## 1. Introduction

UWB impulse radios (UWB-IR) have attracted increasing interest due to their potential to propose high user capacity with low-complexity and low-power transceivers (Win & Sholtz, 2000). It is approved by the Federal Communications Commission’s (FCC) Report in which the UWB spectral mask is released and published in February 2002. Most of these benefits initiate from the distinctive characteristics inherent to UWB wireless transmissions (Yang & Giannakis, 2004). These make UWB connectivity appropriate for indoor and especially short-range high-rate wireless environments, as well as for strategic outdoor communications. However, to harness these benefits, one of the most critical challenges is the synchronization step and more specifically timing offset estimation. Bit error rate (BER) analysis also exposes evident performance degradation of UWB radios due to mistiming (Tian & Giannakis, 2005). The complexity of which is accentuated in UWB owing to the fact that information bearing waveforms are impulse-like and have low amplitude. In addition, compared to narrowband systems, the difficulty of timing UWB signals is increased further by the dense multipath channel that remains unknown at the synchronization step. These reasons give explanation why synchronization has obtained so much importance in UWB research (Fleming et al, 2002; Homier & Sholtz, 2002; Tian & Giannakis, 2003; Yang et al, 2003).

Typically, pulse position modulation (PPM), pulse amplitude modulation or on/off keying (OOK) is employed. PPM modulation transmits pulses with constant amplitude and encodes the information according to the position of the pulse, while PAM and OOK use the amplitude for this purpose. Moreover, PPM is regularly implemented to reduce transceiver complexity in UWB systems. But unlike pulse amplitude modulation (PAM) applied in the context of UWB systems, the difficulty of accurate synchronization is accentuated in PPM UWB systems owing to the fact that information is transmitted by the shifts of the pulse positions.

In the last years, numerous timing algorithms have been studied for UWB impulse radios under various operating environments.Least squares (LS) (Carbonelli et al, 2003) and Maximum-likelihood (ML) approaches (Lottici et al, 2002) are available, but tend to be computationally complex as they need high sampling rates. In (Djapic et al, 2006), a blind synchronization algorithm that takes advantage of the shift invariance structure in the frequency domain is proposed. An accurate signal processing model for a Transmit-reference UWB (TR-UWB) system is given in (Dang et al, 2006). The model considers the channel correlation coefficients that can be estimated blindly. In (Ying et al, 2008), the authors proposed a code-assisted blind synchronization (CABS) algorithm which relies on the discriminative nature of both the time hopping code and a well-designed polarity code.Timing with dirty templates (TDT), which is the starting point of this paper, was introduced in (Yang & Giannakis, 2005) for rapid synchronization of UWB signals and was developed in (Yang, 2006) for PPM-UWB signals with direct sequence (DS) and/or time hopping (TH) spreading.This technique is based on correlating adjacent symbol-long segments of the received waveform.TDT is functional with random and unknown transmitted symbol sequences. When training symbols are approachable, the performance of the TDT synchronizer can be improved by approving a data-aided (DA) mode (Yang & Giannakis, 2005). The DA mode significantly outperforms the non-data-aided (NDA) one. However, the training sequences require an overhead which reduces the bandwidth and energy efficiency. Except (Yang, 2006), all these timing algorithms are developed for PAM-UWB signals. Since their operations greatly rely on zero-mean property of PAM, these presented timing algorithms are not appropriate to PPM-UWB signals.

In this chapter, to address and try to solve the problem of synchronization for Ultra Wideband (UWB) systems in ad-hoc environments, we propose a fine synchronization algorithm for PAM and PPM UWB signals with a spread spectrum involving Time Hopping (TH). We adopt first a blind (or coarse) synchronization technique, which is Timing with dirty templates (TDT). Its principle is to correlate two consecutive symbol-long segments of the received waveform. In particular, synchronization will be asserted when the correlation function reaches its maximum. This allows TDT algorithms to effectively collect the multipath energy even when the spreading codes and the channel are both unknown. However, this technique estimates coarsely (or roughly) the value of timing offset, therefore not precisely, and this may cause a shortfall in performance of our UWB impulse radio systems. To improve synchronization performance of the TDT (Timing with Dirty Templates) algorithm developed in mentioned papers, our contribution will be to implement a new fine synchronization stage and place it after the dirty one, which is TDT approach. The principle of our fine synchronization algorithm is to make a fine research in order to find the exact moment of the beginning pulse (fine estimation of delay time between emitted pulses and those received). This is achieved by correlating two consecutive segments of symbol-length received waveform, but this time in an interval that corresponds to the number of frames included in one data symbol. First, we applied this algorithm in single-user environments and then, have extended the used method in multi-user environments. Simulation results show that this new approach using TDT synchronizer can achieve a lower mean square error (MSE) than the original TDT for both NDA and DA synchronization mode.

The rest of this chapter is organized as follows. We describe our system model (PAM and PPM signals through time hopping spreading) with first stage synchronization (based on TDT) in Section 2, and then we give an outline of the well known TDT approach for UWB TH-PAM and TH-PPM impulse radios to better understand the overall timing synchronization in Section 3. In Section 4, we present the second step or stage of our synchronization approach with UWB time hopping systems in ad-hoc environments. The performance evaluation of our proposed fine synchronization approach with UWB TH-PAM and TH-PPM impulse radio systems in both single-user and multi-user environments is given in Section 5. And finally, we conclude this chapter in Section 6.

## 2. TH-PAM and TH-PPM UWB system model

Common multiple access techniques implemented for pulse based UWB systems are Time Hopping (TH) and Direct Sequence (DS). Appropriate modulation techniques include OOK (Foerster et al, 2001) and particularly PPM and PAM (Hämäläinen et al, 2002). A given UWB communication system will be a mixture of these techniques, leading to signals based on, for example, TH-PPM, TH-BPAM or DS-BPAM. TH-PAM and TH-PPM are almost certainly the most frequently adopted scheme and will be applied in the following as an example for determining the resources existing in a UWB system in single-user and multi-user environments.

### 2.1. TH-PAM UWB system model for single-user links

In UWB impulse radios, each information symbol is transmitted over a T_{s} period that consists of N_{f} frames (Win & Sholtz, 2000). During each frame of duration T_{f}, a data-modulated ultra-short pulse p(t) with duration

where ε is the energy per pulse. _{th}(i), which time-shift the pulse positions at multiples of the chip duration T_{c} (Win & Sholtz, 2000). In this paper, we focus on a single user link and treat multi-user interference (MUI) as noise.

The transmitted signal propagates through the multipath channel with impulse response

where _{0} represents the propagation delay of the channel.

Then, the received waveform is given by

where

where * indicates the convolution operation. We define the timing offset as _{s}) and we will show in the rest of this paper that this assumption will not affect the timing synchronization.

### 2.2. TH-PPM UWB system model for single-user links

With PPM modulation (Durisi & Benedetto, 2003; Di Renzo et al, 2005), the transmitted signal in single-user links is described by the following model

where ε is the energy per pulse, _{th}(i), which time-shift the pulse positions at multiples of the chip duration T_{c} (Win & Sholtz, 2000). In this paper, we focus on a single user link and treat multi-user interference (MUI) as noise.

After the transmitted signal propagation through the multipath channel, the received waveform is given by

where

where * indicates the convolution operation. We define the timing offset as _{s}) and we will show in the rest of this paper that this assumption will not affect the timing synchronization. Let p_{R}(t) the overall received symbol-long waveform defined as follows

Using (8), the received waveform in (6) becomes

### 2.3. TH-PAM UWB system model for single-user links

The UWB time hopping impulse radio signal considered in this paper is a stream of narrow pulses, which are shifted in amplitude modulated (PAM).The transmitted waveform from the *u*th user is

where

where*i*th frame.

After the transmitted signal propagation through the multipath channel, the received waveform from all users is

where N_{u} is the user’s number, *u*th user’s direct path and

Assuming that the nonzero support of waveform _{s}, the received waveform in (3) can be rewritten as

## 3. TDT approach

As mentioned previously, our proposed timing scheme consists of two complementary floors or steps. The first is based on a coarse (or blind) synchronization that is TDT developed in (Yang & Giannakis, 2005). In this section, we will give an outline of the TDT approach to better understand the overall timing synchronization suggested in this paper. The general structure description of our system model with first stage synchronization (TDT) is illustrated in Fig.1.

The basic idea behind TDT is to find the maximum of square correlation between pairs of successive symbol-long segments. These symbol-long segments are called “dirty templates” because: i) they are noisy, ii) they are distorted by the unknown channel, and iii) they are subject to the unknown offset

### 3.1. TDT approach for TH-PAM UWB system in single-user links

For notational brevity and after setting p_{T} (t) := p_{R}(t-τ_{l,0}), the received waveform simplifies to

Thereafter, a correlation between the two adjacent symbol-long segments

Applying the Cauchy-Schwartz inequality and substituting the expressions of

where

By exploiting the statistical properties of the signal and noise, the mean square of the samples in (17) is given by

We notice that ε_{B}(_{+} ε_{A}(_{R} for _{R} represents the constant energy corresponding to the unknown aggregate template at the receiver. Then the mean square of x^{2}(k;τ) can be rewritten as follows

Since the term ε_{A}(^{2}(k;τ)} also reached its unique maximum at

In the practice, the mean square of x^{2}(k;τ) is estimated from the average of different values x^{2}(k;τ) for k ranging from 0 to M – 1 obtained during an observation interval of duration MT_{s}. In what follows, we summarize the TDT algorithm in its NDA form and then in its DA form.

#### 3.1.1. Non-data-aided (blind) mode

For the synchronization mode NDA, the synchronization algorithm is defined as follows

By using (17), the expression of

From (19) and (20), the estimation of delay τ_{0} is made possible due to the presence of the term ε_{A}(_{B}(

#### 3.1.2. Data-aided mode

The number of samples M required for reliable estimation can be reduced noticeably if a data-aided (DA) approach is pursued(Yang & Giannakis, 2003). The delays can be significantly reduced through the use of training sequences with alternating sign between the symbols

This pattern is particularly attractive, since it simplifies the algorithm proposed by the TDT approach, for the DA mode, to become

The estimator in (24) is essentially the same as (22), except that training symbols are used in (24). However, theses training symbols are instrumental in improving the estimation performance. This will be approved by the simulation results.

### 3.2. TDT approach for TH-PPM UWB system in single-user links

For UWB TH-PPM systems, a correlation between the two adjacent symbol-long segments

By applying the Cauchy-Schwartz inequality and exploiting the statistical properties of the signal and noise (Yang, 2006), the mean square of the samples in (25) is given by

where _{B}(_{+} ε_{A}(_{R} for _{R} represents the constant energy corresponding to the unknown aggregate template at the receiver.

Similarly to PAM signals, the term ^{2}(k;τ) is estimated from the average of different values x^{2}(k;τ) for k ranging from 0 to M – 1 obtained during an observation interval of duration MT_{s}. In what follows, we summarize the TDT algorithm for UWB TH-PPM systems in its NDA form and then in its DA form.

#### 3.2.1. Non-data-aided mode

For the synchronization mode NDA, the synchronization algorithm is defined as follows

The estimator _{0, nda} in (27) can be verified to be m.s.s. consistent by deriving the mean and variance of the function

#### 3.2.2. Data-aided mode

For UWB TH-PPM, the training sequence for DA TDT is considered to comprise a repeated pattern (for example (1,0, 1,0)); that is.

With this pattern, it can be easily verified that the mean square in (26) becomes

With the NDA approach, it is necessary to take expectation with respect to s_{k} in order to remove the unknown symbol effects; while the DA mode, this is not needed. Hence, the sample mean

The estimator in (30) is essentially the same as (27), except training symbols used in (30). However, theses training symbols are essential in improving the estimation performance. This will be approved by the simulation results.

### 3.3. TDT approach for TH-PAM UWB system in multi-user links

For multi-user UWB TH-PAM systems, a correlation between the two adjacent symbol-long segments

Applying the Cauchy-Schwartz inequality and substituting the expressions of

where

Substituting the above equation into (31), we find

where

#### 3.3.1. Non-data-aided mode

For the NDA synchronization mode, the timing algorithm is defined as follows

The estimator can be verified to be m.s.s consistent by deriving the mean and variance of

#### 3.3.2. Data-aided mode

The pattern described previously in (23) is particularly attractive, since it simplifies the proposed algorithm to become in the DA mode

With

## 4. Proposed fine synchronization approach

In this section, we will develop a low-complexity fine synchronization approach using TDT synchronizer in order to find the desired timing offset. The block diagram of our synchronization scheme is shown in Fig.2. Our approach will be evaluated in both NDA and DA modes, without knowledge of the multipath channel and the transmitted sequence (Hizem & Bouallegue, 2010; Hizem & Bouallegue, 2011, a; Hizem & Bouallegue, 2011, b).

This second floor achieves a fine estimation of the frame beginning, after a coarse research in the first. The concept which is based this floor is extremely simple. The idea is to scan the interval _{f} on a window of width T_{corr}. ^{th} step nδ as follows

Where

## 5. Simulation results

In this section, we will evaluate the performance of our proposed fine synchronization approach with simulations. The UWB pulse is the second derivative of the Gaussian function with duration _{c} = 50 GHz. Each symbol contains N_{f}= 32 frames each with duration T_{f}= 35 ns. We used a random TH code over _{c} = 35 and T_{c} = 1.0 ns. The width integration window value’s

### 5.1. TH-PAM UWB system in single-user links

In Fig. 4, we first test the MSE of NDA and DA TDT algorithms summarized in Section 3.1. The MSE is normalized by the square of the symbol duration

In Figs. 5-7, we evaluate and compare by simulation the performance (in term of MSE) of our proposed fine synchronizer with the original NDA and DA TDT algorithms. In Fig. 5, we compare the performances of the new fine synchronization approach in both NDA and DA modes. In Fig. 6-7, we compare the performances of both original TDT and fine synchronization approach proposed for different values of M. In comparison with the original TDT approach, we note that the new approach outperforms the NDA mode and offers a slight improvement in DA mode. Even without any training symbol sequence, our synchronizer can greatly outperform the original NDA TDT especially when M is small.

### 5.2. TH-PPM UWB system in single-user links

In addition to other parameters described previously, the time shift associated with binary PPM is δ = 1ns.Then, the performance is tested for various values of M.

In Fig. 8, we first test the MSE of NDA and DA TDT algorithms for UWB TH-PPM systems. We note that increasing the duration of the observation interval M leads to improved performance for both NDA and DA modes. We also note that the use of training sequences (DA mode) leads to improved performance compared to the NDA mode.

In Figs. 9-11, we evaluate and compare by simulation the performance of our proposed fine synchronizer with the original TDT algorithms. In Fig. 9, we compare the performances of the new fine synchronization approach in both NDA and DA modes. In Fig. 10-11, we compare the performances of both original TDT and fine synchronization approach proposed in both NDA and DA modes for different values of M. In comparison with the original TDT approach, we note that the new approach outperforms the NDA mode and offers a slight improvement in DA mode. Even without any training symbol sequence, our synchronizer can greatly outperform the original NDA TDT especially when M is small.

### 5.3. TH-PAM UWB system in multi-user links

In this part, we will evaluate the performance of our proposed fine synchronization approach for UWB TH-PAM signals in ad-hoc multi-user environments. The performance is tested for various values of M.

In Fig. 12 on left, we first test the mean square error (MSE) corresponding to (35) and (36). From the simulation results, we note that increasing the duration of the observation interval M leads to improved performance for both NDA and DA modes. We also note that the use of training sequences (DA mode) leads to improved performance compared to the NDA mode. In Fig. 12 on right, we compare the new fine synchronization approach performances in both NDA and DA modes. In Fig. 13, we compare the performances of both original TDT and fine synchronization approach for different values of M. In comparison with the original TDT approach, we note that the new approach greatly outperforms the NDA mode and offers a slight improvement in DA mode. This performance improvement is enabled at the price of fine synchronization approach introduced in second floor which can further improve the timing offset found in first floor.

## 6. Conclusion

In this chapter, we have discussed the problem of UWB system performance in single-user and multi-user environments. While there is a rich body of literature addressing this problem most of which has emerged recently, this topic is far from being mature. In this context, developing novel approaches with relatively low complexity still represents crucial task in meeting the challenges of UWB communications.

We first describe the TH-PAM and TH-PPM UWB system model in single-user and multi-user environments. Then, we give an outline of the TDT approach. In the rest of this chapter, we propose a novel fine synchronization scheme using TDT algorithm for UWB TH-PAM and TH-PPM radio system in single-user and multi-user links. With the introduced fine synchronization algorithm, we can achieve a fine estimation of the frame beginning. The performance improvement is enabled at the price of fine synchronization approach introduced in second floor which can further improve the timing offset found in first floor (coarse synchronization approach : TDT).The simulation results show that even without training symbols, our new synchronizer can enable a better performance than the original TDT in NDA mode especially when M is small and offers a slight improvement in DA mode.