also very large, usually greater than 0.2,resulting in a sensor with exceptional resolution that alsohas the ability to penetrate many common materials. Moreimportantly, such UWB sensors would be independent of

Doppler shifts but would detect intrusion by measuringchanges in the impulse response of environments. In [2, 3],UWB through-wall motion sensing radars and UWB groundpenetrating radars (GPRs) are introduced to meet therequirements of special war field and the probe and rescueafter a natural disaster. Recently, Liang et al. initiated thetarget detection in foliage using UWB radars and proposedthat the log-logistic model was much suitable to representUWB propagation channel in the foliage [4, 5]. Then, thesense-through-foliage target detection using UWB sensors isinvestigated in [6–8]. These researches significantly benefitthe sense-through-wall and other subsurface sensing prob-lems [9], which has become asymmetric threats in currentand future military operational environments. Although therapid progress in UWB research is originally inspired byradar sensors to a great extent, UWB sensor networks havealso been widely recommended for different applications.For example, UWB network is an ideal candidate for short-range high-data-rate transmission which has been fully

2 EURASIP Journal on Wireless Communications and Networking

discussed in the IEEE standard of wireless personal areanetwork (WPAN), owing to its extremely wide bandwidth[10]. The energy efficiency issue in UWB network is alsoaddressed through medium access control (MAC) protocoldesign in [11].

As the demand of data acquisitions and transmis-sions in various applications continues to grows, such asenvironment pollution sensing, intelligent traffic guiding,and remote medical monitoring, the current spectrumhas become overcrowded and it is hard to allocate fixedfrequency band to these new services. Accordingly, the trendof many networks for different purposes operating in nearbygeographical regions seems inevitable. So, the interferencemitigation and coexistence issues between UWB sensors andother networks should be carefully addressed. The UWBemission power regulation campaign error, launched by U.S.Federal Communications Commission, has been precededfor some years intending for interference mitigation [12].However, this simple power control strategy does notseem sufficient for antagonistic cooperation between thesenetworks [13].

In the emerging optimistic spectrum access infrastruc-ture [14], by sensing and adapting to spectral environment,a cognitive UWB sensor is able to fill in spectrum holes andserves its users without causing harmful interference to otherlegal networks, which are also referred to as primary users(PUs) or authorized users. Correspondingly, signal detectionhere mainly aims to identify whether those perspectivenetworks over UWB band are active, which is quite differentfrom target detection discussed in most radar sensors-relatedliteratures. From aspect of signal processing, the followingtwo functional techniques should be thoroughly studied,in order to build a highly adaptive cognitive UWB sensornetwork that learns from the environment and best servesits users.

(1) Spectrum Sensing. A key element of UWB sensornetwork, in a cognitive paradigm, is the abilityto measure, sense, and be aware of parametersrelated to the radio channel characteristics andavailability of the spectrum. There have been somesensing algorithms including the energy detector(ED) [15], the matched filtering [16], and thecyclostationary detection [17], which have differentrequirements and advantages. ED is robust andsimple but is unfavorable in the presence of noiseuncertainty and interference [18]. Cyclostationarydetection can differentiate PU from interference andnoise; nevertheless, exhaustive search for unknowncyclic frequency makes it extremely computationaland hence impractical. In matched detector, specificpilots are employed to achieve optimum detectionSNR; however, perfect timing usually can hardly beachieved, which may greatly worsen detection perfor-mance. Recently, wavelet-based sensing algorithm isproposed in [19]. In [20], a novel sensing method isdeveloped based on the statistical covariance of thereceived signal, which seems also immune to noiseuncertainty.

(2) Radio Emissions Strategy. After identifying idle spec-trums, UWB sensors need to take real-time adjust-ment on their emitting parameters to best matchcurrent spectral environment. Firstly, the transmitpulse should avoid primary bands to effectively mit-igate mutual interference between UWB sensors andother networks. Also, the emitted waveforms shouldentirely utilize the idle spectrum bands in order toensure communication reliability of UWB sensors.In [21], a novel UWB pulse shaping method basedon prolate spheroidal wave functions (PSWFs) is pre-sented. In [22], Gaussian Hermit functions (HGFs)are introduced to soft-spectrum waveform design,but the spectral efficiency is still unfavorable. TheUWB shaping filter based on the second-order coneprogramming (SOCP) is proposed in [23, 24]; how-ever, it is relatively hard to generate sufficient spectralnotches to avoid other legal networks. Recently, anew spectrum forming technique based on transformdomain communication system (TDCS) is presentedin [25], which can design wideband waveformsaccording to identified idle spectrums. However, win-dowing process is indispensable in order to shortenthe time domain waveform with an infinitely long tailthat may introduce serious inter symbol interference(ISI). As a result, spectrum efficiency of TDCS willbe considerably reduced and the out-of-band leakagebecomes remarkable.

In this paper, we address the issue of interferencemitigation in UWB sensor networks. Unlike the simpleassumption that the working states between two adjacentsensing periods are independent, we employ a finite statemachine to characterize PU’s state transition. On this basis,we further model spectrum sensing as demodulation of acoded sequence with memory. After comprehensively bal-ancing the cost between missing idle spectrums and causinginterference to PU, in different applications, false alarmprobability and missed detection probability are combined asthe overall cost. From the aspect of minimizing the detectionprobability of state symbols, we then employ the maximuma posteriori criterion (MAP) to perform spectrum sensing.Compared with traditional sensing methods, our scheme caneffectively explore potential gain carried by PU’s workingstates and hence significantly reinforce sensing performance.We also reveal the rough interrelation between sensingperformance and the potential information carried by PUand provide a new attractive pattern for future spectrumsensing which can be built into other algorithms to furtherenhance their detection probability.

Subsequently, based on radial basis function (RBF) neu-ral network, we present a novel UWB waveforms generatorwith a versatile spectrum forming capability, which canproduce the emitting signal effectively and flexibly. Thisscheme requires no frequency hopping between multipleisolated bands; thus it can considerably shorten switch timeand reduce hardware complexity. The spectral attenuationof emitted signals can even reach 95 dB in correspond-ing primary bands, which can ensure the highly reliable

EURASIP Journal on Wireless Communications and Networking 3

communications of other legal networks. Also, our designedUWB waveforms can entirely utilize uncontaminated idlespectrum and the whole spectral efficiency is up to 95%.Therefore, seamless data transmission for UWB users canbe basically guaranteed. Meanwhile, by carefully designingthe phase response of emitted signals, orthogonal pulses canbe obtained which can greatly reduce mutual interference ofUWB sensors and enhance the transmission performance ofUWB networks, even when there is synchronization deriva-tion. With the efficient self-adjusting algorithm and well-designed reconfigurability, our proposed spectrum sculptingtechnique totally meets the real-time and highly dynamicdemands in cognitive UWB networks.

The remainder of this paper is outlined as follows.In Section 2, we discuss the system model of monitoringthe other nearby networks. The working state evolutioncharacteristics of PU is further introduced and an optimalsensing algorithm is proposed, in the sense that minimizingthe detection probability, accompanying the robustnessanalysis of this sensing algorithm. A spectrum sculpting RBFis then proposed to design cognitive UWB waveforms witharbitrary spectrum shaping. Section 3 is dedicated to evalu-ate the sensing performance through numerical simulations.The performance of the designed UWB waveforms is alsopresented in this part. Finally, we conclude the whole paperin Section 4.

2. Cognitive-Based Interference Mitigation

In order to effectively mitigate interference between UWBsensors and other legal networks, from the signal processingaspect, two jobs can be suggested in consideration of theunderlay nature of UWB. Firstly, UWB sensors accuratelyidentify available spectrums by monitoring the nearbyperspective networks. Then, based on the discovered spectralenvironment, they adjust the RF emissions to advantageouslyperform their functions, without interfering other networks[26]. These two functions will be elaborated in Sections 2.1and 2.2, respectively.

2.1. Spectrum Sensing in UWB Sensors. In cognitive UWBsensors, spectrum sensing is mainly adopted to obtain thecurrent states of other networks. Most traditional sensingschemes assume that whether the authorized users existmaintains independent between two adjacent detection peri-ods, and the probabilities of active state and idle state remainthe same. This processing strategy can greatly simplify thesensing algorithms; however, it also results in a suboptimalsensing performance.

Practically, the behavior of PU is close associated to itscorresponding wireless service, leading to specific probabilityfeatures on its working states to some extent. This potentialinformation can be properly explored to improve sensingaccuracy. There have existed a few literatures that seekto employ partial probability characteristics to enhancesensing performance [27, 28], including the optimization ofspectrum detection scheduling to improve multiple channelsutilization. Nevertheless, to the best of our knowledge,

extensive investigation on spectrum detection by totallyutilizing the state transition information of PU has not beenaddressed in the literature. The interrelation between sensinggain and the prior information also remains not discussed.

Our main contributions in spectrum detections may liein that, for the first time, we model the working statesof PU as a binary sequence characterized by finite statemachine. Then, by fully exploring the potential informationcarried by PU, we employ MAP to perform optimal spectrumsensing and greatly enhance the detection performance. Thisprocessing strategy provides a novel insight into spectrumsensing, and our original revealment of the rough inter-relation between the achieved sensing gain and PU’s statetransition characteristics may substantially benefit futureresearches in cognitive networks.

2.1.1. General Sensing Strategy. As UWB sensors cannotcause much interference to the authorized networks whenusing spectrum, they should search unused spectrum beforeestablishing their data links. When specific unoccupiedauthorized band has been detected, the UWB sensor willsend its data during the following time slot. However, sincePUs may reclaim their spectrum at any time, UWB usersshould periodically sense the spectrum to avoid interferingnearby networks. So, we adopt the cycle spectrum sensingmode in this paper. The fixed frame duration F is assumed inwhich the sensing duration is T and the remaining durationF-T is used for data transmission [27]. It is noteworthy thatthe transmission here means either the data communicationsor some other dedicated functions, such as target detectionand positioning operations.

Generally, cooperative sensing can alleviate the problemthat one single sensor cannot detect the spectrum correctlywhen there is serious shadow fading [29]. If UWB sensorsare taken into consideration, however, single node spectrumsensing is still a reasonable choice. Firstly, in a distributedUWB sensor network with highly dynamic characteristicscaused by movement or birth-and-death process of sensornodes, effective collaboration in spectrum sensing seemshard to be realized. Moreover, the required overhead maycreate heavy load for UWB network. The cooperative sensingeven becomes impractical when the control channels arenot available [30]. Additionally, the whole sensing time maybecome intolerantly long in a cooperative fashion. So, in thispaper, we mainly focus on the single node spectrum sensing.

2.1.2. Energy Detection. Given the uncomplicated imple-mentation of ED, it always remains the first choice for spec-trum sensing in UWB sensors. Thus, this paper establishesthe general sensing model based on ED. Before proceeding, itis necessary to briefly illustrate ED algorithm, which is alwaysformulated as the following two hypotheses:

y(t) =⎧⎨

⎩

w(t), H0,

s(t) + w(t), H1,(1)

where y(t) is the received signal in UWB sensors, s(t) isthe nearby network’s signal with its variance denoted by σ2

s ,


and w(t) is the additive white Guassian noise (AWGN). In(1), H0 and H1 denote the hypotheses corresponding to theabsence and presence of the primary networks, respectively.In realization, a band-pass filter is usually adopted to extractspectral components of interest. Then, the test statistics isconstructed as the observed energy summation within Mconsecutive segments:

Y =

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

M∑

m=1

|W(m)|2, H0,

M∑

m=1

|S(m) + W(m)|2, H1,

(2)

where S(m) and W(m) (m = 1, 2, . . . ,N) represent thespectral components of the primary signal s(t) and w(t)on the interested subband, respectively. Without loss ofgenerality, we assume that W(m) is white complex Gaussiannoise with zero mean and variance σ2

w. Then, the test statisticsY follows a central chisquare distribution with 2M degrees offreedom under H0, and a noncentral chisquare distributionwith 2M degrees under H1, that is,

P(Y) =⎧⎪⎨

⎪⎩

N(Mσ2

w, 2Mσ4w

), H0,

N(Mσ2

w + Mσ2s , 2Mσ4

w + 4Mσ2wNσ2

s

), H1.

(3)

If a decision threshold τ is properly determined, the falsealarm probability Pf can be defined as P(Y > τ | H0), andthe corresponding detection probability Pd is P(Y > τ | H1).Correspondingly, we have

Pf = P(H1 | H0) = Q

(τ −Mσ2

w√2Mσ2

w

)

,

Pd = P(H1 | H1) = Q

⎛

⎝τ −Mσ2

w −Mσ2s

σ2w

√

2Mσ2w + 4Mσ2

s

⎞

⎠.

(4)

Accordingly, the missed probability is given by 1 − Pd [15].Q(·) is the generalized Marcum Q-function which is givenby

Q(x) = 1√2π

∫ +∞

xe−τ

2/2dτ. (5)

In practice, the probabilities of false alarm and missingdetection have different implications for UWB sensors.Generally, low probability of false alarm is necessary tomaintain high spectral utilization in UWB systems, sincea false alarm would prevent the unused spectral segmentsfrom being accessed by UWB users. One the other hand,the probability of missed detection measures the interferenceof UWB users to PU, which should be limited in theopportunistic spectrum access. The most popular strategy isto determine a threshold to satisfy a false alarm probability,which is based on Neyman-Pearson criterion [27]. Thisscheme maximizes the detection probability for a given falsealarm probability, for example, Pf < 0.1, which is suitablein most sensor networks. However, in some other scenes

t = 0 t = T0 t = 2T0 t = 3T0 t = 4T0 t = 5T0

S1

S0

S

1 1 1 0 0 1

t

Figure 1: The trellis diagram for PU states transition. “1” representsthe nearby network is active, while “0” denotes in idle.

such as UWB radar sensors, the collected data for differentvital applications should be transmitted without delay, whichputs significant importance on spectral utilization, and theNeyman-Pearson criterion is not applicable anymore. There-fore, considering spectrum sensing by combining spectralutilization to unused bands and interference to PU, from amuch wider sense, we minimize the total error probability inthis paper. So the expense of spectrum sensing is given by

Ω = 1− Pd + Pf = Pm + Pf . (6)

2.1.3. State Transition of PU. For most wireless networks, theevolution process of their working states over time can bereasonably abstracted as a finite state machine. Specifically,as is shown in Figure 1, the state transition of PU can bedescribed by a trellis diagram that is similar to NRZI code[31]. If PU is in active state S1 at current moment, then inthe next sensing slot, it will stay in S1 with a probability ofp11 and enter into sleep state S0 with p10. Alternatively, if itis current in sleep state S0, then it will stay in S0 in the nextslot with a probability of p00 and change into S1 with p01.Obviously, we have:

p10 + p11 = 1, p01 + p00 = 1. (7)

Usually, these transition probabilities vary with time.It is found that the state of authorized networks in eachsensing duration corresponds with certain state symbols(t) which constantly changes along the trellis diagram.Specifically, when the state transition occurs at t = kT0,the following primary state keeps different from that in[(k − 1)T0, kT0]. As the state transition further extended,s(t) can be viewed as a BPSK coding sequence with memory,which is also characterized by a Markov chain. Therefore,the main objective of spectrum detection lies in correctlydemodulating this coded sequence s(t). Denoting the twostates of PU as binary symbol “0” and “1”, the optimumspectrum detection in (6) is equivalent to minimizing thesymbol error probability (SER).

The MAP criterion can be properly employed in thesuccessive symbol detection, which is optimum in the sensethat it minimizes the detection probability of symbol errors[31]. Suppose that it is desired to detect the state symbol inthe kth sensing duration, and let [r1r2, . . . , rk, . . . , rk+D] be the


observed test statistics, where D is the delay parameter whichis always chosen to exceed the signal memory. If we denotethe inherent memory of the equivalent sequence s(t) by L, thenwe have D ≥ L. On the basis of the already received signal, wecompute the posterior probability:

P(

s(k) = Am | rk+D, rk+D−1, . . . , r1

)

. (8)

For possible state symbols Am ∈ {0, 1}, we choose Am withthe largest probability. Then, we have

P(

s(k) = Am | rk+D, rk+D−1, . . . , r1

)

=p(

rk+D, rk+D−1, . . . , r1 | s(k) = Am

)

p(

s(k) = Am

)

p(rk+D, rk+D−1, . . . , r1).

(9)

Since the denominator is common for two probabilities,the MAP criterion is equivalent to choose the value of s(k)

that maximize the numerator of (9). Thus, the criterion fordeciding on the kth state symbol is

s̃(k) = arg{

maxs(k)

p(

rk+D, rk+D−1, . . . , r1 | s(k) = Am

)

×p(

s(k) = Am

)}

.

(10)

The solution for (10) recursively begins with thefirst symbol s(1); then the following state symbolss(2), s(3), . . . , s(k+D) are sequentially obtained. The amplitudelevels {Am} are only 2; so the computational complexity isbasically acceptable. But, it is noteworthy that there existfixed D delays in MAP algorithm. Consider that the idlespectrum may be reclaimed again during a short period,this presented detection algorithm with D accessing delaysmay miss most chances of using idle spectrum. Therefore,this original MAP-based sensing algorithm may not beappropriate to UWB sensors.

Furthermore, most recent research shows that the pri-mary state of specific networks can be modeled as analternating renewal source, in practice, which can be exploredto simplify above MAP detection algorithm. As indicatedby investigation in [32], the exponential distribution can beassumed for the probability density functions of the busystate and idle state periods as

fS1 (n) = 1μ

exp(−μn), fS0 (n) = 1

λexp(−λn), (11)

where μ and λ are the transition rates from busy to idle andfrom idle to busy, respectively. With the aid of KomogorovEquation [33], we obtain the probability of the idle stateremaining unchanged during k successive detection periods:

p00(k) = μ

μ + λ+

λ

μ + λexp

(−k(μ + λ))

, k = 1, 2, . . . ,∞.

(12)

Similarly, the probability of the active state lasting for kdetection periods is

p11(k) = λ

μ + λ+

μ

μ + λexp

(−k(μ + λ))

, k = 1, 2, . . . ,∞.

(13)

If we have identified the initial primary state in idle at themoment n0, which means p(s(n0)) = 1, then the probabilitythat the primary state always stays in idle after k sensingtransmission periods can be given by

p(s(n0 + k) = 1) = p(s(n0) = 1)p00(k). (14)

Accordingly, the probability of the primary state enteringinto busy in the kth detection period, after staying idle fork − 1 periods, can be expressed as 1− p00(k).

It is noted from the above discussion that PU wouldstay in present state for certain sensing-transmission periodsbefore jumping into another one. Thus, the key point oftracing a state path is to accurately determine the statetransition moment. Furthermore, a careful observation on(14) shows that the state evolution following an exponentialdistribution has a limited memory, which means that thecurrent state of authorized network is only related to thelatest previous state rather than the upcoming ones. Basedon these two points above, we may further simplify MAPalgorithm in (10). If we have learned that the authorized userenters into state “1” at the moment k − N + 1 and stays forN periods, the optimal state estimation at the kth momentshould meet

s̃(k) = arg{

maxs(k)

p(

s(k) = Am | Yk,

s(n) = 1,n = k − 1, . . . , k −N + 1)}

.

(15)

2.1.4. Spectrum Detection. In early stage, UWB sensors maytake a long duration or employ some other sophisticatedsensing algorithms (i.e., cyclostationary feature detection) toget the initial PU state correctly. Without loss of generality,supposing that the initial primary state is 0, then a priorprobability of staying at this state for k sensing-transmissioncycles is p00(k). In order to maximize a posteriori probabilitydetection, (15) requires determining an optimum decisionthreshold τ0

k to meet

p00(k)P(

Y | s(k) = 1)

(1− p00(k)

)P(Y | s(k) = 0)

= α

1− α. (16)

Here, α is the weighting coefficient ranging in [0 1], whichcan be carefully used to adjust relative preference betweenmissed probability and detection probability. In practice,α > 0.5 means the cost of spectral efficiency declinebecause a missed detection is relatively larger than that ofinterfering the PU, which implies that the nearby networkspossess a strong anti-interference ability. In this situation,we may aggressively improve the utilization efficiency of idlespectrums to facilitate data transmissions of urgent UWBapplications. On the other hand, α < 0.5 implies that weshow much favor to the unperturbed communication linkof PU compared to the spectrum efficiency. Hence, strictprotection to the authorized networks is necessary.


After the optimum decision threshold has been obtainedaccording to (16), the detection probability P0 in the kthmoment can be given by

P0 = P(

Y < τ0k | s(k) = 0

)

. (17)

Similarly, the threshold for initial state 1, τ1k , can be also

obtained. Then, the detection probability P1 can be writtenas

P1 = P(

Y > τ1k | s(k) = 1

)

. (18)

Since the state symbol may not appear equally, the overallprobability of correct detection is

Pc = μ

μ + λ

∑k p00(k)P

(

Y < τ0k | H0

)

∑k p00(k)

+λ

μ + λ

∑k p11(k)P

(

Y > τ1k | H1

)

∑k p11(k)

.

(19)

It is obvious that maximizing Pc gives the minimumsensing expense Ω. Actually, from the information theoryaspect, spectrum sensing is equal to detecting a binary-coded sequence that obeys an unsteady state transition, giventhe reward of detection probability and missed probability.Like in most traditional spectrum sensing algorithms, if twosequential states of authorized users are simply assumed tobe independent, the detection probability would be ratherlimited. However, our MAP-based optimum spectrum sens-ing is supposed to be much superior to ED, in considerationof entire exploration of the implicit state evolution andcorresponding potential coding gain. Compared to matchedalgorithm and cyclostationary detection, our method onlyrequires a statistic traffic model rather than the specific signalparameters of different networks, which can be convenientlyobtained by experiential data or by learning.

2.1.5. Robustness Analysis. When the last state transitionsof PU are exactly estimated, the simplified algorithm isequal to MAP algorithm, and it has optimal detectionperformance. However, from (16), spectrum detection errorsin state transition moment will cause error extension inthe upcoming periods. To avoid this unfavorable situation,following measures are suggested when PU has enteredone state and lasted beyond its mean duration. (1) Wemay change the relative ratio between sensing period andtransmission period. In an extreme case, the whole cycle isallocated for spectrum detection. (2) Other advanced sensingalgorithms can be employed to assist estimating the exactstate transition. (3) After n sensing-transmission periods,usually n being among 5–10, we may employ the truncatedsequential detection and retake a long duration to detect theinitial state and then repeat this process.

The bad effect on detection probability caused by statetransition estimation errors will be discussed in this part,which is instructive if these suggested measures cannot berealized. In the situation with low detection probability, thestate transition point can be correctly estimated by adjusting

sensing duration. Compared to ED, however, detection gainin this case is quite limited but with a high complexity.So, we mainly analyze the performance decline caused bythe state transition estimation errors under high detectionprobability. Assuming that the average detection probabilityis p, in the worst case, the detection error occurs successively,whose length is about (1− p)× (1/λ + 1/μ).

Firstly, we focus on state detection errors that occur nearthe actual state transition point, which has a serious influenceon the upcoming detections. For convenience, suppose thatthe estimation errors take (1−p)×(1/λ+1/μ) detection cyclesin advance the actual transition moment, which is referredto as advanced transition detection error (ATDE). Given thatthe initial state is 0, accordingly, affected by this error initialstate, subsequent optimum thresholds are determined by

p00(k +

(1− p

)(1/λ + 1/μ

))P(

Y | s(k) = 1)

[1− p00

(k +

(1− p

)(1/λ + 1/μ

))]P(Y | s(k) = 0)

= α

1− α.

(20)

The thresholds in following decision are denoted byτk+(1−p)(1/λ+1/μ), and the corresponding detection probabilityis

PAPDE = μ

μ + λ

∑k p00(k)P

(

Y < τ0k+(1−p)(1/λ+1/μ) | H0

)

∑k p00(k)

+λ

μ + λ

∑k p11(k)P

(

Y > τ1k+(1−p)(1/λ+1/μ) | H1

)

∑k p11(k)

.

(21)

Secondly, we investigate the nonideal case that the worstestimation errors occur in the middle of state transition(MPDE); namely, the estimated transition moment is muchearlier than the actual state transition. In order to avoid thisfalse state transition, ED is preferred to MAP detection in(15) after the false state estimation has occurred. Then, acounter is adopted for the sustaining periods of this falsestate. If the sustaining periods are smaller than (1 − p) ×(1/λ + 1/μ), we may conclude that the state transition doesnot actually occur and the upcoming detection still followsthe correct state before. If it is larger than (1−p)×(1/λ+1/μ),then we judge that the state transition indeed happens, andthe current sustaining period of this new transited state is setas (1−p)×(1/λ+1/μ). It can be easily found that the detectionerror is not diffusive in this way; thus the upcoming sensingperformance is basically not affected. When (1− p)× (1/λ +1/μ) is far less than min(1/λ, 1/μ), the detection probabilitylow-bound can be approximated by

PMPDE = μ

μ + λ

[(1− p

)(

1− PEDf

)

+ p(

1− Pf

)]

+λ

μ + λ

[(1− p

)(

1− PEDm

)

+ p(1− Pm)]

,

(22)

where PEDf and PED

m represent the probabilities of false alarmand missed detection of ED algorithm, respectively.


The analysis above provides the detection performance inthe case that the false state estimations cause error diffusionduring following detections. However, it is also noteworthythat the successive estimation errors of (1 − p) × (1/λ +1/μ) are almost impossible to happen; so our analysis onlyprovides a loose low bound for sensing performance withstate estimation errors under high detection probability.

2.2. Spectrum Sculpting in UWB Sensors. Detecting thepresence of other nearby networks in a given primary bandis just the first step in operation of a cognitive UWB sensor.In order to best adapt to current spectral environmentand minimize mutual interference, UWB sensors shoulddynamically adjust the RF emissions after probing thecurrent spectrum. Usually, this process covers the physicallayer design as well as the upper layer joint optimization.Cross layer optimization is recommended for selectingtransmission parameters according to the upper layer qualityof service (QoS). Unfortunately, this process is basicallycomputational and also has intolerable delay in practice. Incontrast, the UWB waveform designing rarely considers QoSinformation from the upper layer, but this flexible strategyallows the simple implementation and fast accessing to idlespectrums and hence is much more suitable for distributedUWB sensors.

2.2.1. RF Requirements in CR. Based on an overall considera-tion of various factors, UWB waveforms design should meetthe following requirements.

(1) Avoid the licensed frequency band flexibly and effec-tively. It is possible to avoid authorized frequenciesbased on frequency hopping technique [34]; but inthis mechanism, UWB sensors can only use onesingle free band, resulting in rather low spectrum uti-lization. In addition, oscillator operating at multiplefrequencies is required, which also complicates thehardware implementation. Moreover, the switchingtime for typical PLL can even reach 1 ms, whichmay prevent UWB sensors from the timely utilizationof idle spectrum. On the other hand, spectrumavoidance-based schemes have a limited spectralattenuation, which can hardly eliminate the accu-mulated interference from multiple UWB sensors toother networks [21, 22].

(2) Use the idle spectrum entirely. Generally, more thanone free spectrum hole exist, which always iso-lates a long spectral distance from each other. Thetraditional methods can use only one free band.Considering the high uncertainty of authorized band,data transmission of UWB nodes is easy to beinterrupted by the reclaim of primary band. In orderto ensure seamless communications, UWB sensorsshould utilize multiple idle bands simultaneously incase one PU reoccupies its primary band. TDCScan take advantage of multiple frequency bands.But, the designed waveform has an infinite long tailwhich inevitably causes ISI and hence undermines

its transmission performance. Yet, truncation by win-dowing will in turn lead to an obvious degradation onspectral efficiency and remarkable out-band leakage[25].

(3) Simplify the upper layer design. Most of traditionalspectrum access strategies are based on competitivemechanism or centralized scheduling. On one hand,it has to occupy remarkable bandwidth resource topass the global control signaling. On the other hand,it also has to take a long time to coordinate transmis-sion of each UWB node, which also inevitably missesmost spectrum holes.

In this part, we suggest a novel UWB waveform basedon the RBF neural network. The designed signal is highlyreconfigurable which can entirely match target spectrumshape after an extremely short switching time. Also, efficientspectral attenuation can be produced to eliminate mutualinterference between PU and UWB sensors. After the spectralholes have been identified based on our presented sensingalgorithm, UWB sensors can immediately access in the fol-lowing transmission slot by means of orthogonal waveforms,without waiting for a coordination control. Thus, the upperlayer control can be considerably simplified, and the UWBsensors capacity can be enhanced at the same time.

2.2.2. System Architecture. With the excellent capability ofthe function approximation, RBF neural network can beproperly applied to design UWB waveforms given any targetspectrum shaping [35]. The main philosophy behind RBFis to adjust a set of basis functions and ultimately matchany function in high dimension, at any precision. In fact,as pointed out in [36], the general spectrum forming canbe viewed as two-dimensional multivariable interpolationproblem, which means that given a set { fi ∈ R1 | i =1, 2, . . . ,N} containing N different frequency values andanother set {ti ∈ R1 | i = 1, 2, . . . ,N} containing N sampledtarget spectrum values, the objective is to find a mappingfunction F : R1 → R1 to meet

F(fi) = ti, i = 1, 2, . . . ,N , (23)

where fi represents the ith discrete frequency value, and ti isthe corresponding sampled spectrum. With the help of thecontinuity of mapping function, spectrum values other thanfi can be also obtained. If a set of basis functions ϕ(‖ f −fi‖) are properly chosen, then the mapping function can berepresented as a linear combination of the basis functions:

F(f) =N∑

i=1

wiϕ(∥∥ f − fi

∥∥). (24)

In UWB waveform designing, the selection of basis func-tions ϕ(‖ f− fi‖) is rather different from the traditional sense.Since the basis functions mainly act as the interpolationfunctions, they are not required to keep orthogonal fromeach other. When selecting basis functions, it should ensurethe localization property firstly, which means limr→ 0ϕ(r) →0. Meanwhile, the basis functions should be central even


1

z−l

z−2l

z−(n2−1)l

w(0)w(1)

w(3)w(2)

w(n2)

Weightingupdating

Transform

Switching

Generalspectrum

IFFTh(n)

Output

Gi( f )Spectrum

sensing

y(t)

−+

−+

Guassianfilter

Networkupdating··

·

Spectrum pruning

H

ta

ϕ0

ϕ1

ϕ2

ϕ3

ϕn2

Figure 2: The structure of the UWB spectrum shaping network. Note that the result of spectrum sensing determines the current expectedoutput.

symmetry, for example, ϕ(−r) = ϕ(r). Besides, theyshould satisfy the requirement as indicated by MicchelliTheorem [37]. For the convenience of analysis, Gaussianfunction is served as the basis function in our followinganalysis; however, other candidate functions meeting aboverequirements include the raised cosine function and theexponential function [35]:

pi(k) = 1√2πδi

exp

(

− fs2

2δ2i

(k − κi)2

)

,

k = 0, 1, . . . ,N − 1, i /= 0,

(25)

where κi and δi are both adjustable parameters of thetransmission functions Ti, which can be employed to modifytheir center and width, respectively; fs is the samplinginterval in frequency domain.

The implementation architecture of the generalizedspectrum shaping network is shown in Figure 2. Based onthe spectrum sensing result in Section 2.1, the target outputt can be firstly determined with a purpose of fully utilizingunoccupied spectrums and also respecting the active primarybands. Then, the parameters of RBF network, includingthe network weight w, the position, and shape of basisfunctions, are modified adaptively until the error signalbetween the network output a and the expected output treaches the minimum value. This adjusting process is shownby the solid line in Figure 2. Meanwhile, by introducing thespectrum pruning technique, further slight adjustments willbe performed on partial network weigh w after convergence,so as to obtain satisfactory spectrum efficiency and also meetspecific spectrum constraints. This process corresponding tothis feedback process is depicted by the dotted line, which iscontrolled by a switching circuit.

Each part of signal is discussed in detail as follows.

(1) Transform Function Ti. Transmission functions Ti aremainly used to produce the discrete input sequence ϕi(n)(n = 0, 1, . . . ,N − 1; i = 0, 1, . . . ,n2), which correspondsto the basis functions in (25). Supposing that ϕi denotes an

N × 1 dimensional vector composed of ϕi(n), then the inputmatrix Φ can be written as

Φ =[

ϕ0 ϕ1 ϕ2 · · · ϕn2−1 ϕn2

]T, (26)

where ϕ0 represents the network offset. In the block diagramabove, the transmission function Ti has to be implementedby the group of filters in practice, and the time bandwidthproduct BT of these Gaussian filters is determined by δ in(25). Note that the number of transform functions is alwaysless than N in order to simplify implementations [37].

(2) Target Output t. The target output t corresponding to theoptimal emission spectrum depends on the current spectralenvironment. If we assume that there are total I kinds ofactive legal systems, then the expected spectrum can beexpressed as

t =I∏

i=1

(1−Gi

(f))

∣∣∣∣∣∣f=k fs

k = 0, 1, . . . ,N − 1, (27)

where Gi( f ) represents the indication gating function corre-sponding to the ith kind of PU. If the legal network locatingat [ fi1, fi2] has been detected using the sensing method inSection 2.1, then the associated gating function Gi( f ) isenabled:

Gi(f) =

⎧⎪⎨

⎪⎩

1 f ∈ [fi1 fi2

]and si(t) = 1,

0 f /∈ [ fi1 fi2]

or si(t) = 0,(28)

where si(t) represents current working state of the ith PU.

(3) Parameters Updating. During the parameters adjustmentprocess, by adaptively changing the network weights w andthe transmission parameters κi and δi, the mean square error(MSE) between the actual output a and the target output twill be minimized. And finally, we obtain the UWB signalwith optimal spectrum shaping. The MSE can be defined as

E = 12‖a− t‖2

2 =12

N−1∑

k=0

n2∑

i=0

[w(i)ϕi(k)− t(k)

]2, (29)


where the coefficient 1/2 is just for facilitating the elabo-ration. The parameters updating of this UWB waveformgenerator, including the network weights and transmissionparameters, can be divided into two phases [37]. Thenetwork weights w are firstly adjusted using Windrow-Hoff rule. Then, the transmission parameters κi and δican be modified by resorting to the gradient descent rule.Correspondingly, the partial derivatives of E on transmissionpara meters can be written as

∂E

∂κi=

N−1∑

k=0

n2∑

i=0

w(i)[w(i)ϕi(k)− t(k)

]∂ϕi

∂κi,

∂E

∂δi=

N−1∑

k=0

n2∑

i=0

w(i)[w(i)ϕi(k)− t(k)

]∂ϕi

∂δi.

(30)

(4) Implementation. In UWB sensors applications, the dura-tion of the learning algorithm directly determines the access-ing delay to idle spectrums. Therefore, we need to optimizethe transmission parameters beforehand to further shortenthe switching time, also simplifying the implementation ofUWB nodes.

In fact, when n2 is big enough, we may let each κi evenlydistributed in frequency axis and employ one single Gaussianfilter to generate the basis function ϕ. Then, the other basisfunctions ϕi can be obtained by l × i samples cycle shiftingoperation on ϕ1, where l represents the shifting factor (l >1). So we can further optimize the single parameter δ. Areasonable parameter δ should actually be neither too largeto avoid serious ripples in the pass band nor too small in casethat the designed waveform has an obvious out-band leakagewhich may interfere PU in adjacent band [35].

Based on the above simplification efforts, the structureof UWB pulse generator can be obtained as is shown inFigure 2. Firstly, an impulse sequences with a period of N isproduced, which is then fed into a Gaussian shaping filterwhose key parameter, the time-bandwidth product BT, isdetermined by the already optimized δ. Then the networkbasis function ϕ(n) can be formed. The sampling frequencyof ϕ(n) is set to 2 fmax, where fmax is the maximum frequencyof UWB signals. After that, the network input sequencesϕi(n) can be constructed after i × 8 (i = 0, 1, 2, . . . ,n2)samples delay has been performed on ϕ(n). Notice that,here, sample delay is equivalent to cycle shift consideringthe periodic input impulse sequence. Finally, in the updatingstage, the UWB waveform shaper makes adjustment to itsweighting vector w according to target output t that relieson nearby spectrum environment.

When the RBF network is directly applied to UWBsensors, it is usually difficult to meet some given spectral con-straints. For example, the designed UWB waveforms underspecific spectral masks will have some serious mismatchnear the abrupt spectral edges [35]. This would bring inserious negative effects in cognitive scenarios and reduce itsapplications significantly. Assuming that there is a spectralmismatch during the frequency band [ fdown fup], then the

corresponding network weight subset is denoted by wsub ={wk : m ≤ k ≤ n}, where m and n can be obtained by

m =⌊

fdown(l × fs

)

⌋

, n =⌈

fup(l × fs

)

⌉

. (31)

The main objective of the spectrum pruning is to repairthe remarkable local spectral mismatch. This process isalso iterative, and the basic idea is to further modify theconverged network weights falling into the mismatch range.When n2 is large enough (n2 > 60) and the maximumtolerance of the spectral mismatch is denoted by ξ, thespectrum pruning can be summarized into

w(k)i

=

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

ηw(k−1)i , i ∈ [m,n] and H2

(f)−M

(f)| f=[ fdown fup]≥ ξ

w(k−1)i , i ∈ [m,n] and H2

(f)−M

(f)| f=[ fdown fup]≤ ξ

w(k−1)i , i /∈ [m,n],

(32)

where η is the pruning step. H( f ) represents the UWBemission spectrum obtained from this shaping network, andM( f ) is the regulatory spectral constraint. This iterativespectrum pruning process will be continued until all fre-quency bands have met the given spectral constraints.

2.2.3. Orthogonal Pulse Design. After both the networkweights and the transmission parameters have convergedto their optimal solutions, the frequency response of thedesigned signal can best approximate to the expected spec-trum. So, we may immediately produce the UWB waveformby IDFT on a:

h(n) = IDFT(�exp

(j2πΘ

)⊗ purelin(a)�)

= IDFT(�

exp(j2πΘ

)⊗ purelin(

wToptφ

)�),

(33)

where purelin(·) is the output function of RBF network [37],[z] denotes the conjugate symmetric spectrum constructedfrom z which is the representative spectrum of the equivalentlowpass form [31]. The N × 1 dimensional vector Θ repre-sents the user defined phase response, and the operator ⊗denotes the vector multiplication between the correspondingtwo vectors.

As is well known, orthogonal waveforms allow multipleUWB sensors to access the same idle band at the same timeand in the same location, without causing serious collision.In a UWB sensor network, therefore, the orthogonal wave-form division multiple accessing (WDMA) can also greatlysimplify the upper layer protocol design and reduce accessingdelay, hence significantly reducing scheduling complexityand improving spectrum efficiency.

For convenience, we assume that the emission powerin idle frequency band is only related with the hardwarespecification of UWB devices. When the idle spectrum isdetected, the emitted waveform remains a constant power,denoted by A, in the unused spectrum. For arbitrary two


orthogonal waveforms h1(t) and h2(t) with their Fouriertransform denoted byH1( f ) andH2( f ), respectively, we have∫

f H1( f )H∗2 ( f )df [31]. So, the following relation should be

satisfied:

A2∫

Bexp

(− j2πθi(f))

exp(

j2πθj(f))

df = 0, (34)

where B is the available frequency bands. It can be found thatcareful design of the phase response θi( f ) can produce themutual orthogonal UWB waveforms. One simple scheme isto let the phase response to be

θi(f) = 1

4ci(f). (35)

Here, we specify ci(k) to be a binary sequence, for example,ci(k) ∈ {−1, 1}. Then, the designed UWB waveformswill keep orthogonal with each other so long as to ensureorthogonality of discrete sequence ci(k). If an appropriatepseudorandom sequence, such as m-sequence, is selectedbased on the length of sampling length N, orthogonal UWBwaveforms can be easily derived.

It is noted that from (34) the orthogonality designrequires UWB signal remain constant in the whole frequencyaxis. If the regulatory UWB emission mask is taken intoaccount, such as the FCC emission limits, however, thisalgorithm has to be further modified. Practically, we mayrepresent the whole spectral line by a combination ofconstant spectral lines along the frequency axis. Thus, thisorthogonality design algorithm is still applicable to eachconstant spectrum.

3. Numerical Simulations and Evaluations

In this part, we evaluate the performance of our presentedalgorithms through numerical simulations, both for thespectrum sensing and the UWB waveform sculpting.

3.1. Numerical Results for Spectrum Sensing. In our analysis,the number of sampling points M is set to 80. With respectto the service traffic parameters (μ, λ), corresponding to busystate and idle state of PU, we select five sets of parameterscombination to comprehensively study the influence frommodel parameters on detection performance, which are asfollows: (1) μ = 1, λ = 1; (2) μ = 1/8, λ = 1/2; (3) μ = 1/8,λ = 1/3; (4) μ = 1/8, λ = 1/5; (5) μ = 1/8, λ = 1/8. Anothergroup parameters combination is also used for systematicalanalysis.

3.1.1. Sensing Performance. According to the optimal deci-sion threshold, the spectrum detection performance isobtained as is shown in Figure 3(a). When the traffic param-eters are set to μ = λ = 1, as we expected, the performance ofour sequence detection based sensing algorithm is the sameas ED. That is because prior information carried by statetransition can be basically ignored in this case, and the statesymbols in adjacent two sensing periods are approximatelyindependent. So, the MAP criterion degenerates to MLdetection, as is done by ED. When either μ or λ is larger

0 2 4 6 8 10

0.7

0.75

0.8

0.85

0.9

0.95

1

Pro

babi

lity

ofde

tect

ion

Energy detectionProposed μ = 1, δ = 1Proposed μ = 1/8, δ = 1/2Proposed μ = 1/8, δ = 1/3Proposed μ = 1/8, δ = 1/5Proposed μ = 1/8, δ = 1/8

SNR (dB)

−10 −8 −6 −4 −2

(a)

0 2 4 6 8 100.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Pro

babi

lity

ofde

tect

ion

Energy detectionProposed μ = 1/1, δ = 1/1Proposed μ = 1/10, δ = 1/10Proposed μ = 1/30, δ = 1/20Proposed μ = 1/30, δ = 1/10Proposed μ = 1/20, δ = 1/10

SNR (dB)

−10 −8 −6 −4 −2

(b)

Figure 3: The detection performance of the proposed algorithm.

than 1, however, it is obvious that the presented algorithmoutperforms ED. Specifically, when the service parametersare (μ = 1/8, λ = 1/3), our proposed algorithm is about2.2 dB better than ED, and 1.2 dB when (μ = 1/8, λ = 1/5).Another five parameters sets are also selected for penetrateddiscussions, as is depicted in Figure 3(b).


0 1 210−4

10−3

10−2

10−1

Pro

babi

lity

ofm

iss

dete

ctio

n

PfEDPmED

SNR (dB)

−7 −6 −5 −4 −3 −2 −1

P f proposedPm proposed

(a)

0 1 2

10−3

10−2

10−1

Pro

babi

lity

ofm

iss

dete

ctio

n

SNR (dB)

−6 −5 −4 −3 −2 −1

PmED, α = 0.4P f ED, α = 0.4

P f proposed, α = 0.4

PmED, α = 0.6P f ED, α = 0.6Pm proposed, α = 0.6P f proposed, α = 0.6

Pm proposed, α = 0.4

(b)

Figure 4: The missed detection and false alarm probabilities underdifferent preferences.

Actually, as we discussed before, the performanceimprovement is mainly attributed to the potential coding gaincaused by the hidden state transition of PU. Theoretically,the achievable gain is related to the minimum code distanceof its corresponding finite state machine [29]. Consider thatthe state transition here is inhomogeneous, which means thatthe state transition probabilities change over time, and wecan hardly employ a transition matrix to describe it, whichalso brings in great difficulty in analyzing the minimum codedistance. Alternatively, we seek to reveal the interrelationshipbetween the detection gain and the service traffic parametersfrom a quantitative angle by numerical simulations. Fromsimulations in Figure 3(a), we note the following. (1) When

the state parameters are (μ = 1/8, λ = 1/2) and (μ =1/8, λ = 1/5), the detection performance can be increasedby 2.2 dB and 1.2 dB, respectively. The same results areobserved in Figure 3(b). Therefore, it can be concluded thatthe performance improvement in spectrum sensing is relatedto the ratio between states duration periods λ/μ. The largerthis duration ratio is, the better the sensing gain is. In anextreme case that the ration tends to be infinite, which meansthat only one state exists, totally correct detection can beachieved going with the common sense. (2) In comparisonwith ED, when the state parameters are (μ = 1/8, λ = 1/8)and (μ = 1/10, λ = 1/10), the detection performance can beincreased by 0.7 dB and 0.95 dB, respectively. So, we may saythat the detection performance is improved with the increaseof cycle duration. However, what to be emphasized is thatthe sensing gain caused by the increase of state durationis much less than that of by improving the ratio λ/μ. Thereason is that the increase of state duration is equivalentto repeat coding; however, the improvement of λ/μ impliesthe minimum coding distance being aggregated. Hence, theachieved coding gain in the former case is limited relatively.Observation from Figure 3 shows that given the serviceparameters, slight enhancement in spectrum sensing can beobtained by only increasing the observed states duration,which is realized by shortening sensing-transmission periodor increasing sampling rates.

3.1.2. Different Preferences. For different preferences betweenfalse alarm probability and missed probability, the relationbetween the sensing performance and signal noise ratio(SNR) is depicted in Figure 4. When α is chosen to 0.5,it is apparent that the false alarm probability has beensignificantly reduced while the missed probability remainsunchanged. Compared to Neyman-Pearson criterion, ouralgorithm can increase the utilization efficiency of unusedspectrum substantially while basically keeps the interferenceto licensed band the same as ED. Accordingly, the capacityof UWB sensor networks can be improved, which is ratherbeneficial to the urgent data transmission. On the otherhand, if we put emphasis on missed probability and letα be 0.4, the false probability of this new algorithm isthe same as ED; but the detection probability has beenobviously enhanced. So, we can provide a much more reliablecommunication link to other legal networks. If we relativelyprefer the missed probability and set α to 0.6, as is shownin Figure 4(b), although the detection probability of thisalgorithm remains close to ED, the false alarm is significantlyoptimized, which is resemble that of α = 0.5.

3.1.3. Performance with Detection Errors. Figure 5 gives thesensing performance when the state estimation errors exist.In this simulation, we assume that the detection probabilityP is .8 and the traffic parameters are set as μ = 1/30,λ = 1/20. It is shown that, when the state transition pointerror estimation gets earlier, the sensing performance willbe declined by 0.61 dB compared to the ideal situation thatthe state transition moment has been precisely identified.On the other hand, if the state transition errors happen


0 2 4 6

0.7

0.75

0.85

0.95

Pro

babi

lity

ofde

teti

n

Energy detection Proposed, ATDEProposed, MTDE

0.8

0.9

1

Proposed, ideal

SNR (dB)

−10 −8 −6 −4 −2

Figure 5: Detection performance with state transition estimationerrors.

far away from the actual transition moment, the detectionperformance would decline by 0.75 dB. As a whole, however,the transition point detection error has little effect on sensingperformance when the mean detection probability is high; soour proposed algorithm is robust to state estimation errorsto some extent.

3.2. Numerical Results for Spectrum Sculpting. In UWBwaveform generation simulations, the length of the basisfunction N is 180, the equivalent filter order n2 is 32, and theshift factor l is 8. We note from the simulations that the UWBpulse can probably reach its convergence after 50 iterations.The out-band attenuation can be further optimized aftertotal 100 iterations. Therefore, our proposed network has afast convergence. Consequently, the switching time can beconsiderably shortened. Hence, with little accessing delay, theutilization of idle spectrum can be enhanced.

3.2.1. UWB Waveforms without Emission Limits. The powerspectrum density (PSD) of the designed UWB signal isillustrated in Figure 6. Also, notice that the maximumfrequency has been normalized. We assume that there isno spectral emission limit on UWB sensors, and the avail-able spectrum locates at [0.17 0.33] and [0.52 0.82]. Thissituation mainly corresponds to certain applications whereonly some geographical adjacent networks operate nearbyUWB sensors simultaneously. When adopting the simplifiedalgorithm, with both κi and δ optimized beforehand, theobtained spectrum efficiency of UWB waveforms is about95%. The spectral attenuation in corresponding primarybands is about 66 dB, which can essentially mitigate out-bandinterference to other networks. By contrast, the frequencyhopping technique can only use one single frequency band,and the maximum spectrum efficiency is no more than 60%in this situation.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−70

−60

−50

−40

−30

−20

−10

Normalised frequency

PSD

(dB

m/M

Hz)

M( f )H( f ): 50 iterationsH( f ): 100 iterations

(a)

0 2 4 6 8 10−95

−90

−85

−80

−75

−70

−65

−60

−55

−50

−45

−40

The primary band

Frequency (GHz)

PSD

(dB

m/M

Hz)

H( f )FCC emission limit M( f )

(b)

Figure 6: The designed UWB signals under different applications.(a) UWB waveform without regulatory emission limits. (b) UWBwaveforms under FCC emission template. Notice that the totalnumber of the basis functions is 64 in (b).

3.2.2. UWB Waveforms with Emission Limits. On the otherhand, the UWB signal in Figure 6(b) is emitted under astrictly regulatory emission mask in order to avoid inter-fering other legal wireless services in indoor applications.Here, we adopt the FCC emission mask [11]. At the sametime, recent investigations indicated that there may still existunbearable interference to some specific legal services evenif the emitted pulse has adopted the regulatory emissionlimit [13]. Therefore, the transmit UWB pulses shouldperform sufficient spectrum avoidance to further eliminateits potential interference to these specific wireless systems.


It can be found that, even in this situation, UWB signalcan still take full advantage of the regulatory spectrumto improve its communication reliability. As is shown byFigure 6(b), spectrum efficiency can be as much as 97.6%in unoccupied bands. We also assume that there is oneactive legal network being detected in [5 5.5] GHz. Withlittle effort, the corresponding subweight vector, denotedby wavoid, can be determined from (31) with fdown and fup

replaced by the vulnerable band. Then by directly settingwavoid to 0, the UWB waveform with spectrum notch canbe generated as shown in Figure 6(b). Spectral notcheswith attenuation larger than 90 dB can be produced, whicheffectively eliminates the interference from UWB sensorsto other networks. Besides, other networks’ signals areusually equivalent to narrow-band interference for UWBsensors; so this spectrum notch can be also employedto mitigate the narrow-band interference. In comparison,the obtained spectrum efficiency of the Hermite-Gaussianfunction based UWB waveform is only 65%, and thespectral attenuation in primary band is 25 dB [22]. Thedesigned shaping filter in [23] can generate UWB waveformswith a spectrum efficiency of 83.7%. However, given aspecific primary user over its working band, the spectralattenuation may be only 30 dB at the expense of the obviousspectrum efficiency decline in nonprimary bands. Whenthe aggregate emission energy from multiple UWB nodesis considered, these exited schemes can hardly mitigatemutual interference between UWB sensors and other legalnetworks.

3.2.3. Orthogonal UWB Waveforms. Furthermore, orthog-onal UWB waveforms can be easily designed based onour suggested method. Taking FCC emission limits forexample, we firstly divide the whole emission mask intomultiple nonoverlapped spectral sections with constantamplitude. Then, by carefully designing the correspondingphase response for each spectral line, the orthogonal pulsescan be derived. The correlation as well as autorelation oforthogonal UWB waveforms is illustrated in Figure 7(a).Multiple UWB sensors apparently keep mutual orthogonalwhen the accurate synchronization has been acquired. Oncespectrum holes are detected, UWB sensors can accesswithout waiting for a coordinate control. So, our orthogonalwaveforms can be applied to UWB sensors to significantlyreduce complexity of the upper layer control so as to avoidunacceptable scheduling delay. Moreover, it should be notedthat the correlation in essence remains zero within a certainsynchronization derivation range (about 0.4 nanoseconds).As a result, in multiple UWB sensor networks with thetiming errors, the performance of our UWB waveforms issupposed to be much superior to that of based on SOCP[23].

In Figure 7(b), we evaluate the transmission performanceof existing different waveforms in a UWB network which isbased on WDMA. In this experiment, we still adopt FCCemission mask and the maximum UWB frequency is 12 GHz.The uncoded binary pulse amplitude modulation (PAM)is adopted in the transmitter, and the coherent correlator

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2×10−9

−0.5

0

0.5

1

Am

plit

ude

AutorelationCorrelation (1th,2th)

Correlation (1th,3th)Correlation (2th,3th)

Time (s)

(a)

0 5 10 15 2010−4

10−3

10−2

10−1

BE

R

Target

Eb/N0 (dB)

Proposed δ = 0, 4 UESOCP in [23] δ = 0, 4 UEProposed δ = 0.2ns, 2 UE

Proposed δ = 0, 2ns, 4 UESOCP in [23] δ = 0, 2ns, 4 UE

−5

SOCP in [23] δ = 0.2ns, 2 UE

(b)

Figure 7: (a) Orthogonality illustrations of the designed wave-forms. (b) Transmission performance of different UWB signals ina WDMA network. Note that target performance corresponds tothe ideal UWB pulse, with spectral efficiency of 1.

is employed to perform optimal receiving in the presenceof AWGN. It is demonstrated from this simulation thatthe BER performance of our proposed pulses, operatingin 4-user WDMA network, can surpass SOCP techniqueabout 2 dB [23], if accurate timing has been acquired inUWB receivers. When there is timing inaccuracy in UWBreceivers, the designed pulses can obtain about 9 dB gaincompared to SOCP-based orthogonal pulses, when the


maximum timing deviation is about 0.2 nanoseconds in2-user WDMA network and the BER drops below 10−4.Therefore, from the aspect of the whole UWB networkperformance, our scheme can indeed enhance transmissionperformance and reduce stringent requirement on networkssynchronization, thus simplifying UWB receiver complexity.Notice that, here, we only show the performance in AWGNchannel. As is discussed in [38], on the other hand,noncoherent receiver is much more suitable for a simpleUWB implementation, and in this case, BER performanceis closed related to spectral energy carried by single UWBwaveforms. Hence, our UWB signal is still supposed tooutperform other methods given the UWB emission lim-its.

4. Conclusion

We address the coexistence issues between UWB sen-sors and others networks in this paper. A cognitive-based dynamic spectrum accessing scheme is suggested tomitigate mutual interference between geographic adjacentnetworks, in which UWB sensors utilize available idlespectrums by monitoring the nearby spectral environmentand identifying the unused spectrum. By introducing statetransition process to describe the working state of PU, wetransform spectrum sensing into the demodulation of anequivalent state sequence. In fact, our presented algorithmprovides a new insight in general spectrum sensing whichmay benefit other specific sensing algorithms. To react tothe highly emission adaptation in UWB sensors, a signalgenerator with great reconfigurable capability is proposedbased on RBF network. The designed UWB waveformscan entirely utilize multiple spectral sections to improvethe transmission reliability of UWB sensors. Also, ouralgorithm can produce signals with sufficient spectrumavoidance and totally eliminate mutual interference betweennearby networks and UWB sensors. The orthogonal cogni-tive UWB waveform is also investigated finally. It can befound that, in WDMA-based UWB sensor networks withtiming deviation, our orthogonal waveforms considerablyoutperform other existed UWB orthogonal signals. Futurework may include profound analysis on sensing performancein the presence of state estimation errors. Also, the accuraterelation between sensing gain and the PU state transitioncharacteristic remains an attractive area in following inves-tigations.

Acknowledgments

This research was partly supported by the Ministry of Knowl-edge Economy, South Korea, under the ITRC support pro-gram supervised by the Institute for Information TechnologyAdvancement (IITA-2009-C1090-0902-0019). This work wassupported by NSFC (60772021, 60972079, 60902046), theResearch Fund for the Doctoral Program of Higher Educa-tion (20060013008, 20070013029), and the National High-tech Research and Development Program (863 Program)(2009AA01Z262).

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Interference Mitigation between Ultra-Wideband Sensor Network and Other Legal Systems

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