Data-aided synchronization algorithm dispensing with searching procedures for UWB communications

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1 . RESEARCH PAPER. SCIENCE CHINA Information Sciences April 1 Vol. 55 No. 4: doi: 1.17/s Data-aided synchronization algorithm dispensing with searching procedures for UWB communications REN ZhiYuan 1, JIANG Ting 1, ZHONG Yi & ZHAO ChengLin 1 1 Key Laboratory of Universal Wireless Communications, Ministry of Education of China; Wireless Network Laboratory, Beijing University of Posts and Telecommunications, Beijing 1876, China; School of Information Engineering, North China University of Technology, Beijing 141, China Received June 8, 1; accepted September 6, 1; published online September 19, 11 Abstract Rapid and accurate synchronization constitutes a major challenge in deploying Ultra-Wideband impulse radio (UWB-IR) for indoor wireless communications. This paper develops a data-aided (DA) synchronization algorithm dispensing with searching procedures for UWB-IR communications. By adopting a stream of alternating orthogonal pulses, frame-level synchronization can be achieved without channel information. Without utilizing any searching procedure, the timing offset estimator is obtained in a closed form. Because exhaustive search can be avoided, both computational complexity and synchronization time are reduced. Simulations and comparisons are provided to illustrate the advantages of our design over the alternatives. Keywords Ultra-Wideband impulse radio, synchronization dispensing with searching procedures, searching space, data-aided estimation Citation Ren Z Y, Jiang T, Zhong Y, et al. Data-aided synchronization algorithm dispensing with searching procedures for UWB communications. Sci China Inf Sci, 1, 55: , doi: 1.17/s Introduction Since the spectral mask was released by the Federal Communications Commission (FCC) in February, Ultra-Wideband impulse radio (UWB-IR) has attracted growing interest especially in the area of short-range indoor wireless communications [1]. Interest in UWB is motivated by several features including ample multipath diversity, low-cost baseband transceivers, high data rates along with low transmission power, potentially large user capacity, and the ability to coexist with narrowband radio systems operating in frequency overlay similar to that of CDMA network []. The basic idea of UWB signaling is to transmit a stream of ultra-short pulses at the sub-nanosecond scale with low power spectral density. To obtain sufficient signal energy for reliable detection, each information-bearing symbol is conveyed by a number of frames with one pulse per frame. The frame duration is much larger than the pulse duration, resulting in a very low duty cycle UWB transmission [1]. In such low-duty-cycle systems, rapid and accurate synchronization (i.e., timing offset estimation) constitutes a major challenge in deploying UWB-IR for indoor wireless communications [3]. In addition, the multipath channel through which the ultra-short pulses pass is generally unknown during synchronization at the receiver, which virtually exacerbates the difficulty to synchronize the received UWB signals. Corresponding author ( tjiang@bupt.edu.cn) c Science China Press and Springer-Verlag Berlin Heidelberg 11 info.scichina.com

2 Ren Z Y, et al. Sci China Inf Sci April 1 Vol. 55 No So far, a number of synchronization algorithms for UWB-IR systems have been developed to break this bottleneck [4 7]. However, each of these approaches inevitably requires a searching procedure. During the searching procedure, an objective function, constructed from the received UWB signals, is computed at dozens of candidate time shifts and the unique time shift corresponding to the maximum (or minimum) of the objective function is considered as the synchronization parameter. Generally speaking, searching space will be enlarged as accuracy of synchronization is enhanced, thus increasing both computational complexity and synchronization time. Long-timg synchronization will affect symbol detection. In order to reduce synchronization time and complexity, two-stage synchronization algorithms for UWB-IR systems have been proposed in a number of papers, e.g., [8 1]. The blind two-step algorithm [8] firstly finds the beginning of individual frames in the first step, and then identifies the first frame of each symbol in the second step. The two-stage scheme [9] quickly locates the area of multipath signal in the first step, and finds the first-arriving path of multipath signal in the second step. The data-aided twostep method [1] exploits double correlation architecture to quickly acquire an arbitrary train sequence in the first step, and searches for the first-arriving path in the second step. For the existing two-stage synchronization algorithms, e.g., [8 1], a common feature is that the two-step structure essentially divides the whole searching space into two-level subspaces to reduce the actual searching space, thus shortening synchronization time and lowering computational complexity. However, the existing two-stage methods still cannot bypass the complicated searching procedures. Recently, some researchers try to propose a class of synchronization schemes without searching procedures [11 13]. Data-aided algorithm [11] dissects the synchronization parameter into symbol-level, frame-level and pulse-level timing offsets. Although the frame-level timing offset estimator is expressed in a closed form, it is actually based on a searching procedure due to its dependence on the searchingbased estimator of the symbol-level offset. Capitalizing on channel information, the data-aided scheme [1] without searching procedures is performed through comparing the energy of the received signal with the so-called mean normalized energy profile, but in practice the prior knowledge on channel is commonly unknown to the receiver at the synchronization stage. Data-aided (DA) and non data-aided (NDA) schemes without searching procedures are introduced by [13]. A fixed preamble pattern of three symbols is transmitted before the training sequence in DA mode and before information-bearing symbols in NDA mode, respectively. In order to estimate synchronization parameter, the authors take it for granted that the receiver begins synchronization at the instant, which is located within the first symbol of the fixed preamble pattern. Nevertheless, this assumption is impractical in cold start-up scenarios [14] such as in wireless ad hoc and sensor networks, where the receiver is unaware of the time when the transmitter begins to send data. The purpose of this paper is to develop a data-aided (DA) frame-level synchronization algorithm dispensing with searching procedures for UWB-IR wireless communications. The proposed algorithm consists of two steps. In the first step, a stream of alternating orthogonal pulses is adopted to assist in estimating the tail energy as well as the head energy of the received symbol-long waveform. In the second step, synchronization parameter is calculated on the basis of the estimates of the tail energy and the head energy. The novelty of the proposed algorithm lies in the derivation of timing offset estimator in a closed form which dispenses with searching procedures. Because exhaustive search can be avoided, both computational complexity and synchronization time are reduced. Furthermore, the proposed algorithm remains operational in cold start-up scenarios and under the condition of unknown multipath propagation. There are clear distinctions between the proposed algorithm and the existing synchronization methods, which are explained as follows. Unlike the existing searching-based synchronization algorithms [4 7], our approach does not need any time-consuming searching procedure, thus considerably shortening the synchronization time. Compared with the existing two-stage synchronization algorithms [8 1] which reduce searching space, the searching space of the proposed algorithm is equal to zero due to bypassing searching procedures, thus further reducing computational complexity and synchronization time. In addition, the timing offset estimator of the proposed algorithm is obtained in a closed form, whereas those of the existing two-stage algorithms are expressed in a searching form. Different from the trainingbased algorithm [1] without searching procedures, our timing offset estimator is derived without any

3 78 Ren Z Y, et al. Sci China Inf Sci April 1 Vol. 55 No. 4 knowledge on channel. Compared with the schemes without searching procedures in [13], the proposed algorithm remains operational for cold start-up scenarios. Simulation confirms that the performance of the proposed scheme is superior to that of the DA mode in [13], and performance degradation of the proposed scheme in the presence of pulse distortion is quite limited. Notation: stands for integer floor operation; E[ ] represents expectation; A mod B denotes the modulo operation with base B, wherea and B are both real. A := B means that A is defined as and equal to B. System modeling and preliminaries In UWB-IR communications, every information symbol is conveyed by N f repeated pulses, with one pulse per frame of duration T f. The resulting transmitted symbol-long waveform is described by p T (t) = N f 1 j= p(t jt f c j T c ), (1) where p(t) is the energy-normalized ultra-short pulse of duration T p at the sub-nanosecond scale (i.e., monocycle). The sequence {c j } represents the user s pseudo-random time-hopping (TH) code to enable multiple access and its elements are integers in the range c j N h 1, satisfying T f (N h 1)T c +T p. T c is the duration of an addressable time bin. The symbol duration spanned by p T (t) isthust s := N f T f. Binary antipodal pulse amplitude modulation (PAM) is considered in this paper. The UWB modulated signal at the transmitter is then expressed as s(t) = + ε b(i)p T (t it s ), () i= where ε is the transmitted energy per pulse, {b(i) {±1}} is the information-bearing symbol sequence with equal probability. The multipath channel is assumed to be quasi-stationary, i.e., the amplitude {α l } and the delay {τ l } of each path are invariant over one transmission burst. The impulse response of an L-path channel can be denoted by L 1 h(t) = α l δ(t τ l ). (3) l= Without loss of generality, we assume τ <τ 1 < <τ L 1 and isolate the propagation delay τ from multipath dispersion as τ l, := τ l τ, l [,L 1]. With the receiver front end acting as an ideal bandpass filter with ultra-wide bandwidth B, the received signal is then given by r(t) = + L 1 ε b(i) α l p T (t it s τ τ l, )+n(t), (4) i= l= where n(t) is the bandpass-filtered mixture of thermal noise and multiple-access interference (MAI), which is modeled as the zero-mean additive Gaussian noise (AGN) with power spectral density (PSD) N / [15]. Evidently, by selecting T f τ L 1, + T p +(N h 1)T c, inter-frame interference (IFI) and inter-symbol interference (ISI) can be avoided effectively [16, 17]. For notational simplicity, we introduce the received symbol-long waveform L 1 p R (t) := α l p T (t τ l, )= l= N f 1 j= g(t jt f c j T c ), (5) where g(t) := L 1 l= α lp(t τ l, ) is the channel response of monocycle. It follows that the received signal in (4) can be rewritten as r(t) = + ε b(i)p R (t it s τ )+n(t). (6) i=

4 Ren Z Y, et al. Sci China Inf Sci April 1 Vol. 55 No Although the received signal starts at τ, the receiver knows neither the transmission starting time at the transmitter side nor the propagation delay τ. Upon detecting the energy/amplitude change in the arriving signals, the receiver initiates synchronization at t (t >τ ). Due to τ only serving as reference, without loss of generality, we can set τ =. Consequently, the observation signal at the receiver can be formulated as r obs (t) :=r(t + t )= + ε b(i)p R (t it s + t )+n(t + t ), t [, + ). (7) i= t can be expressed as an integer multiple of symbol duration T s minus a residue: t = NT s T syn, (8) where N = t /T s and T syn =(NT s t ) [,T s ), as shown in Figure 1. Since the goal of synchronization for UWB signal is identifying the beginning of individual symbols at the receiver end, T syn is the synchronization parameter to be estimated. For data-aided estimation, an all-one training sequence (i.e., b(i) = 1) is transmitted from the transmitter. Substituting t = NT s T syn and b(i) =1into(7)and letting n (t) =n(t + t )gives r obs (t) = + ε p R (t (i N)T s T syn )+n (t), t [, + ). (9) i= 3 Synchronization algorithm The proposed DA synchronization algorithm adopts two orthogonal consecutive-order Hermite pulses p 1 (t) andp (t) with the same duration T p and unitary energy, proposed in [18]. During each symbol, p 1 (t) or p (t) is repeatedly transmitted in N f frames to convey one bit information. The transmitted monocycle is changed according to the following repeated pattern [p 1 (t),p 1 (t),p (t),p (t)]. The transmitted and received symbol-long waveforms are denoted by p T 1 (t) andp R1 (t) whenp 1 (t) is transmitted, and by p T (t) andp R (t) otherwise. According to (9), the observation signal is given by r obs (t) = + ε p Rj(i) (t (i N)T s T syn )+n (t), j(i) {1, }, t [, + ), (1) i= where the index j(i) {1, } indicates which one between p R1 (t) andp R (t) is received within the ith symbol, as shown in Figure. In the sequel, we first estimate the tail energy as well as the head energy of the received symbol-long waveform, and then the synchronization parameter is calculated on the basis of the estimates of the tail energy and the head energy. 3.1 Estimating the tail energy and the head energy Firstly, the expectation of r obs (t) is taken. Since the additive noise n(t) has zero mean, the expectation E[r obs (t)] is expressed as x(t) :=E[r obs (t)] = + ε p Rj(i) (t (i N)T s T syn ), j(i) {1, }, t [, + ), (11) i= which is periodic with period 4T s. Secondly, let us perform the inter-symbol correlation of x(t) to generate the symbol-rate samples: Z 1 k := x(t +(k )T s )x(t +(k 1)T s )dt, k [1, ], (1)

5 78 Ren Z Y, et al. Sci China Inf Sci April 1 Vol. 55 No. 4 Figure 1 The received signal with synchronization parameter. Figure The received signal when orthogonal pulses are employed. where x(t + kt s )fort [,T s )isthekth segment waveform of x(t) with duration T s. According to (11), x(t + kt s )fort [,T s ) is then expressed by x(t + kt s )= + ε p Rj(i) (t (i N k)t s T syn ), t [,T s ), j(i) {1, }. (13) i= Since the received symbol-long waveform p Rj(i) (t), j(i) {1, } has finite nonzero support [,T s ), (13) is zero except a finite number of i values. For any given k and t,oneobtains where q is or 1. Substituting (14) into (13) yields x(t + kt s )= ε i = N + k q, (14) 1 p Rj (t + qt s T syn ), t [,T s ), j {1, }. (15) q= Therefore, when N mod 4 = 1 and k = 1 in (1), Z 1 k in (1) can be written as Z1 1 p R1(t)dt + ε p R1 (t T syn )p R (t T syn )dt. (16) T s T syn In establishing (16), we use the fact that T s p Ri (t + T s T syn )p Rj (t T syn )dt =,i, j {1, } due to the finite support of p Ri (t), i {1, } and substitution T s p R1 (t + T s T syn )dt = T s T s T syn p R1 (t)dt. We define ε Ti (T syn ):=ε T s T s T syn p Ri (t)dt, i {1, } as the tail energy of the received symbol-long waveform p Ri (t), ε Hi (T syn ):=ε T s T syn p Ri (t)dt as the head energy of p Ri(t), and ε Ri : T s p Ri (t)dt as the total energy of p Ri (t). Following [19] and [], we invoke the assumption below: + p i (t τ l, )p j (t τ k, )dt =, i,j {1, }, (17) for l k. That is, we assume that the correlation between signal echoes can be ignored. Invoking assumption (17) results in ε T 1 (T syn )=ε T (T syn ), ε H1 (T syn )=ε H (T syn )andε R1 R. Thus the above three types of energy are denoted by ε T (T syn ), ε H (T syn ), and ε R. The orthogonality between p 1 (t) and p (t) combined with (17) gives rise to T s p Ri (t T syn )p Rj (t T syn )dt =,i, j {1, }, fori j. Therefore, Z1 1 in (16) can be simplified into Z1 1 T (T syn ). Similarly, when N mod 4 = 1 and k =

6 Ren Z Y, et al. Sci China Inf Sci April 1 Vol. 55 No in (1), we can also derive that Z 1 T (T syn ). Hence, when N mod4=1,wedefinethefirsttypeof symbol-rate sample Z 1 as Z 1 =(1/) k=1 Z1 k T (T syn ). Thirdly, let us perform correlation between the pairs of successive symbol-long segments of x(t) again, with x(t) delayed by T s relative to the correlation in (1): Z k := x(t +(k 1)T s )x(t +kt s )dt, k [1, ]. (18) When N mod 4 = 1, mimicking the steps to derive Zk 1, Z can be obtained as Z k k H(T syn )fork [1, ]. Hence, when N mod 4 = 1, the second type of symbol-rate sample Z is defined as Z =(1/) k=1 Z k = ε H (T syn ). In the same way, when N mod 4 is odd or even, Z 1 and Z can be written respectively as { Z 1 T (T syn ), (19) Z H (T syn ), when N mod 4 = 1 or 3, { Z 1 H (T syn ), () Z T (T syn ), when N mod 4 = or. To identify whether N mod 4 = 1 or 3 or N mod 4 = or, we design the following decision variables: Z 3 k := x(t +(k )T s )x(t +(k 1)T s )dt, k [1, ], (1) Zk 4 := x(t +(k )T s )x(t +(k 1)T s )dt, k [1, ]. () Note that the decision variables Zk 3 and Z4 k are the same as the symbol-rate samples Z1 k in (1) except the region of integration: The length of the region of integration for Zk 3 and Z4 k is T s/. It is proven in Appendix that the following decision rule can be used to identify whether N mod 4 = 1 or 3 or N mod 4 = or : { Z 3 Z 4, N mod 4 = 1 or 3, Z 3 Z 4, N mod 4 = or, (3) where the equal sign holds if and only if T syn =,Z 3 =(1/) k=1 Z3 k and Z4 =(1/) k=1 Z4 k. Therefore, we first employ (3) to identify whether N mod 4 = 1 or 3 or N mod 4 = or, and then use (19) or () correspondingly to calculate the tail energy and the head energy. In practice, a period of x(t) in (11) can be estimated using the mean-square sense (MSS) consistent sample average across K segments of r obs (t), each of size 4T s : ˆx(t) = 1 K K 1 k= r obs (t +4kT s ), t [, 4T s ). (4) Therefore, when estimating ε T (T syn )andε H (T syn ), x(t) is replaced by ˆx((t mod 4T s )) in (1), (18), (1) and (). A remark with regard to implementation is provided as follows. Remark. The statistic ˆx(t) =(1/K) K 1 k= r obs(t +4kT s )fort [, 4T s ) can be computed either digitally or in analog form. Analog approaches avoid the possibly high sampling rates needed in the UWB regime, but implementing the analog delay, required to shift the received signal, can be challenging. Nonetheless, chips implementing analog delays from to 1 ns are available in practice now [1], so that the analog implementation is suggested. 3. Estimating the synchronization parameter In light of the multi-frame structure within each symbol in the absence of inter-frame interference (IFI), ε T (T syn )andε H (T syn ) can be expressed as ε T (T syn )=mε h (T f ) ε h (η c Nf mt c ), (5)

7 784 Ren Z Y, et al. Sci China Inf Sci April 1 Vol. 55 No. 4 ε H (T syn )=(N f m)ε h (T f )+ε h (η c Nf mt c ), (6) where ε h (x) :=ε x g (t)dt is the accumulated multipath energy function, m := T syn /T f {1,,...,N f } is an unknown integer, and η := mt f T syn [,T f ) is referred to as tracking error. Adding (5) to (6), ε h (T f )isgivenby ε h (T f ) H(T syn )+ε T (T syn ). (7) N f Then, dividing both sides of (5) by ε h (T f )gives ε T (T syn ) ε h (T f ) = m ε h(η c Nf mt c ) ε h (T f ) = m ε, (8) where ε h (η c Nf mt c )/ε h (T f ) [, 1]. When ε T (T syn )/ε h (T f ) is an integer, it is obvious that t is located at the starting point of a frame. Consequently, the synchronization parameter T syn is estimated by ˆT syn =[ε T (T syn )/ε h (T f )]T f.whenε T (T syn )/ε h (T f ) is not an integer, according to (8), m and ε can be obtained as m = ε T (T syn )/ε h (T f ) and ε = ε T (T syn )/ε h (T f ) ε T (T syn )/ε h (T f ). Recalling that η = mt f T syn and ε h (η c Nf mt c )/ε h (T f ), we can express T syn and ε h (η c Nf mt c )as { yn = mt f η = ε T (T syn )/ε h (T f ) T f η, ε h (η c Nf mt c )=ε ε h (T f ). (9) Notice that η cannot be recovered through the second equation in (9), for the accumulated multipath energy function ε h (x) is unknown at synchronization stage. As t is randomly located within a symbol, it is reasonable to assume that η obeys uniform distribution over [,T f ). Hence, in minimum mean square error (MMSE) sense, the optimal estimate of η is ˆη = T f /. As a result, the frame-level estimate of the synchronization parameter T syn is given by ˆT syn = ε T (T syn )/ε h (T f ) T f T f /. After channel estimation at the receiver, the estimated accumulated multipath energy function ˆε h (x) canbeemployedtoestimateη with higher accuracy through the second equation in (9), which will in return makes channel estimation more accurate. Although our DA synchronization algorithm is designed when channel information is unknown, these findings suggest an effective iterative estimation process between synchronization parameter estimation and channel estimation, which finally improves bit error rate (BER) performance of the receiver. In summary, the proposed DA synchronization algorithm is carried out as follows: Step 1. Use (4) to obtain ˆx(t) fort [, 4T s ), and replace x(t) withˆx((t mod 4T s )) respectively in (1), (18), (1) and (). Step. If the equality holds in (3), ˆT syn =. Otherwise, whether N mod 4 = 1 or 3 or N mod 4 = or is determined through (3). Then ˆε T (T syn )andˆε H (T syn ) are obtained by (19) or () correspondingly. Step 3. Replace ε H (T syn )andε T (T syn ) in (7) with ˆε T (T syn )andˆε H (T syn ) to yield an estimate of ε h (T f ), i.e., ˆε h (T f )=[ˆε T (T syn )+ˆε H (T syn )]/N f. Step 4. If ˆε T (T syn )/ˆε h (T f ) is an integer, the frame-level estimate of synchronization parameter ˆT syn = [ˆε T (T syn )/ˆε h (T f )]T f.otherwise,ˆt syn = ˆε T (T syn )/ˆε h (T f ) T f T f /. 4 Simulations and comparisons In this section, simulations are carried out to validate the performance of the proposed DA synchronization algorithm and compare it with that of DA scheme in [13]. In all test cases, the following assumptions have been made: 1) For DA scheme in [13], the monocycle p(t) is chosen as the second derivative of a Gaussian pulse with unit energy and the duration T p =1 ns.

8 Ren Z Y, et al. Sci China Inf Sci April 1 Vol. 55 No Figure 3 NMSE performance comparisons. Figure 4 BER performance comparisons. Figure 5 The effect of pulse distortion on the proposed algorithm. ) For the proposed DA algorithm, we select the 3rd-order and 4th-order Hermite pulses with unit energy and the duration T p =1 ns as the alternatively transmitted monocycles. 3) Each symbol consists of N f = 16 frames with frame duration T f =4 ns. For TH code, we set N h =1andT c =1ns. 4) The fading channel is modeled as CM1 proposed by the IEEE 8.15 Working Group []. The diminishing tail of the power delay profile is truncated to make the maximum delay spread of the multipath channel equal to 3 ns. 5) Without loss of generality, t is randomly generated from a uniform distribution over [, 4T s ). We first compare the performances between the proposed DA algorithm and DA scheme in [13] in terms of normalized mean square error (i.e., NMSE). Figure 3 depicts NMSE of the proposed DA algorithm and that of DA scheme in [13] versus SNR for different values of averaging K. Here SNR is defined as E b /N,whereE b is the energy per symbol of the received signal. It can be noticed that all curves decrease monotonically as SNR increases. Increasing K also helps to reduce NMSE. Under the same K, the curves of the proposed DA algorithm are all below those of DA scheme in [13]. It suggests that the performance of the proposed algorithm is superior to that of DA scheme in [13]. For the inferior performance of DA scheme in [13], some explanation is provided as follows. In order to estimate synchronization parameter, by ignoring the additive noise, the authors of [13] exploit the correlation of

9 786 Ren Z Y, et al. Sci China Inf Sci April 1 Vol. 55 No. 4 the three-symbol fixed preamble pattern to compare two energy values of the received signal. However, in practice, the probability for correct comparison is small due to the presence of the additive noise, thus lowering the estimation accuracy in [13]. In addition, we make BER performance comparison with the proposed DA algorithm and DA scheme of [13] in Figure 4. To isolate timing from channel estimation errors, the noise-free template is constructed with error-free channel for demodulation. As expected, with increased SNR or K, the BER performance of both approaches improve monotonically and the proposed DA algorithm has smaller values than DA scheme of [13] under the same condition. Thus, a conclusion can be drawn that the proposed DA algorithm has better BER performance than DA scheme of [13]. Finally, we evaluate performance of the proposed algorithm in the presence of pulse distortion caused by transceiver s antennas [18] and propagation [3]. The effects of the transceiver s antennas are modeled as twice differential effects on the transmitted monocycle [18]. After twice differential, the transmitted 3rdorder and 4th-order Hermite monocycles become 5th-order and 6th-order ones, which are still orthogonal. We employ the generalized function (eq. () in [3]) to model propagation-caused pulse distortion. In Figure 5, dot lines represent BER performance of the proposed algorithm with pulse distortion. It is observed that BER performance degradation caused by pulse distortion is just about 1 db. 5 Conclusions This paper introduces a DA synchronization algorithm dispensing with searching procedures for UWB-IR wireless communication systems. Unlike the searching-based synchronization algorithms, our approach does not require any time-consuming searching procedure, thus shortening synchronization time and lowering computational complexity. Without any knowledge on channel, the proposed algorithm can achieve frame-level synchronization at a low sampling rate of once per symbol. Compared with the DA algorithm without searching procedures in [13], the proposed algorithm is operational for cold start-up scenario and provides performance improvements. In the future, we will focus on fine synchronization (tracking) algorithms that need no searching process. Although the proposed synchronization algorithm is developed when channel information is unknown, the estimation accuracy of the synchronization parameter will be improved when the accumulated multipath energy function is known. Hence, our synchronization parameter estimation method suggests an effectively iterative estimation process between synchronization parameter estimation and channel estimation, which finally improves BER performance of the receiver. This will be the direction of our future work. Acknowledgements This work was supported by National Science and Technology Project for New Generation Broadband Wireless and Mobile Communication Networks (Grant Nos. 9ZX36-6, 9ZX36-9). References 1 Win M Z, Scholtz R A. Ultra wide bandwidth time-hopping spread-spectrum impulse radio for wireless multiple access communications. IEEE Trans Commun,, 48: Wang J Z, Milstein L B. CDMA overlay situations for microcellular mobile communications. IEEE Trans Commun, 1995, 43: Tian Z, Giannakis G B. BER sensitivity to mistiming in ultra-wideband impulse radios part II: fading channels. IEEE Trans Signal Process, 5, 53: He N, Tepedelenlioglui C. Joint pulse and symbol level acquisition of UWB receivers. IEEE Trans Commun, 8, 7: Liu B, Lv T J, Qiao Y W, et al. A novel synchronization algorithm in Ultra-Wideband system. In: Proceedings of IEEE International Conference on Ultra-Wideband, Vancouver, BC, Canada, Qiao Y W, Lü T J. Blind synchronization and low-complexity demodulation for DS-UWB systems. In: Proceedings of IEEE Wireless Communications and Networking Conference, Sydney, Australia,

10 Ren Z Y, et al. Sci China Inf Sci April 1 Vol. 55 No Chen S Y, Wang L, Chen G R. Data-aided timing synchronization for FM-DCSK UWB communication systems. IEEE Trans Ind Electron, 1, 57: Ren Z Y, Lü T J. Blind two-step synchronization for direct-sequence UWB systems. In: Proceedings of IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, Tokyo, Japan, Renzo M D, Annoni L A, Graziosi F, et al. A novel class of algorithms for timing acquisition of differential transmitted reference UWB receivers: architecture, performance analysis and system design. IEEE Trans Wireless Commun, 8, 7: Xiao Z Y, Zhang J Q, Jin D P, et al. Two-step data-aided acquisition for high rate DS-UWB systems. In: Proceedings of IEEE International Conference on Communications, Cape Town, South Africa, Tian Z, Giannakis G B. A GLRT approach to data-aided timing acquisition in UWB radios Part I and II. IEEE Trans Wireless Commun, 5, 4: , Shin D H, Cho Y H, Park D J. A new synchronization scheme exploiting mean energy profile in UWB non-coherent receiver. In: Proceedings of IEEE International Conference on Communications, Istanbul, Turkey, Wang J, Mai L, Peng Y J, et al. An energy-proportion synchronization method for IR-UWB communications. In: Proceedings of IEEE International Symposium on Circuits and Systems, New Orleans, LA, USA, Yang L, Giannakis G B. Blind UWB timing with a dirty template. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, Montreal, PQ, Canada, Scholtz R A. Multiple access with time-hopping impulse modulation. In: Proceedings of IEEE Military Communications Conference, Boston, MA, USA, Hu J F, Lü T J. A novel chip-level algorithm for UWB timing. In: Proceedings of IEEE Global Telecommunications Conference, New Orleans, LO, USA, Carbonelli C, Mengali U. Synchronization algorithms for UWB signals. IEEE Trans Commun, 6, 54: Montoya T P, Smith G S. A study of pulse radiation from several broad-band loaded monopoles. IEEE Trans Anten Propag, 1996, 44: Carbonelli C, Mitra U. Clustered ML channel estimation for ultra-wideband signals. IEEE Trans Wireless Commun, 7, 6: Lottici V, DAndrea A, Mengali U. Channel estimation for ultra-wideband communications. IEEE J Select Areas Commun,, : RCD Components Inc. Passive delay lines, dip package P141 and P4, 7. P141-P4.pdf IEEE P8.15 Working Group for WPANs. Channel Modeling Subcommittee Report Final. IEEE P8.15-/368r5- SG3a. 3 Qiu R C, Zhou C M, Liu Q C. Physics-based pulse distortion for ultra-wideband signals. IEEE Trans Veh Tech, 5, 54: Appendix In this appendix, we prove Eq. (3). When N mod 4 = 1 and <T syn T s/, Z 3 k and Z 4 k for k [1, ] are computed as follows: Z 3 1 = = Z 4 1 = yn yn x(t)x(t + T s)dt x(t)x(t + T s)dt + x(t)x(t + T s)dt T syn p R1(t + T s T syn)dt + ε p R1(t T syn)p R(t T syn)dt T syn p R1(t)dt T s T syn T (T syn), =. x(t)x(t + T s)dt (A1) p R1(t T syn)p R(t T syn)dt (A)

11 788 Ren Z Y, et al. Sci China Inf Sci April 1 Vol. 55 No. 4 In the same way, Z 3 and Z 4 are computed as Z 3 T (T syn) andz 4 =. Therefore, Z 3 =(1/) ε T (T syn) andz 4 =(1/) k=1 Z4 k =. Evidently, when N mod 4 = 1 and <T syn T s/, Z 3 >Z 4. When N mod 4 = 1 and T s/ <T syn <T s, Zk 3 and Zk 4 for k [1, ] are computed as follows: k=1 Z3 k = Z1 3 = Z 4 1 = = x(t)x(t + T s)dt p R1(t + T s T syn)dt yn+ T s T syn p R1(t)dt, x(t)x(t + T s)dt yn yn x(t)x(t + T s)dt + p R1(t + T s T syn)dt + ε T s T syn+ p R1(t)dt. T syn x(t)x(t + T s)dt T syn p R1(t T syn)p R(t T syn)dt (A3) (A4) Similarly, we can derive Z 3 T s T syn+ T s T syn p R(t)dt and Z 4 T s p T s T syn+ R(t)dt. Note that the length of the region of integration for Z 3 1 is T s/, while that for Z 4 1 is T syn T s/. It can be deduced that when N mod 4 = 1 and T s/ <T syn <T s, Z 3 1 >Z 4 1, because the length of the region of integration for Z 3 1 is larger than that for Z 4 1 due to T s/ <T syn <T s. For the same reason, we can obtain Z 3 >Z 4. Therefore, Z 3 >Z 4. When N mod 4 = 1 and T syn =,Z 3 k and Z 4 k for k [1, ] are computed as follows: Z 3 1 = Z 4 1 = x(t)x(t + T s)dt x(t)x(t + T s)dt p R1(t)p R(t)dt =, (A5) p R1(t)p R(t)dt =. (A6) Similarly, we can derive Z 3 = Z 4 =. Therefore, when N mod 4 = 1 and T syn =,Z 3 = Z 4. To sum up, when N mod 4 = 1, Z 3 Z 4 where the equal sign holds if and only if T syn =. LikeN mod 4 = 1, when N mod 4 =,, 3 we have the following conclusion: { Z 3 Z 4, N mod 4 = 1 or 3, Z 3 Z 4, N mod 4 = or, where the equal sign holds if and only if T syn =.