The Applications of Decision-Level Data Fusion Techniques in the Field of Multiuser Detection for DS-UWB Systems

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1 Sesors 205, 5, ; doi:0.3390/s Article OPEN ACCESS sesors ISSN The Applicatios of Decisio-Level Data Fusio Techiques i the Field of Multiuser Detectio for DS-UWB Systems Yebo Gu, Miglei Yag 2, Zheguo Shi ad Zhilu Wu, * School of Electroics ad Iformatio Egieerig, Harbi Istitute of Techology, Harbi 5000, Chia; s: guyebo987@gmail.com (Y.G.); shizheguotvt@gmail.com (Z.S.) 2 Shaghai Electro-Mechaical Egieerig Istitute, Shaghai , Chia; ahmiglei989@gmail.com * Author to whom correspodece should be addressed; wuzhilu@hit.edu.c; Tel.: ; Fax: Academic Editor: Vittorio M. N. Passaro Received: August 205 / Accepted: 8 September 205 / Published: 25 September 205 Abstract: I this paper, the decisio-level data fusio techiques are exteded to the multiuser detectio (MUD) field. The two ovel MUD algorithms, that is the chairma arbitratig decisio-level fusio criterio (CA-DFC) based MUD algorithm ad the veto logic decisio-level fusio criterio (VL-DFC) based MUD algorithm, are proposed for DS-UWB commuicatio systems. I CA-DFC based method, the chairma ca make his arbitratio amog the prelimiary decisios from sub-optimal detectors by his ow rule. I the VL-DFC based method, the udetermied bits i these prelimiary decisios are cosidered to costruct a simplified solutio space, ad the the chairma ca make his fial decisio withi this space. Simulatio results demostrate that the performaces of CA-DFC ad VL-DFC based MUD algorithms are superior to those of other sub-optimal MUD algorithms, ad eve close to that of OMD. Moreover, both of these proposed algorithms have lower computatioal complexity tha OMD, which reveals their efficiecy. Compared with CA-DFC, VL-DFC based algorithm achieves a little improvemet i its performace, at the cost of the icremet i its computatioal complexity. Thus, they ca be applied to differet practical situatios. Keywords: data fusio; decisio-level fusio criterio (DFC); multiuser detectio (MUD); DS-UWB

2 Sesors 205, Itroductio Data fusio is a sigificat techique for detectio, estimatio ad decisio makig. As Joit Directors of Laboratories (JDL) defies [], data fusio is a multilevel, multifaceted process hadlig the automatic detectio, associatio, correlatio, estimatio, ad combiatio of data ad iformatio from several sources. Hece, its objective is to make the optimal or sub-optimal use of the iformatio geerated by multiple kowledge sources ad sesors. Now data fusio based systems are widely used i may areas, such as sesor etworks, robotics, video ad image processig, market plaig, data miig, ad kowledge discovery applicatios [2 4]. I the preset literature, data fusio is usually categorized ito three types: data-level, feature-level, ad decisio-level fusios [5,6]. To take accout of the situatios costraied o the commuicatio badwidth or the data storage capacity, the data-level ad feature-level fusios may ot always be applicable, compared with the decisio-level fusio [5]. That is, prelimiary decisios should be made at each local detector i order to compress the bits trasmitted to the decisio fusio ceter. The this ceter will make a global decisio based o these local decisios ad some fusio criterios. Due to the various types of detector (or classifier, sesor) outputs, decisio-level fusio cosidered i the literature ca be divided ito three categories [7]: the abstract level, the rak level, ad the measuremet level. I [8], the authors have classified may typical decisio-level fusio methods ito these three categories. I detail, the Majority Votig [9], Weighted Majority Votig [0], Behavior Kowledge Space [], ad Naive-Bayes Combiatio [2] methods are belog to the first category; the Class Set Reductio methods (icludig itersectio of eighborhoods ad uio of eighborhoods) ad the Class Set Reorderig methods (icludig highest rak method, Borda cout method ad logistic regressio method) [3] belog to the secod category; the Class-Coscious methods [4] ad the Class-Idifferet methods (such as Decisio Template combier[5] ad Dempster-shafer combier [6]) belog to the last category. O the other had, ultra-widebad (UWB) techology is attractive for its potetial applicatios i Wireless Persoal Area Networks (WPAN) [7 9]. It employs the short pulses (with badwidths of several GHz) to trasmit its iformatio symbols at low power [20]. The advatages of UWB also stem from its ultra-widebad ature, such as good iformatio hidig ability ad less sesitivity to multipath fadig [2,22]. To reiforce its multiple-access (MA) ability i the multiuser occasio, UWB ca be combied with traditioal spread-spectrum (SS) techiques, which were firstly proposed by Scholtz i [23], ad with subsequet aalyses i [24 26]. Amog them, direct sequece UWB (DS-UWB) is a efficiet MA scheme [2,27,28], where biary phase-shift keyig (BPSK) ca be employed ad a large umber of active users ca share the same frequecy badwidth simultaeously, iterferig with others [29]. (Please ote that, aother importat spectrum sharig strategy is the cogitive radio techique. However, due to the space limitatio, this techique will ot be studied i this paper. The iterested readers ca refer to [30] for more iformatio.) Therefore, the multiple access iterferece (MAI) exists ad coduces to the performace aggravatio of the covetioal detector (CD) (also called the sigle-user matched filter). (For this reaso, a lot of receiver solutios have bee proposed i the literature. I [3], the multiple atea diversity was employed i sigle-user UWB systems. I [32], a stop-ad-go strategy based o eergy detectio i CD receiver was applied to alleviate excessive oise collectio i sigle-user UWB clustered multipath chaels. I [33], a zoal based Rake receiver was further proposed for multiuser UWB systems.) Besides these, the multiuser detectio (MUD) techique that ca

3 Sesors 205, elimiate or weake the egative effects of MAI is studied i [34 43]. Verdu proposed the optimum multiuser detector (OMD) for code divisio multiple access (CDMA) systems [34], ad it ca achieve the optimal bit error rate (BER) performace [35] ad the perfect ear-far effect (NFE) resistat ability [36]. To DS-UWB systems, this OMD method was itroduced by Yoo ad Koho [20]. However, the computatioal complexity of OMD growig expoetially with the umber of active users makes it impractical to use [37]. Cosequetly, i order to make the tradeoff betwee performace ad complexity, various sub-optimal MUD algorithms have bee studied i literatures. I [38], a Reduced Complexity Maximum Likelihood (RCML) algorithm was proposed, but its practical use seems still impossible. I [39], a multiuser frequecy-domai (FD) turbo detector combig FD turbo equalizatio schemes with soft iterferece cacelatio was preseted, whereas its BER performace is usatisfactory. A multiuser detectio method usig a ovel geetic algorithm base o complemetary error fuctio mutatio (CEFM) was discussed for UWB systems i [40] ad other swarm itelligece based MUD algorithms were studied i [4 43]. However, it is clear that a sigle multiuser detector caot always be well suited for a particular occasio, particularly whe the multipath or shadow fadig happes. I [44,45], distributed sigal detectio was exteded to the multiuser problem, the the joitly optimum criterio ad the idividually optimum criterio were proposed for cooperatig receivers. Essetially, the performace gai obtaied by this overall procedure is due to its iheret diversity. However, this distributed MUD scheme is still of high computatioal complexity, as well as OMD. Besides, more ateas ad more commuicatio loads are ivolved i this procedure. I this paper, motivated by the cocepts of decisio-level fusio ad distributed sigal detectio i [4,45], we firstly apply the decisio-level fusio techiques ito the field of MUD. The two ovel MUD algorithms, that is the chairma arbitratig decisio-level fusio criterio (CA-DFC) based MUD algorithm ad the veto logic decisio-level fusio criterio (VL-DFC) based MUD algorithm, are proposed for DS-UWB systems. I both of these methods, a set of sub-optimal detectors (icludig the miimum mea square error (MMSE) detector, the decorrelatig (DEC) detector ad the successive iterferece cacellatio (SIC) detector) are used, ad the prelimiary decisios from these detectors will be merged together by CA-DFC or VL-DFC i the fusio ceter. The umerical results demostrate that these two proposed MUD algorithms both have the much better BER performace ad NFE resistat ability tha other sub-optimal MUD algorithms, ad eve close to OMD. Meawhile, the computatioal complexity of these ovel methods is sigificatly lower tha that of OMD. Compared with CA-DFC, VL-DFC based MUD method ca achieve a little superior performace at the expese of its higher complexity. So these two proposed algorithms have their differet applicatio rages. The remaider of this paper is orgaized as follows. I Sectio 2, some typical sub-optimal MUD algorithms are reviewed ad the decisio-level fusio based MUD system model is costructed for DS-UWB systems. I Sectio 3, the optimal decisio-level fusio criterio (O-DFC) ad its simplified form, which is the majority votig decisio-level fusio criterio (MV-DFC), are discussed. O the problem aalysis of O-DFC ad MV-DFC, two ovel MUD algorithms based o CA-DFC ad VL-DFC are proposed respectively, i Sectio 4. I Sectio 5, simulatio experimets that compare the performace of differet MUD algorithms are made. Coclusios are i Sectio 6.

4 Sesors 205, Problem Statemet 2.. Some Typical MUD Algorithms for DS-UWB Systems Here, we let a K-user sychroous DS-UWB system uder the additive white Gaussia oise (AWGN) chael, which could also be regarded as the results of the processig of rake receivers i the multipath chael. For this reaso, we oly give the multiuser DS-UWB model i the AWGN case, while it ca be geeralized to the multipath case easily. I this multiuser DS-UWB system, each iformatio symbol is spread over multiple pulses usig pseudo radom sequeces (PRS). The BPSK modulatio is employed by each user ad the trasmitted sigal of the kth user ca be expressed as: N c ( k) ( k) ( k) tr = j tr f c j= = 0 S () t b p w ( t jt T) () where {bj (k) } is the iformatio symbols of the kth user, {p (k) } deotes the PRS assiged to the kth user, Tc is the pulse repetitio period (amely the chip period), Tf is the time duratio of iformatio symbol that satisfies Tf = NcTc, ad Nc is the legth of PRS. Besides, wtr(t) represets the trasmitted pulse waveform that ca be characterized as the secod derivative of Gaussia pulse [20,2]: t w t = π π 2 2 tr ( ) [ 4 ( ) ] exp[ 2 ( ) ] m m t τ τ (2) where τm is the parameter that cotrols the width of this pulse. If these K- users are all active, the whole received sigal of this system is K ( k ) () = k tr () + () k = rt AS t t (3) where Ak is the amplitude of the kth received sigal ad (t) represets the received oise modeled as the AWGN, with a ormal distributio N(0,σ 2 ). Accordig to [46], the output of a bak of sigle-user matched filters (MFs), called a covetioal detector (CD), ca be expressed i the followig matrix ad vector forms: y = RAb + y (4) T f ik tr tr 0 () i ( k) where R deotes the K K ormalized cross-correlatio matrix with the i-kth etry ρ = S () t S () t dt, A is a K K diagoal matrix with the amplitude of the kth user s received sigal {Ak}k=,2,,K alog the diagoal, b = (b, b2,, bk) T is the K vector cotaiig the trasmitted iformatio bits from K users ad the superscript T deotes a vector traspose operatio. I additio, = (, 2,, K) T is the K T f ( k ) zero-mea Gaussia radom oise vector with = () t S () t dt ad its covariace matrix equal to k 0 T E[b ] tr 2 = σ R (5) Due to the crude assumptio that the MAI ca be modeled as a zero-mea Gaussia radom variable (called Gaussia approximatio ) for CD [47], its performace ad multiuser capacity are limited. To improve this, Verdu proposed the optimum multiuser detectio (OMD), which is based o the maximum likelihood (ML) criterio [35]. The objective fuctio of OMD is give as:

5 Sesors 205, ˆ T T b = arg max (2 b Ay b ARAb) K b {, + } (6) From Equatio (6), it is obvious that the selectio of this optimal solutio ˆb i the K-dimesioal Euclidea solutio space is geerally a No-determiistic Polyomial (NP) hard problem [37]. That is, the computatioal complexity of OMD is O (2 K ), which grows expoetially with the umber of active users. For this reaso, despite its sigificat performace ad capacity gais over CD, it is useless i practice. As a result, several sub-optimal MUD algorithms have bee proposed to make the tradeoff betwee performace ad complexity. Liear MUD algorithm is oe kid of sub-optimal approach, which processes the output of CD through multiplyig by a matrix M. For example, i the decorrelatig (DEC) detector, its trasformig matrix is M = R ; i the miimum mea square error (MMSE) detector, its trasformig matrix is M A A 2 2 = [R + σ ] (7) Moreover, as the liear detectors, such as CD, DEC, ad MMSE detectors, the matrix multiplicatio is usually followed by a /+ decisio module: bˆ sg( My) = (8) where ˆb is the prelimiary decisio vector. No-liear MUD algorithm is aother kid of sub-optimal approach. For example, i the successive iterferece cacellatio (SIC) detector, the decisio of the kth user ca be expressed as [46]: bˆ = sg( y A ρ bˆ ) k k j jk j j= k+ K (9) where the decisio of the ith user, i = k +,k + 2,, K, should be correctly demodulated, otherwise, its performace will be affected drastically. Thus, the order of demodulatig users is the key problem for this detector. Here, we order users through Equatio (0), which ca be estimated easily from the outputs of CD: T E[( r() t S () t dt)] = σ + A + A ρ 0 ( k ) tr k j jk j k (0) 2.2. Decisio-Level Fusio Based MUD System Model I this paper, we cosider the applicatio of decisio-level fusio techiques ito the field of MUD. The decisio-level fusio based MUD system model is costructed as Figure shows. The characteristics of this scheme cotai: () The outputs of CD y = (y, y2,, yk) T are passed to the prelimiary sub-optimal detectors, icludig SIC, DEC, ad MMSE detectors; (2) The prelimiary decisios of SIC, DEC, ad MMSE (let X, X2 ad X3) are set to the fusio ceter; (3) The fusio ceter cosists of two parts: committee ad fusio criterios. Depedig o differet decisio-level fusio criterios (DFCs), the committee ca make a differet fial decisio ˆb o the basis of these prelimiary decisios. (4) This scheme is ot distributed i fact, for it oly eeds oe atea to receive sigals. Cosequetly, the computatioal complexity ad apparatus itegratio are saved.

6 Sesors 205, y X rt () S () tr () t y 2 S (2) tr () t y X 2 ˆb y K X 3 S ( K ) tr () t Figure. The structure of decisio-level fusio based MUD system model. 3. Optimal Decisio-Level Fusio Criterio (O-DFC) ad Its Simplified Form Sice O-DFC has bee discussed i the distributed detectio system [48,49] (i Figure 2), here we simply review it ad exted it to our decisio-level fusio based MUD model (i Figure ) i Sectio 3.. The the majority votig decisio-level fusio criterio (MV-DFC), which is the simplified form of O-DFC, is give i Sectio 3.2. Figure 2. Distributed detectio system with decisio-level fusio ceter. 3.. Optimal Decisio-Level Fusio Criterio (O-DFC) I the distributed detectio system as Figure 2 shows, sigal processig is accomplished at the sesor ad prelimiary decisios are trasmitted to the data fusio ceter. The the global decisio will be obtaied as the output of this ceter, based o differet DFCs. The optimal DFC (O-DFC) was derived by Chair ad Varshey [48]. Here, we review it at first ad the exted it to our model i Figure. Assume a biary hypothesis testig problem, with two hypotheses: H0 : the sigal is abset H : the sigal is preset ()

7 Sesors 205, where the priori probabilities of these hypotheses are P(H0) = P0 ad P(H) = P. Cosider there are detectors i Figure 2 ad the observatios of each detector are deoted by yi, i =, 2,, with the assumptio of statistical idepedece. I additio, the coditioal probability desity fuctio is p(yi Hj), i =, 2,,, j = 0,. As Figure 2 depicts, each detector ca make its ow decisio ui by applyig a decisio rule gi(yi), i =, 2,,, where, if H0is decided ui = +, if His decided (2) These local prelimiary decisios ui will be set to the decisio-level fusio ceter for the further processig. I geeral, the global decisio is a fuctio of these prelimiary decisios as: u f u u u = (, 2,, ) (3) Accordig to [48], the miimum probability of error criterio ca be employed to derive the O-DFC, which ca be summarized as: +, if a + au i i > 0 = = (4), otherwise 0 u f( u, u2,, u ) i= where the weights are give by a 0 = log P P 0 (5) a i PM i log, if ui =+ PF i = PF i log, if ui = PM i (6) where PFi = P(ui = + H0) is the false alarm probability ad PMi = P(ui = H) is the miss alarm probability of the ith detector, respectively. For more iformatio of the detailed derivatio, iterested readers ca refer to [48]. I our decisio-level fusio based MUD model, however, these two hypotheses should be modified as: H0m : is trasmitted by the mth user Hm : + is trasmitted by the mth user (7) As a result, the false alarm probability P _ Fim = P( u _ im = + H _ 0 m) ad the miss alarm probability P _ Mim = P( u _ im = H _ m) of the ith sub-optimal detector for the mth user are both equal to its bit error rate (BER) Peim, we have that is PFim = PMim = Peim, i =, 2,,, m =, 2,, K ad K is the umber of users i this multiuser system. For the equiprobable source assumptio, we have a0 = 0. Therefore, the O-DFC i our model ca be rewritte by

8 Sesors 205, , if a u > 0 u = f u u u = =, otherwise im im m ( m, 2m,, m) i (8) where um is the fial decisio for the mth user, uim is the prelimiary decisio of the ith sub-optimal detector for the mth user, ad a im = log I particular, for the special case whe there are it {} = 3 detectors, a propositio has bee proposed by Che et al. i [49]. Assumig the BER for the mth user at each detector be Peim, i =, 2, 3, this propositio reveals that the BER achieved at the fusio ceter, which is deoted as Pecm_O, is: P P eim eim P mi{ P, P, P, P } ecm _ O e0m em e2m e3m (9) = (20) where Pe0m = PemPe2m + PemPe3m + Pe2mPe3m 2PemPe2mPe3m. Therefore, from Equatio (20), we ca see that to achieve the improvemet of performace by this fusio scheme, the followig coditio should be satisfied P mi{ P, P, P } < (2) e0m em e2m e3m Otherwise, we should simply choose the detector havig the lowest BER for the best performace, which also meas that there is o performace gai i the fusio of these three detectors The Simplified form of O-DFC: the Majority Votig Decisio-Level Fusio Criterio (MV-DFC) To reder the O-DFC tractable, we make a further assumptio that for all sub-optimal detectors, their Peim are all equal to Pem, regardless of the differeces betwee these detectors. That is, aim are all equal to aim i Equatio (9). Besides, it is clear that the BER satisfies Pem < 0.5 (otherwise, the commuicatio is meaigless), so that Pem > Pem ad am > 0. The we ca derive the majority votig DFC, called MV-DFC, as follows: +, if u > 0 u = f( u, u,, u ) = =, otherwise im m m 2m m i (22) For this case, the propositio obtaied i [49] ca be simplified to P mi{ P, P } = (23) ecm _ MV e0m em where P e0m = 3P em 2 2P em3. So i order to improve the performace from Pem, the followig coditio should be satisfied: That is, P e0m < Pem (24) 2 3Pem 2Pem < (25)

9 Sesors 205, here we ca get Pem < 0.5 or Pem > from Equatio (25). Nevertheless, cosider Pem is the BER coditioed o 0< Pem <, the coditio 0 < Pem < 0.5 should be satisfied to make a improvemet. Obviously, it is quite easy to satisfy this coditio i the ormal commuicatio systems. 4. Two Improved Decisio-Level Fusio Criterios for MUD 4.. The Problems i O-DFC ad MV-DFC Although two decisio-level fusio criterios (O-DFC ad MV-DFC) have bee aalyzed above, their performaces are ot acceptable i our decisio-level fusio based MUD model, due to the followig reasos: () The optimal decisio-level fusio performace that O-DFC ca gai, is coditioed o the assumptio that these local detectors are statistically idepedet with each other; meawhile, the accurate BER value of each detector should be a priori kowledge. To our kowledge, these two assumed coditios are usatisfied i fact. O oe had, i Figure, the iputs of these sub-optimal detectors (SIC, DEC ad MMSE) are all the outputs of CD. For this reaso, their performaces have a defiite relatioship with each other. Further, their correlatio degree ca be estimated [46] quatitatively: ρ f N = N N N + N f r f (26) where is the total umber of sub-optimal detectors, N is the total umber of iformatio bits for umerical tests, N f deotes the umber of bits that are detected wrogly by all detectors while N r is the bits detected correctly by all. Figure 3 depicts the correlatio degree ρ3 of SIC, DEC, ad MMSE detectors versus Eb/N0, whe 0 active users are i this system ad 06 iformatio bits are used for this simulatio. From this figure, we ca see that as the Eb/N0 icreases, their correlatio degree rises obviously util Eb/N0 = 0 db (from 0.48 to 0.87), while after that, it fluctuates slightly above ρ E b /N 0 [db] Figure 3. The correlatio degree of SIC, DEC, ad MMSE detectors, whe K = 0.

10 Sesors 205, O the other had, sice the commuicatio chael is radom, we are ulikely to estimate the BER of each detector accurately i practice. (2) Compared with O-DFC, MV-DFC does ot eed the accurate estimatio of the BER of each detector. Moreover, from Equatio (22), oly the operatio of additio is demaded. However, its defects are also evidet: (i) to make a fial decisio, the umber of its sub-optimal detectors should be odd; (ii) the assumptio of statistical idepedece is still ecessary; (iii) eve though the accurate estimatio of BER is ot eeded, the coditio Peim = Pem, i =, 2,,, should still be satisfied, which is impossible for differet sub-optimal detectors i our model. From all the aalysis above, we ca coclude that both the O-DFC ad the MV-DFC are ot acceptable i our decisio-level fusio based MUD model, ad this will also be autheticated by umerical simulatios i Sectio The Chairma Arbitratig Decisio-Level Fusio Criterio (CA-DFC) As Figure shows, the prelimiary decisios (let X, X2, ad X3) of SIC, DEC, ad MMSE detectors are trasmitted to the committee sychroously. Note that it is a feature of the committee that there is a chairma i it, whose role is to evaluate these prelimiary decisios ad make the global decisio [47]. The differet ways to acquire this global decisio correspod to the differet DFCs. So here, we cosider a situatio where the chairma ca make his arbitratio amog these sub-optimal or prelimiary decisios with its ow arbitratig rule, to select which oe is the best. This method is called the chairma arbitratig DFC (CA-DFC) i this paper ad discussed below. Takig the objective fuctio of OMD i Equatio (6) ito accout, we defie a approvig degree fuctio for the chairma to make his arbitratio: D b Ay X ARAX 2 T T i i i = (27) where i =, 2,,. The the CA-DFC ca be derived: If the term D j = max i=,2,, D i (28) satisfies, the prelimiary decisio Xj is arbitrated as the global decisio by the chairma. I our model, equals 3 for SIC, DEC, ad MMSE detectors are employed, ad this ca be geeralized ito the case that has more tha three detectors without difficulties. Differig from O-DFC ad MV-DFC, this CA-DFC does t require the assumptio of statistical idepedece betwee these sub-optimal detectors, as well as the accurate BERs of them. Furthermore, it ca be speculated that the BER performace of this CA-DFC based MUD method is better tha that of ay of these sub-optimal detectors, due to the operatio of Equatio (28). That is, its BER achieves 4.3. The Veto Logic Decisio-Level Fusio Criterio (VL-DFC) Pecm _ CA < mi{ Pem, Pe 2m, Pe 3m } (29) Aother DFC itroduced ito the field of MUD i this paper is the veto logic (called VL-DFC). The veto logic implies that all sub-optimal detectors (all members) have to agree with the fial decisio that the chairma makes. If ayoe of them dissets, the fial decisio should be abolished.

11 Sesors 205, I this method, the votig bit is defied at first: +, if uim = + i= um = f ( um, u2m,, um) =, if uim =. (30) i=, otherwise where m =, 2,, K ad K is the umber of users. Besides, the symbol meas this bit caot be determied betwee + ad i this veto logic, while the term uim i= =+ (or uim i= = ) meas that + (or ) is the uaimous agreemet reached by all sub-optimal detectors. Through Equatio (30), the K-dimesioal votig vector is U = (u, u 2,, u K ) T, ad the umber of udetermied bits i it is L (L < K). It is evidet that there are 2 L likely solutios that the chairma should make a further decisio. Here, we costruct a simplified solutio space, which cosists of all these likely solutios, for the chairma to make his fial decisio. The approvig degree fuctio (Equatio (27)) i CA-DFC is also applied to select the best oe as the output of VL-DFC. To summarize, this VL-DFC ca be represeted by the followig steps: () Calculate the K-dimesioal votig vector U by Equatio (30); (2) Costruct a simplified L-dimesioal solutio space based o U, ad L is the umber of udetermied bits i U; (3) Compare the 2 L likely solutios i this space, ad cosider the solutio that has the largest value of Equatio (27) as the fial decisio made by the chairma. Note that, the CA-DFC is a special case of VL-DFC, for the fial decisio i CA-DFC is boud to be ivolved i the simplified solutio space of VL-DFC. Cosequetly, the BER performace of VL-DFC is better tha that of CA-DFC, that is, Pecm_VL < Pecm_CA. Whereas, the performace improved by VL-DFC, compared with CA-DFC, is at the cost of its computatioal complexity icreased. The detailed discussio about this is located i the followig sectio. 5. Numerical Results ad Aalysis I order to test ad aalyze these two proposed CA-DFC ad VL-DFC based MUD algorithms (hereiafter called CA-DFC ad VL-DFC, respectively), Mote Carlo simulatios are utilized. As Figure shows, a decisio-level fusio based MUD receiver for DS-UWB systems is desiged; meawhile, i our experimets, the fusio ceter applies four DFCs: O-DFC, MV-DFC, CA-DFC, ad VL-DFC. The major parameters used for these simulatios are summarized i Table. The performaces of CD, SIC, DEC, MMSE, O-DFC, MV-DFC, CA-DFC, VL-DFC, ad OMD are compared, icludig the BER performace versus Eb/N0, the ear-far effect (NFE) resistat capability, the BER performace versus the umber of users K, ad also their BER performace i the idoor multipath eviromet. Before them, the computatioal complexity of CA-DFC ad VL-DFC is compared with that of OMD to demostrate their efficiecy.

12 Sesors 205, Table. Simulatio parameters. System DS-UWB Modulatio Mode BPSK Pseudo radom sequeces (PRS) m sequeces The legth of PRS 3 Commuicatio chael AWGN or IEEE a (CM2) The umber of testig iformatio symbols 0 5 The width of UWB pulse s The pulse repetitio period 2 s The umber of active users K = 5, 0, 5, The Computatioal Complexity Compariso To compare the computatioal complexity of CA-DFC ad VL-DFC with that of OMD, the total umber of calculatig the value of the objective fuctio i Equatio (6) per K iformatio bit vector b is cosidered here (listed i Table 2). As the calculatio of this fuctio is ot ivolved i CD, SIC, DEC, MMSE, O-DFC, ad MV-DFC, the computatioal complexity of them is egligible. Table 2. The computatioal complexity compariso. MUD Algorithms CA-DFC VL-DFC OMD Calculatio Number 2L 2K I Table 2, we defie is the umber of sub-optimal detectors used for fusio, ad i this paper, = 3. Besides, L is the umber of udetermied bits i the votig vector, ad K deotes the umber of active users i this system. It is clear that the value of L has a relatioship with K, ad i geeral, the greater K is (ad the stroger the MAI is), the greater L is. Therefore, the ratio L/K is adopted ad the the computatioal complexity of VL-DFC ad OMD is depicted i Figure 4, coditioed o L/K = 0., 0.3, 0.5, respectively. From the simulatio results i Figure 4, we ca see that as the umber of users icreases, the more computatioal complexity will be saved by VL-DFC, particularly whe L/K is smaller tha 0.3. I fact, this demad is satisfied as Figure 5 shows, which gives the average L versus Eb/N0 curves coditioed o K = 5, 0, 5 ad 20 i AWGN chael. From this figure, three coclusios are obtaied as follows: First, as K icreases, the average L also icreases obviously, which is due to the ehacemet of MAI. Secod, all the situatios (poits i this figure) ca achieve L/K < 0.3. The last is that, as the Eb/N0 is lower, the average L is greater, which meas the solutio space costructed i VL-DFC becomes larger for the chairma to make his global decisio.

13 Sesors 205, The Computatioal Complexity VL-DFC (L/K=0.) VL-DFC (L/K=0.3) VL-DFC (L/K=0.5) OMD K Figure 4. The computatioal complexity of VL-DFC ad OMD The average L K=5 K=0 K=5 K= E b /N 0 [db] Figure 5. The average L versus Eb/N0 curves whe K = 5, 0, 5, ad 20 i AWGN chael The BER Performace versus Eb/N0 Compariso The BER versus Eb/N0 curves i the AWGN chael are depicted i Figure 6, whe the umber of users i this system is 0 ad the eergy per bit of all users is esured to be equal by perfect power cotrol, that is, Eb = Eb2 = = Eb0. It ca be see from Figure 6 that the BER performaces of these MUD algorithms ca be divided ito two types: oe is the algorithms that the decisio-level fusio is ot cosidered, ivolvig CD, SIC, DEC, MMSE, ad OMD; the other is the algorithms that the decisio-level fusio is cosidered o the basis of SIC, DEC, ad MMSE as Figure shows, ivolvig O-DFC, MV-DFC, CA-DFC, ad VL-DFC.

14 Sesors 205, I the first type, the BER performace of CD is the worst while that of OMD is the best, which has bee demostrated i the literature. However, due to the assumptio of statistical idepedece betwee SIC, DEC, ad MMSE is ot satisfied, the BER performaces of O-DFC ad MV-DFC are eve ot better tha that of MMSE. O the other had, CA-DFC ad VL-DFC both have much better BER performaces tha MMSE, O-DFC, ad MV-DFC. Besides, compared with CA-DFC, VL-DFC is still a little better, which we have aticipated i Sectio BER CD SIC DEC MMSE O-DFC MV-DFC CA-DFC VL-DFC OMD E b /N 0 [db] Figure 6. The BER versus Eb/N0 curves i AWGN chael whe K = 0 ad perfect power cotrol is employed. Note that there is still a performace gap betwee VL-DFC (also CA-DFC) ad OMD. To our kowledge, the reaso is that i both our proposed methods, the situatio whe the prelimiary detectio results of these sub-optimal detectors (here, SIC, DEC, ad MMSE) are all wrog is ot cosidered. Sice the assumptio of statistical idepedece is ot established, the estimatio of this probability is out of this paper The NFE Resistat Ability Compariso The BER performaces of these algorithms without power cotrol, amed the ear-far effect (NFE), are discussed i this simulatio. I this DS-UWB system, there are also 0 users ad the commuicatio chael is AWGN. Figure 7 shows the BER performace curves of the first user, whe the eergy per bit of this user is fixed with its E b /N 0 equal to 5 db while that of other ie users E b2~0 /N 0 varies from 0 db to 20 db sychroously. That is, the ratio E b2~0 /E b chages from 5 db to 5 db. From this figure, we ca see that the NFE resistat ability (o sese with E b2~0 /E b ) of OMD is the best amog them. Those of CA-DFC ad VL-DFC are evidetly much better tha those of other sub-optimal detectors, ad eve close to that of OMD. Moreover, those of O-DFC ad MV-DFC are still ot better tha that of MMSE for the same reaso as well as Figure 6 shows.

15 Sesors 205, Furthermore, the BER performace curve of SIC has a iflexio at the poit where Eb2~0/Eb = 0 db, due to its detectio method i Equatios (9) ad (0). O oe had, whe the eergy per bit of users 2~0 calculated by Equatio (0) is smaller tha that of the first user, that is Eb2~0/N0 < 5 db ad Eb2~0/Eb < 0 db, the the iformatio bits of user will be detected at first, the same as CD does. This is the reaso the BER performace curve of SIC is idetical with CD util Eb2~0/Eb = 0 db. O the other had, whe Eb2~0/N0 > 5 db ad Eb2~0/Eb > 0 db, the iformatio bits of users 2~0 will be detected before those of the first user, with more reliability. Cosequetly, after the iterferig sigal subtracted from the origial received sigal by Equatio (9), the BER performace of SIC is improved dramatically BER CD SIC DEC MMSE O-DFC MV-DFC CA-DFC VL-DFC OMD E b2~0 /E b [db] Figure 7. The BER versus Eb2~0/Eb curves i AWGN chael whe K = 0 ad o power cotrol is employed The BER Performace versus K Compariso The BER performace curves of these detectors versus the umber of active users K are displayed i Figure 8, whe the eergy per bit of all users is set Eb/N0 = 5 db. I geeral, as the umber of users icreases, the BER performaces of all detectors become worse. I detail, OMD has the best capability to resist the effect of the icremet of K, while CD has the worst. I additio, we ca see that as K icreases, the gap betwee VL-DFC ad OMD elarges. The reaso for this pheomeo is that, the more users i this system, the more severely the MAI will be affected. So as K icreases, the probability that the prelimiary detectio results of SIC, DEC, ad MMSE are all wrog is bigger, resultig i the elargemet of this gap. But most importatly, the BER performaces of CA-DFC ad VL-DFC are both much better tha other sub-optimal MUD algorithms. The achievemet by itroducig decisio-level fusio techiques ito MUD is sigificat.

16 Sesors 205, BER CD SIC DEC MMSE O-DFC MV-DFC CA-DFC VL-DFC OMD K Figure 8. The BER versus K curves i AWGN chael whe Eb/N0 = 5 db The BER Performace Compariso i Multipath Eviromet I order to verify the performaces of CA-DFC ad VL-DFC based MUD algorithms i the idoor eviromet, which is the most commo situatio where UWB techology ca be employed, we carry out this experimet. Without loss of geerality, the recommeded IEEE a CM2 multipath chael [50,5] is used here, ad the path with the strogest eergy is gathered at the receiver. The BER performace curves of these MUD algorithms are compared i Figure 9. It is clear that the performaces of these two proposed fusio-based algorithms are much better tha those of other sub-optimal MUD algorithms, ad eve close to that of OMD. Takig accout of the lower computatioal complexity they have, we ca see that the good tradeoff betwee performace ad complexity is realized by these ovel fusio based algorithms BER CD SIC DEC MMSE O-DFC MV-DFC CA-DFC VL-DFC OMD E b /N 0 [db] Figure 9. The BER versus Eb/N0 curves i multipath chael whe K = 0.

17 Sesors 205, Coclusios I this paper, motivated by the cocept of data fusio, we have proposed two ovel decisio-level fusio based MUD algorithms, called the CA-DFC based MUD algorithm ad the VL-DFC based MUD algorithm. I the CA-DFC based scheme, the chairma at the fusio ceter ca do his arbitratio to select oe of the prelimiary decisios from sub-optimal MUD algorithms as the output of this scheme; while i the VL-DFC based scheme, the udetermied bits amog these prelimiary decisios are cosidered to costruct a simplified solutio space, ad the the chairma should select the best solutio withi this space as the global decisio. Computer simulatios show that the BER performace ad the NFE resistat ability of these two proposed algorithms are superior to those of other sub-optimal algorithms, ad eve close to those of OMD. Besides, the computatioal complexity of them is much lower tha that of OMD, which idicates their practical use. Ackowledgmets First ad foremost, I would like to show my deepest gratitude to my supervisor, Zhilu Wu, a respectable, resposible ad resourceful scholar, who has provided me with valuable guidace i every stage of the writig of this article. Without his elighteig istructio, impressive kidess ad patiece, I could ot have completed this article. His kee ad vigorous academic observatio elightes me ot oly i this article but also i my future study. I shall exted my thaks to Zhiyua Zog, Miglei Yag ad Zheguo Shi for all her kidess ad help. I would also like to thak all my teachers who have helped me to develop the fudametal ad essetial academic competece. My sicere appreciatio also goes to the teachers ad studets from Harbi Istitute of Techology, who participated this study with great cooperatio. Last but ot least, I d like to thak all my frieds, especially my lovely roommates, for their ecouragemet ad support. Author Cotributios Yebo Gu cotributed to the coceptio of the study; Miglei Yag cotributed sigificatly to aalysis ad mauscript preparatio; Zheguo Shi performed the data aalyses ad wrote the mauscript; Zhilu Wu helped perform the aalysis with costructive discussios. Coflicts of Iterest The authors declare o coflict of iterest. Refereces. White, F.E. Data Fusio Lexico: Data Fusio Subpael of the Joit Directors of Laboratories Techical Pael for C3; IEEE Tras.: Sa Diego, CA, USA, Khaleghi, B.; Khamis, A.; Karray, F.O.; Razavi, S.N. Multisesor data fusio: A review of the state-of-the-art. If. Fusio 203, 4, Saporta, G. Data fusio ad data graftig. Comput. Stat. Data Aal. 2002, 38,

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20 Sesors 205, Blum, R.S.; Hu, J. Distributed multiuser detectio. I Proceedigs of the Coferece Record of the Thirty-Third Asilomar Coferece o Sigals, Systems, ad Computers, Pacific Grove, CA, USA, October Verdu, S. Multiuser Detectio; Cambridge Uiversity Press: Cambridge, UK, Durisi, G.; Beedetto, S. Performace evaluatio of TH-PPM UWB systems i the presece of multiuser iterferece. IEEE Commu. Lett. 2003, 7, Chair, Z.; Varshey, P.K. Optimal data fusio i multiple sesor detectio systems. IEEE Tras. Aerosp. Electro. Syst. 986, AES-22, Che, J.G.; Asari, N.; Sivesk, Z. Improvig multiuser detectio performace by data fusio. I Proceedigs of the Global Telecommuicatios Coferece, Lodo, UK, 8 22 November996; Volume 3, pp Goebel, K.; Ya, W.; Cheetham, W. A method to calculate classifier correlatio for decisio fusio. I Proceedigs of the Decisio ad Cotrol, Las Vegas, NV, USA, December 2002; pp Abou-Rjeily, C. Performace aalysis of UWB systems over the IEEE a chael model. IEEE Tras. Commu. 20, 59, Hao, K.; Guber, J. Theoretical performace aalysis of the IEEE a UWB chael model. I Proceedigs of the IEEE Global Telecommuicatios Coferece, Washigto, DC, USA, November 2007; pp by the authors; licesee MDPI, Basel, Switzerlad. This article is a ope access article distributed uder the terms ad coditios of the Creative Commos Attributio licese (