On Rake Reception of Ultra Wideband Signals over Multipath Channels from Energy Capture Perspective
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1 IEICE TRANS. FUNDAMENTALS, VOL.E88 A, NO.9 SEPTEMBER PAPER Specia Section on Utra Wideband Systems On Rake Reception of Utra Wideband Signas over Mutipath Channes from Energy Capture Perspective Mohammad Azizur RAHMAN a), Student Member, Shigenobu SASAKI, Jie ZHOU, and Hisakazu KIKUCHI, Members SUMMARY Performance of Rake reception of Utra Wideband (UWB) signas is evauated from energy capture perspective. In addition to ordinary a Rake (ARake) and seective Rake (SRake) receivers which are considered in conventiona spread spectrum communications, we introduce optimum ARake and SRake receivers which incude the estimation of deay of the combining mutipaths. Impact of puse-width is discussed on their performances considering the reationship between puse-width and fading. Time hopping M-ary puse position moduation (TH-MPPM) and binary phase shift keying (TH-BPSK) are considered as moduation schemes. Extensive simuation resuts are presented showing the performances of the Rakes introduced using IEEE a UWB channe modes (CM1 to CM3). Performance of MPPM is shown for various vaues of M and moduation parameters. The impact of puse-width is iustrated mainy using BPSK. It is shown that the tota energy capture (i.e. by ARake) strongy depends on the puse-width, and the shorter the puse-width the more is the amount. The energy capture aso varies a ot for empoying either optimum or ordinary Raking method. Energy capture by SRake additionay strongy depends on the number of combined paths unti the number is 20 for optimum SRake and 10 for ordinary SRake; however, afterwards saturating effects are seen. Severa aspects regarding the performance versus compexity issue of Rake receivers are aso discussed. key words: utra wideband, mutipath, Rake reception, energy capture, puse-width 1. Introduction Utra Wideband (UWB) technoogy has been one of the most promising new technoogies for wireess communications [1]. Athough there are severa aternatives to design UWB systems, in this work we are interested in time hopping (TH) impuse radio (IR) UWB communications [2]. One of the most attractive features of the UWB signas is identified as their better mutipath resovabiity [3]. It is known that Rake receivers that are often empoyed in conventiona spread spectrum communications are attractive soutions in UWB communications over mutipath channes as we [4], [5]. Throughout this paper we use correation type Rake receivers [4] that use a reference signa consisting of puses matched with an isoated received puse. An a Rake (ARake) is one that coects a possibe Manuscript received August 23, Manuscript revised December 3, Fina manuscript received May 18, The authors are with the Department of Eectrica and Eectronic Engineering, Niigata University, Niigata-shi, Japan. Presenty, with the Department of Information and Communications, Nanjing University of Information Science and Technoogy, China. a) E-mai: aziz@teecom0.eng.niigata-u.ac.jp DOI: /ietfec/e88 a resoved mutipaths and combines the energy by maxima ratio combining (MRC) [6], [7]. However, there exist hundreds of resoved mutipaths for UWB systems. Aso, the number of resovabe paths increases with communication distance and bandwidth [3]. As a consequence, ARake reception wi cost unacceptabe compexity though the performance improvement is expected. As a compromise between performance and compexity, the concept of seective Rake (SRake) receiver has evoved in iterature [3], [6], [7]. SRake combines L c paths which has the first to the L c th argest magnitude out of a resoved paths L(L c < L) by MRC. In conventiona Rake type receivers, each correator is paced at each integer mutipe of the puse-width. ARake and SRake receivers that foow this method, we ca them ordinary a Rake (Or ARake) andordinary seective Rake (Or SRake) receiver respectivey. In UWB communications, puse waveform is not radiated continuousy, but at some time during the puse repetition interva. Additionay, mutipaths are not usuay received at deays that are mutipes of puse-width. It offers another option for Rake reception of UWB signas by estimating the deays of the mutipaths. System performance depends on the fraction of energy that can be captured by the Rake receiver [5]. If the estimation of optima deays of the mutipaths is avaiabe in spite of increasing compexity, it is suggested that more energy coud be captured by Rake receiver [3], [5]. ARake and SRake receivers that estimate the best deays and pace the correators at those deays, we ca them optimum a Rake (Op ARake) and optimum seective Rake (Op SRake) receiver respectivey. Athough the concept of optimum ARake and SRake woud be an attractive soution to fight mutipath fading, no performance comparison with ordinary Rake has been carried out yet either for ARake or SRake. Because the UWB channe is very frequency seective, the channe response shoud be highy dependent on the width of the puse transmitted. The amount of fading experienced by the signa shoud depend on the puse-width and so as the performances of the Rake receivers. However, many of previous works on Rake reception of UWB signas were mainy based on specific puse-width [3], [5], [8] [16]. Additionay, there have been no previous papers considering both ordinary and optimum Rakes discussing the performance versus compexity trade-off in reaistic UWB channes. In this paper, we discuss the effects of empoying or- Copyright c 2005 The Institute of Eectronics, Information and Communication Engineers
2 2340 IEICE TRANS. FUNDAMENTALS, VOL.E88 A, NO.9 SEPTEMBER 2005 dinary and optimum methods of Raking, puse-width variations and various moduation schemes on the performance of the above-mentioned Rake receivers over reaistic UWB channe modes to answer many previousy unanswered questions described above [17]. We consider time hopping M-ary PPM (TH-MPPM) incuding both overapped and orthogona signa set for MPPM [8] and TH-binary phase shift keying (TH-BPSK). First, we present a genera framework on cacuating error probabiities for the above-mentioned signaing schemes over mutipath channes. Then, we discuss the effect of puse-width on fading from the view point of indoor channe statistics. Finay, we present extensive simuation resuts using IEEE a UWB channe modes (CM1 to CM3) [18] investigating the effects of fading due to non ine of sight (NLOS) reception and increase in communication distance. We present error performances of the Rakes introduced and discuss severa aspects of performance versus compexity issue of Rake receiver considering severa points incuding the effect of puse-width from energy capture perspective. Our paper is organized as foows. In the next section we describe the signaing scheme, the receivers considered and derive the error probabiities. In Sect. 3, we discuss the reationship between puse-width and fading experienced over indoor mutipath channes. In Sect. 4, we first present simuation mode and then simuation resuts with reevant discussions. Finay, we concude in Sect. 5. It is assumed that each frame is subdivided into N c equay spaced chips giving, T f = N c T c, and symbo duration T s = N s T f. It is further assumed that δ M 1 + T p T c. The user dependent TH code C (k) j is a random number uniform over {0, 1,...,N c 1} and has a periodicity equa to N s. The signaing structure of TH-MPPM for an arbitrary user k is shown in Fig. 2. For the MPPM under consideration, it wi be caed orthogona MPPM whie δ i+1 δ i = T p and overapped MPPM, generay speaking, whie δ i+1 δ i < T p, i = 0, 1,, M 2. We consider the we known received monocyce puse shape as shown in Fig. 3. This provides a minimum autocorreation of at deays 0.212T p.ifδ i+1 δ i = 0.212T p, i = 0, 1,, M 2 is paced, it maximizes the Eucidian distance among the MPPM signa sets. It is caed the optimum overapped MPPM [8]. We consider a singe user environment. Hence, eaving the superscript k from now on, the received signa can be given by [9], r d (t) = s d (t) h(t) + n(t) 2. System Mode 2.1 Signas and Channe Mode We consider a TH system, a bock diagram of which is shown in Fig. 1. A transmitted symbo of the k-th user in TH-MPPM system is represented by [2], s (k) d (t) = β d N s 1 Ep j=0 w(t jt f C (k) j T c δ (k) d ), 0 t N s T f (1) Fig. 2 TH-MPPM signas for an arbitrary user k with M = 4, N s = 2, N c = 2 and TH sequence C (k) = {0, 1}. where δ d {δ 0 = 0 <δ 1 <δ 2...<δ M 1 } represent the time shifts that identify the symbo, d represents data that can be any one from a tota of M symbos, d {0, 1, 2,, M 1},β d = 1forad, T f is the frame time, T c is the chip time, C (k) j is the user dependent TH code, N s is the tota number of frames used to represent one symbo, E p is the transmitted energy of each puse and w(t) is the unit energy puse used for UWB communication. Let us assume that the puse-width is T p and the system bandwidth is W 1/T p. Fig. 1 Bock diagram of the system. Fig. 3 Received monocyce puse given by [1 4π{(t T p /2)/τ m } 2 ]exp [( 2π){(t T p /2)/τ m } 2 ] and its normaized autocorreation for T p = ns and τ m = 0.39T p. The minimum correation of occurs at deay = 0.212T p ns.
3 RAHMAN et a.: ON RAKE RECEPTION OF ULTRA WIDEBAND SIGNALS 2341 = N s 1 E p j=0 g(t jt f C j T c δ d ) + n(t) (2) where h(t) is the channe impuse response, n(t) is additive white Gaussian noise (AWGN) and represents convoution. Note that though the transmitted puse w(t) had unit energy, mutipath profie of the puse g(t) = w(t) h(t) has energy E g = T g g 2 (t)dt, 1, because of path oss. Here 0 T g is the duration of the mutipath profie g(t) known as the maximum deay spread of the channe. 2.2 Receiver Mode At the end of the mutipath channe Rake type receiver is used. The Rake receiver is impemented by using deayed versions of the reference signa ˆv d (t) [4]. The output of the correator corresponding to the -th finger of the Rake receiver can be given by Z d, = + r d (t)ˆv d (t τ )dt, (3) = 0, 1,, L o 1 for each d = 0, 1,, M 1 Note that we need to use M correators [19]. Here L o is the number of paths captured and τ is the deay where the -th correator is paced. For an Or ARake, L o = L or where L or is the tota number of resoved paths by the Or ARake and L or = T g /T p,. being ceiing function. And τ = τ or = T p, = 0, 1, 2,, L or 1. For an Or SRake, L o = L c where L c is the number of combined paths and τ are ocations of the best L c paths from τ or.for an Op ARake, L o = L op where L op is the tota number of resoved paths by the Op ARake. In this case, ocations of the paths τ = τ op, = 0, 1, 2,, L op 1 depend entirey on the channe. In other words, Op ARake paces a its L op paths so as to maximize the captured energy. Op SRake captures L o = L c best paths choosing best L c ocations from τ op.figure 4 shows a simpified representation of the finger (correator) pacement of Or ARake and Op ARake. Note that in ordinary method, finger pacements are simpy T p apart. In optimum method, fingers are first paced in the peaks of the mutipath intensity profie (MIP). Later, the rest of the MIP is covered in such a way that fingers can be paced sighty coser than T p to maximize the captured energy, as ong as the correation is neary zero (see Fig. 3). We assume that the foowing normaized reference signas are empoyed ˆv d (t) = N s 1 j=0 1 Ns w rec (t jt f C j T c δ d ), 0 t N s T f and d = 0, 1,, M 1 (4) where w rec (t) is a unit energy puse that matches we with an isoated received puse. Without oss of generaity, et us consider that symbo 0 is transmitted. The received signa, negecting the transmission deay, can be given by Fig. 4 Pacing the correators for Or ARake and Op ARakeinanarbitrary mutipath intensity profie. Bottom and top arrows denote the positions of the center of the tempate for Or ARake and Op ARake respectivey. r 0 (t) = N s 1 E p j=0 g(t jt f C j T c ) + n(t) (5) Let us define a cross-correation function between g(t) and w rec (t) at deay τ to be [9], α(τ) = + g(t)w rec (t τ)dt (6) Note that α(τ) = 0ifτ T p or τ T g. As a resut (3) can be rewritten as, Z d, = ζα(τ + δ d ) + n d, (7) = 0, 1,, L o 1 for each d = 0, 1,, M 1 where n d, = + n(t)ˆv d(t τ )dt, = 0, 1,, L o 1 for each d = 0, 1,, M 1andζ = N s E p E g. A maxima ratio combiner (MRC) is used to combine the mutipath signas. It is assumed that the MRC can correcty predict the channe parameters: ampitude, phase and deay as needed. So, MRC output per decision hypotheses becomes Z d = L o 1 ζ α(τ )Z d,, d = 0, 1,, M 1 L o 1 = ζ α(τ )α(τ + δ d ) + n d (8) where n d = ζ L o 1 α(τ )n d,, d = 0, 1,, M Error Probabiities Now, from (8) the decision variabe can be written as, M 1 D 0 = Z 0 Z d (9) d=1 Here, D 0 is assumed to be conditionay Gaussian (conditioned on the channe parameters) with mean [4]
4 2342 L o 1 E[D 0 ] = ζ E (0) (10) and variance [4], var[d 0 ] = E[D 2 0 ] E[D 0] 2 which can be rewritten as L o 1 var[d 0 ] = ζn o E (0) (11) E (0) where N o is the one sided AWGN variance and M 1 = α 2 (τ ) α(τ )α(τ + δ i ) (12) i=1 The conditiona probabiity of symbo error (again conditioned on the channe parameters and the symbo 0 is sent) can be given by SEP d = P[D d < 0, symbo d sent] E[D d ] = Q 2 var[d d ] = Q ζ L o 1 E (d) (13) with d = 0whereQ(x) = (2π) 1/2 exp( u 2 /2)du. If x symbo d is transmitted where d = 1, 2,, M 2, simiary, it can be shown that the symbo error probabiity (SEP) is given by (13) with d 1 = α 2 (τ ) α(τ )α(τ (δ d δ i )) E (d) E (d) M 1 i=d+1 i=0 N o α(τ )α(τ + (δ i δ d )) (14) And for symbo M 1, the SEP is given by (13) with M 2 = α 2 (τ ) α(τ )α(τ (δ M 1 δ i )) (15) i=0 where d = M 1. Finay, the average SEP for TH-MPPM is SEP= 1 M 1 SEP d (16) M d=0 Equations (13) and (16) representing SEP for TH- MPPM that uses (12), (14), (15) shown above can be easiy simpified for an AWGN channe as a function of the normaized correation function of an isoated received puse γ(δ) which is given by, γ(δ) = + w rec(t)w rec (t δ),> 1. By assuming M = 2andδ d {(δ 0 = 0) < (δ 1 = δ)} in the above anaysis, the bit error probabiity (BEP) equations for TH-BPPM can be obtained [20]. For TH-BPSK system because puses of opposite signs are used to represent bits 0 and 1, we get β 0 = β 1 and δ 0 = δ 1 = 0 in (1). Foowing simiar procedure as given above, we get equa bit error rate for both 0 and 1 in BPSK given by 2ζ L o 1 α 2 (τ ) BEP BPS K = Q (17) N o IEICE TRANS. FUNDAMENTALS, VOL.E88 A, NO.9 SEPTEMBER Puse-Width vs. Fading In this section we discuss the effects of puse-width on the received channe response and its impact on Rake reception. It is we accepted that increasing spreading bandwidth increases mutipath resovabiity [5] [7]. The energy in the received mutipath profie is received generay through two types of receptions. These are isoated receptions and overapped receptions (i.e. diffused paths). If a singe ray (path) is received during one puse duration, we ca it an isoated path. Isoated paths experience no fading. Ese, if more than one ray is received within one puse duration, we ca those overapped paths. Overapped paths are responsibe for the mutipath fading (ampitude fuctuations). If an impuse is transmitted over a mutipath channe, the received mutipath profie is the impuse response of the channe where a the receptions are received as isoated paths. At reasonaby high SNR, most of the energy present in the channe can be captured by Rake if deay estimation strategy is empoyed. An impuse can be considered to have a puse-width that tends to zero. But as practica communications use wider puses, some paths wi be received as overapped receptions. So, mutipath fading wi exist the amount of which wi depend on the puse-width. It can be understood intuitivey that mutipath resovabiity and hence the fraction of energy that can be captured depends on how the tota number of received mutipaths and their energy content is divided into isoated and overapped receptions. This, in turn, depends on puse-width other than the channe. Recenty doube Poisson process of [21] has been proposed with some modifications for the arrivas of mutipath components in indoor UWB communications [18]. Two Poisson processes have been defined: one for the arriva of (the first component of) custers with average custer arriva rate Λ and another for the arriva of rays within the custers with average ray arriva rate λ [18], [21]. To expore the impact of puse-width variations on the received profie, we assume that rays of any of the previous custers have no effect on the current custer (a reasonabe assumption, especiay in exponentiay decaying power deay profie [18], [21], [22]). Upon this assumption, the approximate probabiity that we wi have at east one reception within an arbitrary short duration of time t is (Λ +λ) t [23]. The probabiity that there wi be no reception within t is simpy 1 (Λ +λ) t. For a puse duration of T p, we assume that there exist S time sots of duration t where S = T p / t (T p is assumed to be divisibe by t). So, after reception of a path at any time, the probabiity that there wi be no new reception for next T p duration is {1 (Λ +λ) t} S. Aso, the probabiity that there was no reception for T p duration before receiving that path is the same {1 (Λ+λ) t} S.So the probabiity of an isoated reception becomes equa to {1 (Λ+λ) t} 2S. An iustration of it is shown in Fig. 5 using Λ=1/43,λ = 2.5, t = 0.01 ns corresponding to IEEE a CM1 of [18] for 0 < T p 2ns.
5 RAHMAN et a.: ON RAKE RECEPTION OF ULTRA WIDEBAND SIGNALS 2343 Tabe 1 Channe modes. Mode LOS/NLOS Distance CM1 LOS 0 4 m CM2 NLOS 0 4 m CM3 NLOS 4 10 m Fig. 5 Probabiities of isoated and overapped receptions vs. pusewidth for Λ=1/43,λ= 2.5, t = 0.01 ns corresponding to IEEE a CM1. 4. Computer Simuations 4.1 Simuation Mode In this section, the ideas deveoped in the previous sections are iustrated by providing extensive simuation exampes. We use IEEE a UWB indoor mutipath channe modes (Tabe 1) for simuations [18], [24]. As we have mentioned earier, IEEE a modes use the modified Saeh-Vaenzuea indoor channe mode [21]. The programs provided in [18] are used to produce the discrete time impuse response with continuous time arriva and ampitude vaues. The impuse response of the i-th reaization can be given by [18], N c N ray h i (t) = X i a i j, δ D(t T i τi j, ) (18) j=0 where δ D is Dirac deta function, {a i j, } are the mutipath gain coefficients, {T i } is the deay of the -th custer, {τi j, } is the deay of the j-th mutipath component (ray) reative to the -th custer arriva time {T i }, {X i} is the og-norma shadowing term, N c is the tota number of custers and N ray is the number of rays in each custer. The main simuation parameters for the simuation process are shown in Tabe 2. The received monocyce puse shape [5], ( ) t T w rec (t) = 1 4π p /2 2 τ m ( ) t T exp ( 2π) p /2 2 τ (19) m as shown in Fig. 3 is used where T p is the puse-width and τ m = 0.39T p. As mentioned in Sect. 2, this provides a minimum correation of at deay τ op = 0.212T p.asa resut, for optimum overapped MPPM we set, δ i = iτ op and Tabe 2 Simuation parameters for each channe mode. N s 1 N c 1 Data Rate 3 Mega symbos/s Moduation BPSK and MPPM ISI and ICI No Receivers Op ARake, Or ARake, Op SRake and Or SRake, MRC T p ns to 4.0 ns Puse Shape Received monocyce for orthogona MPPM, we set δ i = it p, with β i = 1 for both, i = 0, 1, 2,, M 1. For BPSK, δ 0 = δ 1 = 0andβ 0 = β 1. Rake performance is evauated from energy capture perspective [3], [5]. Simpy N s = N c = 1andT s = T f = T c = 333 ns are used. This heps us assume the mutipath components to be uncorreated even for cosey spaced Rake fingers [6], [7]. Our system is assumed to be free from interchip-interference (ICI) and inter-symbo-interference (ISI). In addition, idea channe estimations are assumed avaiabe. Ampitude and phase of each mutipath component are assumed known for Or ARake; and ampitude, phase and deay of each mutipath component are assumed known for Op ARake. Furthermore, for an SRake with L c paths, ocations of L c best paths are assumed known for respective ordinary or optimum method. Received energies are normaized over E g to be abe to make a fair comparison over the channe modes. 4.2 Simuation Resuts and Discussions Performance of ARake A. Performance vs. Puse-Width Figure 6 shows two truncated noise-ess channe responses over CM1 for transmitting unit energy puses of duration ns and 1.0 ns. It can be seen that the use of shorter puse provides more isoated receptions and ess ampitude fuctuations (fading). Figure 7 shows the BEP performance of both types of ARake over CM1 for BPSK. For certain puse-width, Op ARake is found to perform better than Or ARake. At BEP = 10 5,useofOpARake experiences an SNR oss of 0.6 db for using T p = ns whereas 4.35 db for using T p = 2.0 ns as compared to performance in AWGN. The simiar SNR osses for using Or ARake are 6.5dBand 8.5 db respectivey. However, at any specific SNR, the BEP advantage due to the puse-width shortening decreases at ow SNR. This is because, a number of owenergy-paths get submerged beow noise eve whose energies can t be captured.
6 2344 IEICE TRANS. FUNDAMENTALS, VOL.E88 A, NO.9 SEPTEMBER 2005 Fig. 6 Truncated noise-ess channe responses over CM1 for transmitting unit energy puses of duration ns (top) and 1.0 ns (bottom). Fig. 9 Statistics of the percentage energy capture per path for Op ARake and Or ARake (CM1, BPSK, T p = 1 ns). Here pdf (eft y-axes) stands for probabiity density function, and cdf (right y-axes) stands for cumuative distribution function = Probabiity {percentage energy capture per path abscissa}. Fig. 7 BEP for ARake in CM1 with BPSK. Fig. 8 Percentage energy capture by ARake in CM1 with BPSK. SNR = 20 db. B. Energy Capture vs. Puse-Width Figure 8 shows the percentage energy capture by ARake vs. puse-width for CM1. BPSK is used as moduation and SNR is set at 20 db. An Op ARake can identify the ocations of the isoated paths and if a reasonaby high SNR is maintained, the energy can be captured amost entirey irrespective of the puse-width. In harmony with the probabiistic prediction presented in the previous section, the net contribution in the tota energy capture from the isoated paths increases exponentiay whie the puse-width is shortened. Percentage energy coming from the overapped paths first increases with puse-width shortening and then starts decreasing. This is because the amount of energy received through overapped paths decreases consideraby whie the puse-width is shortened. The tota energy capturedbyanoparake is the summation of energies from both the isoated and overapped paths that increases monotonicay whie we shorten the puse-width. However, finay sighty diminishing returns are noticed. Note that the tota energy present in the mutipath profie doesn t change that much with puse-width variations [25]. But, the amount of energy that can be captured varies consideraby due to variations in the amount of fading experienced. On the other hand, an Or ARake tries to capture energy bindy by pacing the correator at each mutipe of the puse-width. Since it cannot distinguish between isoated and overapped receptions, most of the received paths experience partia correation and captured energy decreases consideraby as compared with Op ARake. Energy capture increases with puse-width shortening for both Op ARake and Or ARake, but in Or ARake it increases with much sower rate. Additionay, Or ARake output experiences greater diminishing effects much earier. However, the performance difference between Op ARake and Or ARake decreases as the puse-width becomes wider. Figure 9 shows the the probabiity density function (pdf) and cumuative distribution function (cdf) of the percentage energy capture per path for both types of the ARakes in CM1 with T p = 1 ns considering a noise-ess case. It is seen from pdf that the probabiity of receiving
7 RAHMAN et a.: ON RAKE RECEPTION OF ULTRA WIDEBAND SIGNALS 2345 paths containing infinitesimay sma energy is very high, whearas the probabiity of receiving high energy paths decreases. Aso both from pdf and cdf, the maximum energy content of a path is much ower in Or ARake. Here note that in a mutipath profie, the paths (i.e. the correator pacements) are different for ordinary and optimum methods. Furthermore, the energy content per path and the energy that can be captured from that path are different due to fading. C. Performance with MPPM In Figs. 10 and 11 we present average SEP vs. symbo SNR performance of Op ARake and Or ARake in CM1 for optimum overapped and orthogona MPPM respectivey with M = 2, 4 and 8. Symbo energy is kept constant irrespective of the vaue of M. For optimum overapped MPPM (Fig. 10), it is found at ow SNR that the performance becomes sighty better as M is increased. However, mutipe crossovers are seen afterwards as SNR is increased. Curves for wider puse-widths are seen to experience crossovers at Fig. 10 SEP of optimum overapped MPPM with a δ i = 0.212iT p, i = 0, 1, M 1 over CM1 whie ARakes are empoyed. Fig. 11 SEP of orthogona MPPM with δ i = it p, i = 0, 1, 2,, M 1 over CM1 whie ARakes are empoyed. higher SEP and SNR sets. Note that these crossovers appear ony in optimum overapped MPPM, not in orthogona MPPM. In optimum overapped MPPM, the deay between adjacent puses δ i+1 δ i, i = 0, 1,, M 2 is paced where the adjacent puse has the argest Eucidian distance. In this case, puses next to the adjacent puse coud have positive crosscorreation according to Fig. 3. It affects the SEP curves in Fig. 10 and crossovers occur among the curves for different M at midium to high SNR. Additionay, the curves for mutipath take simiar ooking shapes as those for AWGN because the autocorreation property of a mutipath profie doesn t deviate that much from that of a singe puse [3], [16]. For orthogona MPPM (Fig. 11), extensive simuations have shown that if δ i+1 δ i, i = 0, 1,, M 2aresetarger than or equa to the minimum deay beyond which puse autocorreation is zero or negigibe (see Fig. 3), system performance remains amost unchanged. Performance aso remains neary unchanged with variations in the vaue of M, though (12) (15) predicts performance variations with M even when the symbo SNR is fixed. This is again because the mutipath profies are not that much correated and the orthogonaity of the transmitted puses are more or ess reserved [3], [16]. Performance degradation for using MPPM as compared to BPSK doesn t depend on puse-width. The cost incurred in SNR for using optimum overapped MPPM (Fig. 10) rather than using BPSK (Fig. 7) is ess than around 1dBatSEP= The simiar cost for using orthogona MPPM (Fig. 11) is around 2.85 db. D. Performance in Different Channe Modes PerformanceinCM2ascomparedwithCM1woudhep us understand the effects of LOS/NLOS receptions on Rake reception over the same communication distance whereas performance in CM3 woud hep us understand the effects of fading due to distance. Note that [18] doesn t incude path oss mode and hence neither do we. Performances over different CMs are compared under same SNR. Figure 12 shows BEP performance comparisons over CM1,2and3whieOpARake and Or ARake are used. BPSK is considered. Op ARake is found to be more sensitive to fading due to the distance of communication rather than LOS/NLOS receptions over the same distance. Hence, Op ARake performs comparaby over CM1 and CM2. However, performance over CM3 as compared with CM1 experiences an SNR oss of 0.3dBforT p = 0.167ns and 1.0dB for T p = 2 ns at BEP of Or ARake is found to be sensitive to fading due to both NLOS receptions and communication distance. In a LOS channe (such as CM1), there exists a comparativey strong first path (see Fig. 6) that is aways captured by an Or ARake. As a resut, Or ARake performance over CM2 as compared with CM1 experiences an SNR oss of 1.0dB at BEP= 10 5 which seems not to depend on T p. Performance over CM3 experiences a oss of 1.2dBforT p = 0.167ns and 2.2dBfor T p = 2ns.
8 2346 IEICE TRANS. FUNDAMENTALS, VOL.E88 A, NO.9 SEPTEMBER 2005 Fig. 12 BEP for Op ARake and Or ARake over CM1, 2 and 3 for T p = ns and 2.0 ns whie BPSK is used as moduation. Fig. 13 Percent energy capture vs. number of seective combined paths L c over CM1, CM2 and CM3. SNR = 20 db and the moduation is BPSK. Tabe 3 Number of paths captured by ARake. (SNR = 20 db, BPSK) (Notation: X represents mean vaue of X) T p (ns) CM1 CM2 CM3 T g = ns T g = 118 ns T g = 203.6ns L or L op L or L op L or L op Performance of SRake A. Energy Capture vs. L c in Different Channe Modes Tabe 3 shows some of the simuation resuts namey mean maximum deay spread and mean number of combined paths by ARake for CM1, CM2 and CM3. The mean number of combined paths heps us reaize the impementation compexity that renders ARake impractica. Figure 13 shows percentage energy capture by Or SRake and Op SRake versus seective combined paths L c in a three channe modes. It s worth noting that the initia rate of increment of the energy capture with L c is the fastest in CM1 and the sowest in CM3 eaving CM2 in between. Interestingy, if SRakes are used, 10 paths of Or SRake and 20 paths of Op SRake can capture most of the energy captured by Or ARake and Op ARake respectivey in a three CMs. However, the energy capture becomes saturated graduay in a cases as L c becomes arge. B. Performance vs. Compexity Figure 14 shows the BEP performance of SRake receivers (L c = 4 & 8) for BPSK. According to the resuts in Fig. 13, the Or SRake resuts experience saturation earier than Op SRake and the rate of increment of energy capture is the fastest whie L c is beow 10 in both cases. So, to be abe to make comparison, we present the resuts of Fig. 14 for L c = 4 and 8. It is seen from the resuts of CM1 in Fig. 14 BEP of Op SRake (L c = 4 and 8) and Or SRake (L c = 4 and 8) in CM1, and Or SRake (L c = 4) in CM2 and 3. The moduation is BPSK. Fig. 14 that if the ocations of the best paths can be estimated optimay, Op SRake can provide considerabe performance improvement as compared to Or SRake with same L c.additionay, Op SRake gains more performance improvement for increasing L c from 4 to 8. Moreover, Op SRake with L c = 4offers better performance than Or ARake. For exampe, from Fig. 7, the required SNR at BEP = 10 5 is 18 db for Or ARake in the case of T p = 2.0 ns. In contrast, from Fig. 14, the required SNR at the same BEP is 14.3 db for Op SRake (L c = 4), which is 3.7 db ower even though the number of combined paths is much smaer than Or ARake. Let s now take a different ook on the matter. Op SRake resuts as presented in Fig. 14, experience considerabe performance degradation as compared with Op ARake performances presented in Fig. 7. But, Or SRake experiences much ess degradation in a simiar comparison with Or ARake. If Rake compexity is simpified, increased SNR woud be necessary to maintain the same BEP performance. This gives us a way to find out the cost incurred in SNR (db) for simpifying Rake compexity at any specific BEP. Some of the resuts are isted in Tabe 4.
9 RAHMAN et a.: ON RAKE RECEPTION OF ULTRA WIDEBAND SIGNALS 2347 Tabe 4 Cost incurred in SNR to simpify Rake compexity. (CM1, BPSK and BEP = 10 5 ) Compicated to Simper Cost in SNR (db) one one T p = T p = T p = 167 ps 1ns 2ns Op ARake Or ARake Op SRake8 Or SRake Op SRake4 Or SRake Op ARake Op SRake Op SRake Or ARake Or SRake Or SRake Tabe 5 Cost incurred in SNR (db) to simpify Or ARake by Or SRake. (L c = 4) (BPSK and BEP = 10 5 ) T p = ns T p = 2.0ns CM (db) 0.24 (db) CM (db) 0.90 (db) CM (db) 1.80 (db) Fig. 15 BEP vs. puse-width for Or SRake (L c = 4) in CM1, 2 and 3. The moduation in BPSK and SNR = 20 db. The cost depends on the puse-width T p. When an ARake is simpified by another ARake of the simper kind, or by an SRake of the same kind, the cost decreases for using wider T p.however,whenanopsrake is simpified by an Or SRake (having the same number of combined paths L c ), there seems to be an optimum T p for which the cost is minimum. A cose inspection on a more detai set of data reveas that the optimum vaue of T p is around 1.0 ns for L c = 8and beow ns for L c = 4. Additionay, the cost in SNR for simpifying an ARake by an SRake depends on the channe mode. Tabe 5 shows some resuts for an Or ARake being simpified by an Or SRake (L c = 4). As the channe mode changes from CM1 to CM2 and to CM3, the cost increases because the tota energy becomes scattered over more number of paths and the power deay profies (PDP) of the channes go a bit fatter [18], [26]. Finay, there is another interesting finding from Tabe 4 that the cost of simpifying an Op SRake (L c = 4) by an Or SRake (L c = 4) is ess than that in simpifying an Op ARake by an Or ARake. Note aso from Fig. 14 that Or SRake (L c = 4) performs quite we over a channe modes as ong as reasonaby high SNR can be maintained. This woud draw attention to Or SRake (L c = 4) because of its impementation simpicity. C. Or SRake Performance vs. Puse-Width In Fig. 15 we present BEP vs. puse-width for communications using Or SRake (L c = 4) over CM1 to 3. SNR is set at 20 db and BPSK is used. Best BEP performances are obtained at puse-widths (i.e. the optimum puse-widths) around 0.2 ns for CM1, 0.3 ns for CM2 and 0.5 ns for CM3. This can be more ceary seen from Fig. 16 that shows a magnified version of Fig. 15. For an SRake with certain L c, wider puses are supposed to suppy more fractiona energy, but they experience more fading. Oppositey, shorter puses though possess ess energy experience ess fading. This trade-off is supposed to provide an optimum pusewidth for UWB communications using SRake [17], [26] Fig. 16 BEP vs. puse-width for Or SRake (L c = 4) in CM1, 2 and 3. The moduation in BPSK and SNR = 20 db. Magnified version of Fig. 15. [28]. The optimum puse-width is defined as the puse-width using which provides the minimum achievabe BEP performance at any specified SNR. However, here for L c = 4, when the puse-width becomes shorter than 1.0 ns, the performance variation is very sma, especiay in CM2 and 3 (see Fig. 15). Finay, it shoud be noted that the optimum pusewidths presented in this paper are soey based on IEEE a channe modes and puse shape as shown in Fig. 3. Use of different puse shapes and different channe modes wi ead to different optimum puse-widths. Note aso that optimum puse-width aso depends on L c, operating SNR, the channe characteristics i.e. maximum deay spread, PDP etc. [26], [27] and antenna characteristics that may modify the puse shape. D. The Guarantee of Performance For practica purposes, especiay for commercia appications, a high guarantee of performance may be desired. Figure 17 presents the cumuative distribution function (cdf) curves for BEP of Or SRake (L c = 4) in CM1, 2 and 3. SNR
10 2348 IEICE TRANS. FUNDAMENTALS, VOL.E88 A, NO.9 SEPTEMBER 2005 References Fig. 17 Cumuative distribution curves of BEP for Or SRake (L c = 4) in CM1, 2 and 3. The moduation in BPSK and SNR = 20 db. is set at 20 db and BPSK is used. Figure 17 can be used to obtain the BEP at any specific desired guarantee eve. For exampe, Fig. 16 shows the average BEP of Or SRake (L c = 4) to be around for T p = 0.2ns(whichis the optimum vaue) in CM1. However from Fig. 17, we may take a further decision that in CM1, at 20 db SNR, BEP of or ess is guaranteed with a probabiity of 90% for the same puse-width. 5. Concusions Performance of ordinary and optimum Rake receiver have been investigated in TH-MPPM and TH-BPSK UWB communications. The SEP have been derived and those resuts have been used to simuate the performance of Rake reception of UWB signas over reaistic mutipath channes. The performances of various Rake receivers were compared for severa moduation schemes and puse-width over various channe modes. The puse-width has been identified as an important system parameter that, in genera, affects Rake performance. Optimum Rakes have been shown to perform better than the ordinary counterpart, because the estimation of path deay brings more fractiona energy capture. It has been shown that if the path deay estimation is avaiabe in spite of increasing system compexity, Op SRake with ony 4pathsoffers better performance than Or ARake. However, from performance vs. compexity trade-off point of view, Or SRake may appear to be attractive. Acknowedgments This work was supported in part by the Grant-in-Aid for scientific research (No ) of JSPS, Internationa Communication Foundation (ICF) and Union Too Schoarship Foundation of Japan. Graduate studies of Mr. Rahman are funded by the Government of Japan under the Monbukagakusho schoarship program. [1] D. Porcino and W. Hirt, Utra-wideband radio technoogy: Potentia and chaenges ahead, IEEE Commun. Mag., vo.41, no.7, pp.66 74, Juy [2] R.A. Schotz, Mutipe access with time-hopping impuse moduation, Proc. MILCOM, vo.2, pp , Boston, MA, Oct [3] M.Z. Win and R.A. Schotz, Characterization of utra-wide bandwidth wireess indoor channes: A communication-theoretic view, IEEE J. Se. Areas Commun., vo.20, no.9, pp , Dec [4] J.G. Proakis, Digita Communications, 4th ed., McGraw Hi, New York, [5] M.Z. Win and R.A. Schotz, On the energy capture of utrawide bandwidth signas in dense mutipath environments, IEEE Commun. Lett., vo.2, no.9, pp , Sept [6] M.Z. Win and Z.A. Kostic, Impact of spreading bandwidth on Rake reception in dense mutipath channes, IEEE J. Se. Areas Commun., vo.17, no.10, pp , Oct [7] M.Z. Win, G. Chrisikos, and N.R. Soenberger, Performance of Rake reception in dense mutipath channes: Impications of spreading bandwidth and seection diversity order, IEEE J. Se. Areas Commun., vo.18, no.8, pp , Aug [8] F. Ramirez-Mirees, M.Z. Win, and R.A. Schotz, Signa seection for the indoor wireess impuse radio channe, Proc. 47th VTC 1997, vo.3, pp , May [9] J.D. Choi and W.E. Stark, Performance of utra-wideband communications with suboptima receivers in mutipath channes, IEEE J. Se. Areas Commun., vo.20, no.9, pp , Dec [10] D. Cassioi, M.Z. Win, F. Vataaro, and A.F. Moisch, Performance of ow-compexity Rake reception in a reaistic UWB channe, Proc. ICC 2002, vo.2, pp , Apri/May [11] A. Rajeswaran, V.S. Somayazuu, and J.R. Foerster, Rake performance for a puse based UWB system in a reaistic UWB indoor channe, Proc. ICC 2003, vo.4, pp , [12] B. Mieczarek, M.O. Wessman, and A. Svensson, Performance of coherent UWB Rake receivers using different channe estimators, Proc. IWUWBS 2003, CD ROM, June [13] J. Zhang, R.A. Kennedy, and T.D. Abhayapaa, Performance of Rake reception of utra wideband signas in a ognorma-fading channe, Proc. IWUWBS 2003, CD ROM, June [14] H. Sheng, A.H. Haimovich, A.F. Moisch, and J, Zhang, Optimum combining for time hopping impuse radio UWB Rake receivers, Proc. UWBST 2003, pp , Nov [15] F. Ramirez-Mirees, M.Z. Win, and R.A. Schotz, Performance of utra-wideband time-shift-moduated signas in the indoor wireess impuse radio channe, Proc Asiomar Conf., pp , [16] S. de Rivaz, B. Denis, J. Keignart, M. Pezzin, N. Daniee, and D. Morche, Performances anaysis of a UWB receiver using compex processing, Proc. UWBST 2003, pp , Nov [17] M.A. Rahman, S. Sasaki, J. Zhou, S. Muramatsu, and H. Kikuchi, Performance evauation of Rake reception of utra wideband signas over mutipath channes from energy capture perspective, Proc. Joint UWBST and IWUWBS 2004, pp , May [18] J. Foerster, Channe modeing sub-committee report fina, IEEE P /368r5-SG3a, Dec [19] J.M. Wozencraft and I.M. Jacobs, Principes of Communication Engineering, John Wiey, [20] L. Ge, G. Yue, and S. Affes, On the BER performance of puse-position-moduation UWB radio in mutipath channes, Proc. UWBST 2002, pp , May [21] A.A.M. Saeh and A. Vaenzuea, A statistica mode for indoor mutipath propagation, IEEE J. Se. Areas Commun., vo.sac-5, no.2, pp , Feb [22] J. Foerster and Q. Li, UWB channe contribution from Inte, IEEE
11 RAHMAN et a.: ON RAKE RECEPTION OF ULTRA WIDEBAND SIGNALS 2349 P /279r0-SG3a, March [23] R.C. Larson and A.R. Odoni, Urban Operations Research, chapter 2, Prentice-Ha, New Jersey, 1981, avaiabe at or book/www/book. [24] A.F. Moisch, J.R. Foerster, and M. Pedergrass, Channe modes for utrawideband persona area networks, IEEE Wire. Commun., vo.10, no.6, pp.14 21, Dec [25] T.S. Rappaport, Wireess Communications: Principes and Practice, section , Prentice Ha, New Jersey, [26] M.A. Rahman, S. Sasaki, J. Zhou, S. Muramatsu, and H. Kikuchi, Evauation of seective Rake receiver in direct sequence utra wideband communications, IEICE Trans. Fundamentas, vo.e87-a, no.7, pp , Juy [27] W.C. Lau, M.S. Aouini, and M.K. Simon, Optimum spreading bandwidth for seective Rake reception over Rayeigh fading channes, IEEE J. Se. Areas Commun., vo.19, no.6, pp , June [28] D. Cassioi, M.Z. Win, and A.F. Moisch, Effects of spreading bandwidth on the performance of UWB Rake receivers, Proc. ICC 2003, vo.5, pp , Mohammad Azizur Rahman received his Bacheor s degree in Eectrica and Eectronic Engineering (EEE) in August 2001 from Bangadesh University of Engineering and Technoogy (BUET), Dhaka, Bangadesh. From August 2001 to March 2002 he served as a Lecturer in the Department of EEE of the same university. From Apri 2002, he is attached with Niigata University, Niigata, Japan as a Japanses Government (Monbukagakusho) schoar. In October 2002, he entered the Department of EEE of the university as a research student, where he ater in Apri 2003 entered as a Master s degree student. He is presenty working toward a Doctora degree in the same pace. His research interests incude Spread Spectrum and Utra Wideband Communications, Communication Theory, Rake and Diversity Receivers, Signaing Design, Mutipe Access Communications etc. Mr. Rahman is a student member of the IEEE. Jie Zhou was born in Sichuan, China, in He received B.E and M.E degrees from Nanjing University of Posts and Teecommunications, China in 1985 and 1990, respectivey and Dr. Eng. degree from the Department of Computer Science, Gunma University, Japan in March Afterwards, he joined Chongqing University of Posts and Teecommunications, where he became an engineer in 1992 and an associate professor in From Apri 2001 to March 2005, he was with the Department of Eectrica and Eectronic Engineering, Niigata University, Japan where he was a Research Associate. Since March 2005, he has been with the Department of Information and Communications, Nanjing University of Information Science and Technoogy, where he is currenty a Professor. His research interests ie in the areas of DATA, ATM and radiowave propagation in mobie communications. Hisakazu Kikuchi received the B.E. and M.E. degrees from Niigata University in 1974 and 1976, respectivey, and Dr. Eng. degree in eectrica and eectronic engineering from Tokyo Institute of Technoogy in From 1976 to 1979 he worked at Information Processing Systems Laboratory, Fujitsu Ltd., Tokyo. Since 1979 he has been with Niigata University, where he is a professor of eectrica engineering. He was a visiting professor at Eectrica Engineering Department, University of Caifornia, Los Angees during a year of 1992 to He hods a visiting professorship at Chongqing University of Posts and Teecommunications, China since His research interests are in digita signa processing and image/video processing as we as utra wideband systems. Dr. Kikuchi is a member of the ITEJ (Institute of Image Information and Teevision Engineers of Japan), IIEEJ (Institute of Image Eectronics Engineers of Japan), JSIAM (Japan Society for Industria and Appied Mathematics), RISP (Research Institute of Signa Processing), IEEE, and SPIE. He served the chair of Circuits and Systems Group, IEICE, in 2000 and the genera chair of Digita Signa Processing Symposium, IEICE, in 1988 and Karuizawa Workshop on Circuits and Systems, IEICE, in Shigenobu Sasaki received B.E., M.E. and Ph.D. degrees from Nagaoka University of Technoogy, Nagaoka, Japan, in 1987, 1989 and 1993, respectivey. Since 1992, he has been with Niigata University, where he is now an Associate Professor in the Department of Eectrica and Eectronic Engineering. From 1999 to 2000, he was a visiting schoar at the Department of Eectrica and Computer Engineering, University of Caifornia, San Diego. Since 2003, he has been with the UWB technoogy institute, Nationa Institute of Information and Communication Technoogy (NICT) as an expert researcher. His research interests are in the area of digita communications with specia emphasis on spread spectrum communication systems, utra-wideband communication systems and wireess communications. He is a member of the IEEE and SITA.
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