**1. Introduction**

14 Ultra Wideband – Current Status and Future Trends

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The interest for Ultra Wide Band (UWB) technology is growing fast especially in the shortrange indoor wireless communication, for example, in wireless personal area networks (WPAN). The basic concept is to transmit and receive baseband impulse waveform streams of very low power density and ultra-short duration pulses (typically at nanosecond scale). These properties of UWB give rise to fine time resolution, rich multipath diversity, low probability of detection, enhanced penetration capability, high user-capacity, and potential spectrum compatibility with existing narrowband systems [1]. However, one of the most critical challenges in enabling the unique benefits of UWB transmissions is timing synchronization, because the transmitted pulses are narrow and have low power density under the noise floor [2].

Timing synchronization in wireless communication systems typically depends on the sliding correlator between the received signal and a transmit-waveform template (Clean Template). In Impulse-Radio Ultra-Wideband (IR-UWB) devices however, this approach is not only sub-optimum in the presence of rich resolvable multipath channel, but also incurs high computational complexity and long synchronization time [2, 3]. Some research for improving the synchronization performance for IR-UWB systems has been reported in [4-9]. Each of these approaches requires one or more of the following assumptions: 1) the absence of multipath; 2) the absence of time-hopping (TH) codes; 3) the multipath channel is known; 4) high computational complexity and long synchronization time; and 5) degradation of bandwidth and power efficiency. Timing with Dirty Templates (TDT) is an efficient synchronization approach proposed for IR-UWB, introduced in [10-13]. This technique is based on correlating the received signal with "dirty template" extracted from the received waveforms. This template is called dirty; because it is distorted by the unknown channel and by the ambient noise. TDT allows the receiver to enhance energy capture even when the

© 2012 Alhakim et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Alhakim et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

$$u(t) = \sqrt{\mathcal{E}\_{\rm s}} \sum\_{n=0}^{\infty} \mathbf{s}[n] p\_T(t - nT\_{\rm s}) \tag{1}$$

$$r(t) = \sqrt{\mathcal{E}\_s} \sum\_{n=0}^{\infty} s[n] p\_R(t - nT\_s - \tau\_0) + \mathcal{w}(t) \circ \tag{2}$$

$$p\_R(t) \colon= \sum\_{j=0}^{N\_f - 1} p\_r \{ t - jT\_f - c\_j T\_c \} = \sum\_{l=0}^{L-1} \alpha\_l p\_T \{ t - \tau\_{l,0} \} \tag{3}$$

$$r(t) = \sqrt{\mathcal{E}\_s} \sum\_{n=0}^{\infty} \mathbf{s}[n] p\_R(t - nT\_s - n\_s T\_s - \tau) + \mathbf{w}(t) \boldsymbol{\upalpha} \tag{4}$$

$$\mathbf{x}(t+nT\_{\sf S}) = \mathbf{w}(t+nT\_{\sf S}) + \begin{cases} \sqrt{\mathcal{E}\_{\sf S}} \mathbf{s}[n-n\_{\sf S}-1] p\_{R}(t+T\_{\sf S}-\tau) \colon t \in [0,\tau) \\ \sqrt{\mathcal{E}\_{\sf S}} \mathbf{s}[n-n\_{\sf S}] p\_{R}(t-\tau) & : t \in [\tau, T\_{\sf S}) \end{cases} \tag{5}$$

$$R\_{\mathbf{X},\mathbf{x}}[n] = \int\_0^{T\_s} \mathbf{x}(t + nT\_s) \mathbf{x}(t + (n+1)T\_s) \, dt \tag{6}$$

$$\begin{split} \int\_0^{T\_s} \{\mathbf{w}(t + nT\_s) + \sqrt{\mathcal{E}\_s} \sum\_{m=0}^1 s[n - n\_s - m] p\_R(t + mT\_s - \tau)\} \times & \{\mathbf{w}(t + (n+1)T\_s) + \sqrt{\mathcal{E}\_s} \} + \\ \sqrt{\mathcal{E}\_s} \sum\_{m=0}^1 s[n - n\_s - m + 1] p\_R(t + mT\_s - \tau) \} \, dt \\ = \tilde{\mathbf{x}}[n] + A \int\_0^{T\_s} p\_R^2(t + T\_s - \tau) \, dt + B \int\_0^{T\_s} p\_R^2(t - \tau) \, dt \end{split} \tag{6}$$

$$\widecheck{\omega}[n] \sim \mathcal{N}\left(0, \sigma\_{\text{w}}\,^{2} = \frac{N\_{\text{o}}\,^{2}}{2}B T\_{\text{s}} + N\_{\text{0}}\underbrace{\mathcal{E}\_{\text{s}}\mathcal{E}\_{\text{max}}}\_{\widetilde{\mathcal{E}\_{\text{r}}}}\right) \tag{7}$$

$$R\_{\chi,\mathbf{x}}[n] = \left\vert \mathfrak{s}[n] + A \int\_{T\_{\mathbf{s}}-\mathbf{r}}^{T\_{\mathbf{s}}} p\_R^2(t) \, dt + B \int\_0^{T\_{\mathbf{s}}-\mathbf{r}} p\_R^2(t) \, dt \right\vert \tag{8}$$

$$where \begin{cases} A = \mathfrak{E}\_{\mathbf{s}} \mathfrak{s}[n - n\_{\mathbf{s}} - 1]. \mathfrak{s}[n - n\_{\mathbf{s}}] \\ B = \mathfrak{E}\_{\mathbf{s}} \mathfrak{s}[n - n\_{\mathbf{s}}]. \mathfrak{s}[n - n\_{\mathbf{s}} + 1] \end{cases}$$


$$R\_{\mathbf{x},\mathbf{x}}[n] = \mathbb{E}\_{\mathbf{s}} \int\_{0}^{T\_{\mathbf{s}}} P\_{R}^{2}(t) \, dt \, + \,\widetilde{\omega\_{d1}}[n] = \underbrace{\mathbb{E}\_{\mathbf{s}} \mathbb{E}\_{\max}}\_{\widetilde{\mathcal{E}\_{T}}} + \widetilde{\omega\_{d1}}[n] = \mathbb{E}\_{r} + \widetilde{\omega\_{d1}}[n] \tag{9}$$

$$\mathcal{H}\_0 \colon R\_{\mathbf{x}, \mathbf{x}}[n] = \widetilde{\omega\_{d0}}[n] \qquad \qquad n = 0, 1, \ldots, M\_1 - 1$$

$$\mathcal{L}\_1 \colon R\_{\mathbf{x}, \mathbf{x}}[n] = \mathcal{E}\_r + \widetilde{\omega\_{d1}}[n] \qquad \qquad n = n\_{\mathbf{s}\prime} n\_{\mathbf{s}} + 1, \ldots, n\_{\mathbf{s}} + M\_1 - 1 \tag{10}$$

$$
\widetilde{\omega\_{d0}}[n] \sim \mathcal{N}\left(0, \sigma\_0^2 = \frac{N\_0^{\
u}}{2} B T\_s\right),
$$

$$\widetilde{u\_{d1}} \widetilde{\ } [n] \sim \mathcal{N} \left( 0, \sigma\_1^{\; 2} = N\_0 \mathcal{E}\_r + \frac{{N\_0}^2}{2} B T\_s \right) \tag{11}$$

$$f(n) = \frac{p(R\_{\chi x}[n]; \Omega\_1)}{p(R\_{\chi x}[n]; \Omega\_0)} > \eta \tag{12}$$

$$f(n) = \frac{\frac{1}{\left(\pi \sigma\_1^2\right)^{M\_1/2}} \exp\left[-\frac{1}{\omega \sigma\_1^2} \sum\_{m=n}^{n+M\_1-1} \left(R\_{\chi x}[m] - \xi\_r\right)^2\right]}{\left(\frac{1}{\left(\pi \sigma\_0\right)^{M\_1/2}} \exp\left[-\frac{1}{2\sigma\_0^2} \sum\_{m=n}^{n+M\_1-1} \left(R\_{\chi x}[m]\right)^2\right]} > \eta$$

$$= \left(\frac{\sigma\_0}{\sigma\_1}\right)^{M\_1} \exp\left[-\frac{1}{2\sigma\_1^2} \sum\_{m=n}^{n+M\_1-1} \left(R\_{\chi x}[m] - \xi\_r\right)^2 + \frac{1}{2\sigma\_0^2} \sum\_{m=n}^{n+M\_1-1} \left(R\_{\chi x}[m]\right)^2\right] > \eta$$

$$\left(\eta\right) = \left(\frac{\sigma\_0}{\sigma\_1}\right)^{M\_1} \exp\left[\sum\_{m=n}^{n+M\_1-1} \left\{\left(-\frac{1}{2\sigma\_1^2} + \frac{1}{2\sigma\_0^2}\right) R\_{\chi x}^2[m] + \frac{\xi\_r}{\sigma\_1^2} R\_{\chi x}[m] - \frac{\xi\_r^2}{2\sigma\_1^2}\right\}\right] > \eta$$

$$\ln\left\{f(n)\right\} = M\_1 \ln\left(\frac{\sigma\_0}{\sigma\_1}\right) + \sum\_{m=n}^{n+M\_1-1} \left\{ \left(-\frac{1}{2\sigma\_1^2} + \frac{1}{2\sigma\_0^2}\right) R\_{\mathbf{x},\mathbf{x}}^2[m] + \frac{\mathcal{E}\_r}{\sigma\_1^2} R\_{\mathbf{x},\mathbf{x}}[m] - \frac{\mathcal{E}\_r^2}{2\sigma\_1^2} \right\} > \ln(\eta)$$

$$\Sigma\_{m=n}^{n+M\_1-1} \left\{ \left(-\frac{1}{2\sigma\_1^2} + \frac{1}{2\sigma\_0^2}\right) R\_{\mathbf{x},\mathbf{x}}^2[m] + \frac{\mathcal{E}\_r}{\sigma\_1^2} R\_{\mathbf{x},\mathbf{x}}[m] \right\} > \ln(\eta) - M\_1 \ln\left(\frac{\sigma\_0}{\sigma\_1}\right) + \frac{M\_1 \mathcal{E}\_r^2}{2\sigma\_1^2}$$

$$\Sigma\_{m=n}^{n+M\_1-1} \left\{ \frac{\sigma\_1^{\sigma\_1} - \sigma\_0^{\sigma\_0}}{2\mathcal{E}\_r \sigma\_0^2} R\_{\mathbf{x},\mathbf{x}}^2[m] + R\_{\mathbf{x},\mathbf{x}}[m] \right\} > \left(\ln(\eta) - M\_1 \ln\left(\frac{\sigma\_0}{\sigma\_1}\right) + \frac{M\_1 \mathcal{E}\_r^2}{2\sigma\_1^2}\right) \frac{\sigma\_1^{\sigma\_1}}{\mathcal{E}\_r}$$

$$\left\{ \sum\_{m=n}^{n+M\_1-1} \left\{ \frac{N\_0}{2\sigma\_0^2} R\_{\mathbf{x},\mathbf{x}}^2[m] + R\_{\mathbf{x},\mathbf{x}}[m] \right\} > \left( \ln(\eta) - M\_1 \ln \left( \frac{\sigma\_0}{\sigma\_1} \right) + \frac{M\_1 \mathcal{E}\_r}{2\sigma\_1^2} \right) \frac{\sigma\_1^2}{\mathcal{E}\_r} \right\}$$

$$T = \Sigma\_{m=n}^{n+M\_1-1} \left\{ R\_{\mathbf{x},\mathbf{z}}^2[m] + N\_0 B T\_s R\_{\mathbf{x},\mathbf{z}}[m] \right\} \ge \underbrace{\left( \ln(\eta) - M\_1 \ln \left( \frac{\sigma\_0}{\sigma\_1} \right) + \frac{M\_1 \mathcal{E}\_r^2}{2 \sigma\_1^2} \right) \frac{\sigma\_1^2 \cdot N\_0 B T\_\delta}{\xi\_r}}\_{\vec{\xi}} \tag{13}$$

$$P\_{FA} = Pr\{T > \xi; \mathcal{H}\_0\} \mathbb{0} \tag{14}$$

$$P\_D = Pr\{T > \xi; \mathcal{H}\_1\} \mathbb{0} \tag{15}$$

$$\mathfrak{H}\_{\mathfrak{s}} = \arg\max T(\mathfrak{n}\_{\mathfrak{s}}); \qquad T(\mathfrak{n}\_{\mathfrak{s}}) = \sum\_{m=n\_{\mathfrak{s}}}^{n\_{\mathfrak{s}}+M\_{1}-1} \left\{ R\_{\mathbf{x},\mathbf{x}}^{2}[m] + N\_{0} B T\_{\mathbf{s}} R\_{\mathbf{x},\mathbf{x}}[m] \right\} \tag{16}$$

$$\mathbf{f}\_{0} = \underset{\mathbf{m}}{\arg\max} \frac{1}{\mathbf{1}\_{M\_{2}}} \sum\_{n=0}^{M\_{2}-1} \left( \int\_{0}^{T\_{\text{s}}} \mathbf{x} (\mathbf{t} + nT\_{\text{s}} + \tau\_{m}) . \mathbf{x} (\mathbf{t} + (n+1)T\_{\text{s}} + \tau\_{m}) \, dt \right)^{2} \tag{17}$$

$$\text{l.s}[n] = \begin{cases} -1, \; if \{ n \bmod 4 \} = 0, or; 1\\ +1, \; if \{ n \bmod 4 \} = 2, or; 3 \end{cases} : n \in [0, M\_2 - 1] \tag{18}$$

$$\text{fit}\_0 = \mathop{\arg\max}\_{\substack{M\_2\\m}} \frac{1}{\Delta\_{n=0}} \sum\_{t=0}^{M\_2 - 1} \left( \int\_0^{T\_\mathbf{s}} \mathbf{x}(t + nT\_\mathbf{s} + \tau\_m) . x(t + \{n+1\} T\_\mathbf{s} + \tau\_m) . W(t) dt \right)^2 \tag{19}$$

$$W(\mathbf{t}) = \sum\_{j=0}^{N\_f - 1} c\_j p\{\mathbf{t} - jT\_f\}; \ p(\mathbf{t}) = \begin{cases} 1 & \text{si } 0 \le \mathbf{t} \le T\_p + \tau\_{L-1, 0} \\ 0 & \text{otherwise} \end{cases} \tag{20}$$

derivative of the Gaussian function with unit energy and duration �� ≈ 1ns. Each symbol contains �� = 24 frames with duration �� = 100ns. The simulations are performed in a Saleh-Valenzuela channel [20]. The parameters of this channel are chosen with (1/Λ, 1/λ, Γ, γ) = (2, 0.5, 30, 5) ns. The maximum channel delay spread of the channel is about 99 ns, and the inter-symbol interference (ISI) is negligible. We generate �� randomly from a uniform distribution over [0� ��). We employ TH spreading codes of period ��, which is generated from a uniform distribution over [0� �� − 1], with �� = 6, and �� = 10ns. We supposed the size of the increment ∆� equal to ��⁄2.

Timing Synchronisation for IR-UWB Communication Systems 27

**Figure 14.** Correlator output energy (TH codes, SNR=20 & ��=16)

MSE results are normalized by ��

computational complexity.

We compare the accurate acquisition between the DT estimator without any window mentioned in (17) and the modified estimator with window size equal to ��� as mentioned in (19). Figures 15-16 show the comparison of mean square error (MSE) performance in DA & NDA modes with dirty templates for various values of ��. In these figures, the

pulse. The simulations confirm that, the DT estimator with window (*solid lines*) has higher timing estimation performance than the DT estimator without window (*dashed lines*). In general, as �� increases the normalized MSE decreases. Increasing SNR also helps to reduce the MSE. That means, when the observation number �� or the signal-to-noise ratio SNR is increased, the mean square error MSE is reduced and the estimation performance is improved. In addition, we can clearly notice that all curves with high SNR reach an error floor, which depends on the synchronization accuracy. This error floor can be reduced by decreasing the size of (∆�), but with increasing simulation time and

The results also show that the timing estimator for DA mode in Figure 15 has smaller MSE values and more accurate timing simulation than NDA mode in Figure 16 for the same SNR & ��, but with less bandwidth efficiency. Moreover, Figure 15 shows that the DA estimator could be used with small training pattern size such as �� = 4, that helps to reduce the

In this section, we present the original TDT algorithm used for achieving rapid, accurate and low-complexity timing acquisition. It relies on searching a peak in the output of the correlation between the received signal and a dirty template. But we have found the presence of multiple maxima points around the peak at the output of the correlator, and that may increase the complication to estimate the timing offset error (TOE). To avoid this problem, we modify the structure of the cross-correlation, by adding the suitable window

number of operations performed at the receiver as well as the synchronization time.

�, and plotted versus the signal-to-noise ratio (SNR) per

**Figure 12.** Correlator output energy (without TH codes, SNR=20 & ��=16)

**Figure 13.** Correlator output energy (TH codes, SNR=3 & ��=16)

**Figure 14.** Correlator output energy (TH codes, SNR=20 & ��=16)

size of the increment ∆� equal to ��⁄2.

**Figure 12.** Correlator output energy (without TH codes, SNR=20 & ��=16)

**Figure 13.** Correlator output energy (TH codes, SNR=3 & ��=16)

derivative of the Gaussian function with unit energy and duration �� ≈ 1ns. Each symbol contains �� = 24 frames with duration �� = 100ns. The simulations are performed in a Saleh-Valenzuela channel [20]. The parameters of this channel are chosen with (1/Λ, 1/λ, Γ, γ) = (2, 0.5, 30, 5) ns. The maximum channel delay spread of the channel is about 99 ns, and the inter-symbol interference (ISI) is negligible. We generate �� randomly from a uniform distribution over [0� ��). We employ TH spreading codes of period ��, which is generated from a uniform distribution over [0� �� − 1], with �� = 6, and �� = 10ns. We supposed the

> We compare the accurate acquisition between the DT estimator without any window mentioned in (17) and the modified estimator with window size equal to ��� as mentioned in (19). Figures 15-16 show the comparison of mean square error (MSE) performance in DA & NDA modes with dirty templates for various values of ��. In these figures, the MSE results are normalized by �� �, and plotted versus the signal-to-noise ratio (SNR) per pulse. The simulations confirm that, the DT estimator with window (*solid lines*) has higher timing estimation performance than the DT estimator without window (*dashed lines*). In general, as �� increases the normalized MSE decreases. Increasing SNR also helps to reduce the MSE. That means, when the observation number �� or the signal-to-noise ratio SNR is increased, the mean square error MSE is reduced and the estimation performance is improved. In addition, we can clearly notice that all curves with high SNR reach an error floor, which depends on the synchronization accuracy. This error floor can be reduced by decreasing the size of (∆�), but with increasing simulation time and computational complexity.

> The results also show that the timing estimator for DA mode in Figure 15 has smaller MSE values and more accurate timing simulation than NDA mode in Figure 16 for the same SNR & ��, but with less bandwidth efficiency. Moreover, Figure 15 shows that the DA estimator could be used with small training pattern size such as �� = 4, that helps to reduce the number of operations performed at the receiver as well as the synchronization time.

> In this section, we present the original TDT algorithm used for achieving rapid, accurate and low-complexity timing acquisition. It relies on searching a peak in the output of the correlation between the received signal and a dirty template. But we have found the presence of multiple maxima points around the peak at the output of the correlator, and that may increase the complication to estimate the timing offset error (TOE). To avoid this problem, we modify the structure of the cross-correlation, by adding the suitable window

$$\begin{cases} R\_e = \int\_0^{T\_\varsigma} r(t)\chi(t-\hat{\tau}+\Delta) \, dt\\ R\_l = \int\_0^{T\_\varsigma} r(t)\chi(t-\hat{\tau}-\Delta) \, dt \end{cases} \tag{21}$$

$$\mathbf{y}(t) = \frac{1}{M} \boldsymbol{\Sigma}\_{n=1}^{M} \left( p\_R(t - nT\_s) + \boldsymbol{\omega}\_n(t) \right); \quad t \in \{0, T\_s\} \tag{22}$$

$$\mathbf{w}(\mathbf{t}) \cong p\_R(\mathbf{t}) + \overline{\mathbf{w}}(\mathbf{t}) \colon \quad \overline{\mathbf{w}}(\mathbf{t}) = \frac{1}{M} \Sigma\_{n=1}^M \mathbf{w}\_n(\mathbf{t}) \sim \mathcal{N}\left(0, \overline{\sigma}^2 = \frac{\varkappa\_0}{2M}\right) \tag{23}$$

$$R\_{\varepsilon,l}[\epsilon,n] = \int\_0^{T\_\varepsilon} \{\mathbf{s}[n]p\_R(t) + \boldsymbol{\omega}\_n(t)\} \times \{p\_R(t-\epsilon \pm \Delta)\overline{\mathbf{w}}(t)\}dt; \quad t \in [0, T\_\varepsilon) \tag{24}$$

$$R\_{e,l}[\epsilon, n] = \mathbf{s}[n]\Gamma\_{e,l}[\epsilon] + n\_{e,l}[\epsilon, n] \tag{25}$$

$$\Gamma\_{e,l}[\epsilon] = \int\_0^{T\_s} p\_R(t)p\_R(t-\epsilon \pm \Delta) \, dt$$

$$n\_{e,l}[\epsilon, n] = \xi\_1 + \xi\_2 + \xi\_3 \tag{26}$$

$$m\_{e,l}[\epsilon, n] \colon \begin{cases} \xi\_1 = \int\_0^{T\_s} p\_R(t - \epsilon \pm \Delta) w\_n(t) \, dt \\ \xi\_2 = \int\_0^{T\_s} \mathfrak{s}[n] p\_R(t) \overline{w}(t) \, dt \\ \xi\_3 = \int\_0^{T\_s} w\_n(t) \overline{w}(t) \, dt \end{cases}$$

$$e[\epsilon, n] = R\_e[\epsilon, n] - R\_l[\epsilon, n]. \tag{27}$$

$$e[\epsilon, n] = \mathfrak{s}[n] \underbrace{(\Gamma\_{\mathfrak{e}}[\epsilon] - \Gamma\_{l}[\epsilon])}\_{\mathfrak{S}[\epsilon]} + \underbrace{n\_{\mathfrak{e}}[\epsilon, n] - n\_{l}[\epsilon, n]}\_{\eta[n]} = \mathfrak{s}[n] \cdot \mathfrak{S}[\epsilon] + \eta[n] \tag{28}$$

$$e[\epsilon, n] = (R\_{\epsilon}[\epsilon, n] - R\_l[\epsilon, n]) \times \text{sign}(R\_{\epsilon}[\epsilon, n] + R\_l[\epsilon, n])\tag{29}$$

$$e[\epsilon, n] = \mathbb{S}[\epsilon] + \eta[n] \tag{30}$$

$$\begin{array}{rcl} \eta[n] \sim \mathcal{N}\{0, \sigma\_{\eta}^{2}\} & : \sigma\_{\eta}^{2} = \frac{N\_{0}(M+1)}{M}(\mathbb{S}\_{max} - \Gamma\_{rr}(2\Delta)) \end{array} \tag{31}$$

$$
\tau(t) = \tau\_0 + mt \tag{32}
$$

$$
\omega\_n^2 = m \,\lambda \,\sigma\_\eta^{-1}, \quad \xi = \sqrt{2}/2 \tag{34}
$$

$$B\_L = 0.53\,\mu\_n \ll 1/T\_s \quad k\_2 = \sqrt{2}/\omega\_n \; , \; k\_1 = A/\omega\_n^2 \tag{35}$$

$$\mathbb{S}[n] = \text{sign}\left[\int\_0^{T\_\mathbf{s}} r(t + nT\_\mathbf{s}) y(t - \hat{\mathbf{r}}) dt\right] \tag{36}$$

$$\mathbf{y}(t) = \frac{1}{\nu} \boldsymbol{\Sigma}\_{n=1}^{K} \boldsymbol{\S}[n] \boldsymbol{r}(t + nT\_{\rm s}); \quad t \in [0, T\_{\rm s}) \tag{37}$$

Timing Synchronisation for IR-UWB Communication Systems 37

Figure 23, which shows how many symbols (iteration steps) DLL requires to match efficiently �(�). It is clear that when �� increases, the required number of symbols would decrease and transient response would be better. The BER comparisons for various �� are depicted in Figure 24. We observe that for high SNR values, an increase in �� (Simultaneously, �� augments) leads to speed up the tracking operation and to improve BER performance. On the other hand, for small SNR values, the bandwidth �� should be decreased for alleviating the noise effects, but that degrades the transient performance. Consequently, increasing �� helps

In this section, we design a second-order DLL used for tracking timing offset variations in the received waveform, taking Doppler effects into account. We combine DLL with TDT, which enables enhancing the received energy capture even when the multipath channel and the TH codes are both unknown. Consequently, the proposed approach contributes to improve tracking performance for UWB systems and to reduce receiver structure complexity. For selecting the optimum parameter values for the proposed DLL, we apply Wiener-filter theory. Simulation results show the performance of the proposed DLL and conform that increasing �� helps to reduce the transient error effect, but in the price of noise

In this chapter, we use TDT algorithms for carrying out low-complexity high-performance timing synchronization, which constitutes a major challenge in realizing the UWB communications. TDT technique is based on correlating the received signal with "dirty template" extracted from the received waveforms. This template is called dirty; because it is distorted by the unknown channel and by the ambient noise. TDT allows enhancing received energy capture and reducing receiver structure complexity. The described technique can be applied to UWB systems even in the presence of time hopping TH codes, Inter-Frame Interference (IFI) and rich multipath environment, where Inter-Symbol

TDT synchronization system consists of three main blocks: signal detection, timing acquisition and tracking. Each block of them is explained in a separated section of this chapter. In signal detection section: the dirty template detector is derived by applying the Neyman-Pearson theory. Then, Monte Carlo simulations are performed to find the probabilities of false alarm (���) and detection (��). The results of simulation analysis show that the detection performance of the dirty template approach is improved by increasing the signal-to-noise ratio (SNR) or data-aided (DA) number. After detecting the UWB signal, the

Next section presents the timing acquisition in both DA and NDA modes. Then, we improve the timing estimator by adding a suitable window filter to the structure of the crosscorrelation. Both the theoretical analysis and Matlab simulation results show the

symbol-level timing offset estimation relies on searching the best statistics �.

to reduce the transient error effect, but in the price of noise handling ability.

handling ability.

**6. Conclusion** 

Interference (ISI) is absent.

**Figure 23.** DLL transient performance (symbol number vs. natural frequency)

**Figure 24.** BER for the proposed DLL (� � ��� �(�) � �������)

Figure 23, which shows how many symbols (iteration steps) DLL requires to match efficiently �(�). It is clear that when �� increases, the required number of symbols would decrease and transient response would be better. The BER comparisons for various �� are depicted in Figure 24. We observe that for high SNR values, an increase in �� (Simultaneously, �� augments) leads to speed up the tracking operation and to improve BER performance. On the other hand, for small SNR values, the bandwidth �� should be decreased for alleviating the noise effects, but that degrades the transient performance. Consequently, increasing �� helps to reduce the transient error effect, but in the price of noise handling ability.

In this section, we design a second-order DLL used for tracking timing offset variations in the received waveform, taking Doppler effects into account. We combine DLL with TDT, which enables enhancing the received energy capture even when the multipath channel and the TH codes are both unknown. Consequently, the proposed approach contributes to improve tracking performance for UWB systems and to reduce receiver structure complexity. For selecting the optimum parameter values for the proposed DLL, we apply Wiener-filter theory. Simulation results show the performance of the proposed DLL and conform that increasing �� helps to reduce the transient error effect, but in the price of noise handling ability.
