中国科技论文在线 http://www.paper.edu.cn Jitter Distribution Evaluation and Suppression Method in UWB Systems Weihua Zhang, Hanbing Shen, Zhiquan Bai, and Kyung Sup Kwak UWB Wireless Communications Research Center (INHA UWB-ITRC), Inha University, 402-751, Incheon, Korea {zhweihua2000}@hotmail.com Abstract. For the extreme short duration of the baseband Impulse Ra- dio (IR) Ultra-Wideband (UWB) transmission waveforms, even small amounts of timing jitter can bring out considerable system performance degradation. Thus jitter performance evaluation and corresponding sup- pression methods are very important for UWB high rate transceiver. We analyzed the jitter distribution function in UWB systems, also a jitter suppression method is proposed by modification of template waveforms. Performance of our proposed waveforms and traditional template wave- forms are compared by analysis and simulation, and the results verify our jitter suppression method works.1 1 Introduction Ultra-wideband (UWB) is proposed as the primary candidate for the physical layer technology of next high speed short range wireless communication for per- sonal area networks (PAN) [1]. This radio technology is based on the radiation of waveforms formed by a sequence of very short, about nanosecond or below nanosecond, base band pulses [2]. The impulsive nature means that synchro- nization error (or jitter) influences the correlation of the received waveform and the template waveform generated in the receiver, thus deteriorates the system perform. Some past researches about this problem have been proposed: The effects of timing jitter on the bit error rate (BER) of UWB have been analyzed [3][4]. To suppressing this degradation system clock with higher stability is proposed which has the capability of precisely positioning the sub-nanosecond pulses with Gaussian distributed root-mean-squared (RMS) jitter of 10ps and within a 50ns time window [5]. However, even if the system clocks are very stable and introduce very little jitter, other issues such as relative velocities between transmitter and receiver introduce additional degradation [6]. 1 This research was supported by the MIC (Ministry of Information and Communi- cation), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Advancement). (IITA-2006-(C1090-0603-0019)). Y.-H. Lee et al. (Eds.): ICESS 2007, LNCS 4523, pp. 810–817, 2007. 转载 c Springer-Verlag Berlin Heidelberg 2007 中国科技论文在线 http://www.paper.edu.cn Jitter Distribution Evaluation and Suppression Method in UWB Systems 811 We offered an approach to suppress the system BER degradation introduced by timing jitter in the paper. This approach is based on modification of the re- ceiver template according to the jitter distribution function to gain more corre- lation with the jittered received signals. We also offered two evaluation methods of jitter distribution function which can be adopted in our proposed schemes. 2SystemModel 2.1 Signal Model of Transmission and Receiving Generic transmission signal s(t) of BPSK and PPM systems for the n-th bit can be given by: − ∞ Ns 1 Eb BPSK: s(t)= bnwt(t − nTf − jTh) Ns n=−∞ j=0 − , (1) ∞ Ns 1 Eb δ PPM: s(t)= wt t − nTf − jTh − (1 − bn) Ns 2 n=−∞ j=0 where bn ∈{−1, +1} is the n-th transmitted binary data bit. Eb is the energy of one bit signal. wt(t) is the transmitted waveform with unit energy. Ns is the number of pulses per bit. Th is the nominal interval between two pulses. Tf = NsTh , which is the average time duration of one transmission symbol. δ is the modulation index if the modulation is PPM. The received signals are given by: − ∞ Ns 1 Eb BPSK: s(t)=α bnwr(t−nTf −jTh −τj(n))+n(t) Ns n=−∞ j=0 (2) ∞ Ns−1 Eb δ PPM: s(t)=α wr t−nTf −jTh − (1−bn)−τj(n) +n(t) Ns 2 n=−∞ j=0 where α is attenuation amplitude in the transmission path and n(t) is additive white Gaussian noise (AWGN) with double sided spectrum of N0/2. wr(t)is the received signal waveform with unit energy corresponding to wt(t). τj (n)is transmission delay for the j-th pulse of the n-th bit. 2.2 Timing Jitter Jitter is simply the time difference between when a pre-defined event should have occurred and when it actually did occur [7]. In a UWB correlator receiver, the template signal can be given by: − ∞ Ns 1 v(t)= wr (t−nTf −jTh −τˆj(n))+n(t), (3) n=−∞ j=0 中国科技论文在线 http://www.paper.edu.cn 812 W. Zhang et al. whereτ ˆj (n) is the estimate value of τj(n). The time offset between these two delays j(n)=ˆτj(n) − τj(n) is called timing jitter. The exact value of j(n) can not be easily evaluated, whereas its distribution function can be evaluated. Timing jitter distribution characteristics models the timing jitter j(n)asa sequence of Gaussian random variables with zero means and standard deviation of σ . The probability density function (pdf) can be given by: 1 τ 2 f(σ, τ )=√ exp − . (4) 2πσ 2σ2 σ is also the average timing error of the jitters from the ideal template timing position, and it is the only parameter defining the jitter distribution. 3 Templates with Jitter Suppression Abilities 3.1 Pulse Shape of Proposed Templates We assume that the template is jitter free and all the jitters come only from the received waveforms in analysis and simulation of this paper. To improve the system perform, higher correlation coefficient is required. Thereby a novel template is proposed to replace the original template waveform wr(t). We set ∞ wˆr(t)= f(σ, τ )wr (t − τ)dτ (5) −∞ as the novel template waveform. The correlation coefficient between timing shifted received waveform and proposed template is given by: ∞ ∞ w (t − τ)ˆw (t)dt w (t − τ)ˆw (t)dt ˆ −∞ r r −∞ r r Rwj (τ)= ∞ ∞ = ∞ . (6) 2 − 2 2 −∞ wr (t τ)dt −∞ wˆr (t)dt −∞ wˆr (t)dt The correlation between the timing shifted received waveform and jitter free template waveform is R(τ).Thus the integral correlation coefficient between the jitter free template waveform and the jittered received waveform is given by: ∞ ∞ ∞ ∞ ρ= f(σ, τ )R(τ)dτ= f(σ, τ ) wr(t − τ)wr(t)dtdτ= wˆr(t)wr(t)dt. (7) −∞ −∞ −∞ −∞ The integral correlation coefficient between the jitter free proposed template waveform and the jittered received waveform is given by: ∞ ∞ ˆ 2 ρˆ = f(σ, τ )R(τ)dτ = wˆr (t)dt. (8) −∞ −∞ Next we will compare the correlation coefficients ρ andρ ˆ.Wehaveˆρ ≥ 0in(8). 中国科技论文在线 http://www.paper.edu.cn Jitter Distribution Evaluation and Suppression Method in UWB Systems 813 Fig. 1. General structure of proposed jitter suppression UWB correlator receiver If ρ<0,ˆρ ≥ ρ deservedly. If ρ ≥ 0, we use the method below to compare two correlation coefficients: ∞ 2 2 ρ −∞wˆr(t)wr(t)dt = ∞ . (9) 2 ρˆ −∞wˆr (t)dt Applying the Schwartz inequality to (9), we obtain: 2 ≤ 2 · 2 2 wˆr(t)wr(t)dt wˆr (t)dt wr (t)dt = wˆr (t)dt. (10) So we haveρ ˆ ≥ ρ,consequently. The conclusion is that our proposed template waveform has higher correla- tion value with the jittered received signal waveform than the original template waveform in any jitter distribution schemes. 3.2 Receiver Structure and Novel Template Waveforms Functions The structure of the proposed receiver is given in Fig.1, where timing jitter distribution evaluator and an integrator used to realize our proposed template are added to the template waveform generator. If the jitter free pulse waveform is given by t 2 t wr(t)= 1 − 4π exp −2π , (11) τm τm the proposed template waveforms can be deduced as: − 2 − 2 2 − 2 2πt wˆr(t)= f(σ, τ )wr (t τ)dτ = μ τm +4πσ 4πt exp 2 2 , (12) τm +4πσ where μ is attenuation parameters which can be used to adjust the amplitude of the template waveform. Fig.2(a) and Fig.2(b) give out the samples of our proposed 中国科技论文在线 http://www.paper.edu.cn 814 W. Zhang et al. jitter robust template waveforms, where the original jitter free waveform is same as (11), and proposed waveforms corresponding to different jitter distribution pa- rameters (σ =0.1ns, σ =0.2ns and σ =0.5ns) are given, respectively. Energy Normalized Proposed Template Waveforms for BPSK(τ =0.25ns) Energy Normalized Proposed Template Waveforms for PPM(τ =0.25ns) m m 1 1 Original w (t) Original w (t) rx rx σ Proposed Waveform with σ=0.025ns 0.8 Proposed Waveform with =0.025ns σ 0.8 Proposed Waveform with σ=0.05ns Proposed Waveform with =0.05ns σ Proposed Waveform with σ=0.1ns Proposed Waveform with =0.1ns 0.6 0.6 0.4 0.2 0.4 0 0.2 −0.2 Normalized Amplitude Normalized Amplitude 0 −0.4 −0.6 −0.2 −0.8 −0.4 −1 −5 −4 −3 −2 −1 0 1 2 3 4 5 −6 −4 −2 0 2 4 6 −10 −10 Time (s) x 10 Time (s) x 10 (a) BPSK system (b) PPM system Fig. 2. Original template and the proposed jitter robust templates 4 Jitter Evaluation Methods Timing jitter distribution evaluator is the key function module in proposed jitter suppression scheme. As jitter distribution is a Gaussian i.i.d function, the target of jitter distribution evaluation is to achieve the unique Gaussian distribution parameter σ. There are two different schemes to evaluate this parameter σ: pilot impulse sequence (PIS) and waveform parameter evaluation (WPE): 4.1 Pilot Impulse Sequence (PIS) Method This method depends on such a scheme: the transmitter sends fixed pilot se- quence of impulse-like waveforms periodically, which is given by: − Nt 1 ST (t)= δ(t − nTd), (13) n=0 where Nt is the number of impulse-like waveforms, and Td is the fixed time interval of the waveforms.