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A Novel Fine Synchronization Method for Dirty Template UWB Timing Acquisition. Rshdee Alhakim1, Kosai Raoof 2, Emmanuel Simeu1. 1 TIMA Laboratory ...

A Novel Fine Synchronization Method for Dirty Template UWB Timing Acquisition Rshdee Alhakim1, Kosai Raoof 2, Emmanuel Simeu1 1

2

TIMA Laboratory (CNRS – Grenoble University), 46 Av. Félix Viallet, 38031 Grenoble Cedex, France GIPSA-LAB, (CNRS – Grenoble University), 961 Rue de Houille Blanche, 38402 St. Martin d’Hères, France [email protected], [email protected], [email protected]

Abstract—Timing acquisition constitutes a major challenge in carrying out highly efficient ultra-wideband (UWB) communications. The timing with dirty template (TDT) approach is a promising candidate, which is low-complexity highperformance timing acquisition. In this paper, we describe the dirty template (DT) technique, in order to develop and test timing algorithms in both data aided (DA) and non-data aided (NDA) modes. Then we propose a new method based on TimeHoping TH codes to improve the performance estimation of the original dirty template algorithms. Simulation shows the estimation error results of the modified method in the DA and NDA modes. It confirms the high performance and fast timing of DA mode, compared to NDA mode, but with less bandwidth efficiency. Index Terms—synchronization, timing acquisition, ultrawideband (UWB), dirty template (DT) .

I.

INTRODUCTION

The interest for Ultra wideband (UWB) technology is growing fast especially in the short-range indoor wireless communications. 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 the timing synchronization, because the transmitted pulses are narrow and have low power density under the noise floor. Accurate timingoffset estimation (TOE) imposes major challenges to pulsed UWB systems in achieving their potential bit error rate (BER) performance, capacity, and throughput [2]. Numerical tests show that a delay (timing jitter) is higher than a tenth of the impulse width leads to a total loss of information. In general, timing synchronization in wireless communication systems typically depends on the sliding correlator between the received signal and a transmitwaveform template (Clean Template). However, this approach is herein not only sub-optimum in the presence of dense multipath, but also incurs high computational complexity and

long synchronization time [2]. Several timing algorithms have been proposed recently for UWB Impulse Radio (UWB-IR) systems. For example, coarse bin reversal searching [3], coded beacon sequence in conjunction with a bank of correlators [4], the inherent cyclo-stationarity (CS) approach [5], transmitted reference (TR) approaches [6]. 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. In this paper, we use “Dirty Template” (DT) algorithms to provide timing synchronization [7]. Unlike exiting UWB timing synchronization techniques, the techniques described depends on searching a peak in the output of the correlation between the received signal and a dirty template, which is extracted from the received waveform. This template is called dirty, because it is distorted by the unknown channel; moreover, it is noisy and subjects to the unknown timing offset. As shown herein, the principal advantages of Timing with Dirty Template (TDT) can be summarized as follows: increased rich-multipath energy capture can be obtained even when the channel and the spreading codes are both unknown, resulting in improved Synchronization performance and enabling reduced receiver complexity [7]. The following Section II introduces the signal model and operating transceiver conditions. Section III describes a timing acquisition technique based on the original dirty template algorithms. Then it derives a modified timing method by depending on TH codes. The simulation results are discussed in Section IV and conclusions are drawn in Section V. Notation: ‫ہ‬ȉ‫ ۂ‬represents the floor operation; (A mod B) denotes the modulo operation, where A and B are both real. II.

SYSTEM MODEL

Consider an impulse radio UWB-IR system, where every symbol is transmitted over ܶ௦ period that consists of ܰ௙ pulses over ܰ௙ frames (one pulse per frame). Every frame of duration ܶ௙ contains ܰ௖ chips. The symbol waveform of duration ே೑ ିଵ ܶ௦ ǣ ൌ ܶ௙ ܰ௙ is ‫ ்݌‬ሺ‫ݐ‬ሻ ൌ σ௝ୀ଴ ‫݌‬ሺ‫ ݐ‬െ ݆ܶ௙ െ ܿ௝ ܶ௖ ሻ, where ‫݌‬ሺ‫ݐ‬ሻ is

978-1-4244-3709-2/10/$25.00 ©2010 IEEE

un ultra-short pulse, that has durationܶ௣ (‫ܶ ا‬௙ ), and ܶ௖ ǣ ൌ ܶ௙ Ȁܰ௖ is the chip duration with pseudo-random time-hopping (TH) codes ሼܿ௝ ሽ ‫ א‬ሾͲǡ ܰ௖ െ ͳሿ, ‫ א ݆׊‬ൣͲǡ ܰ௙ െ ͳ൧ (see Fig. 1). The symbol waveform has unit energy ሺ‫ ்݌ ׬‬ଶ ሺ‫ݐ‬ሻ݀‫ ݐ‬ൌ ͳሻ. By focusing on pulse amplitude modulation (PAM), where the information-bearing symbols ‫ݏ‬ሾ݇ሿ ‫ א‬ሼേͳሽ are modelled as binary independent and identically distributed with energy Ԫ௦ spread over ܰ௙ frames. The transmitted UWB waveform is then given by [7]: ஶ

‫ݑ‬ሺ‫ݐ‬ሻ ൌ ඥԪ௦ ෍ ‫ݏ‬ሾ݇ሿ‫ ்݌‬ሺ‫ ݐ‬െ ݇ܶ௦ ሻ Ǥሺͳሻ

TIMING ACQUISITION

III.

A. Signal Detection & Symbol Level Acquisition “find ݊௦ ” At the receiver, detecting the received signal ‫ݎ‬ሺ‫ݐ‬ሻ and identifying the symbol-level offset ݊௦ are achieved herein by using the DT data-aided timing acquisition algorithms. Supposing that we send ‫ܯ‬ଵ training symbols, which have the ெభ ିଵ same value ሼ‫ݏ‬ሾ݇ሿ ൌ ͳሽ௞ୀ଴ , they are thus received during [߬଴ ǡ ߬଴ ൅ ‫ܯ‬ଵ ܶ௦ ሿǤ The first step is to observe ܰሺ൐ ‫ܯ‬ଵ ሻ received waveform segments of duration ܶ௦ . Under mistiming (߬଴ ് Ͳ), the any ܶ௦ -long received segment of ‫ݎ‬ሺ‫ݐ‬ሻ can be represented by parts of two consecutive symbols, as bellow: ‫ݔ‬ሺ‫ ݐ‬൅ ݊ܶ௦ ሻ ൌ ‫ݓ‬ሺ‫ ݐ‬൅ ݊ܶ௦ ሻ

௞ୀ଴

The signal ‫ݑ‬ሺ‫ݐ‬ሻ propagates through a multipath channel, whose impulse response ݄ሺ‫ݐ‬ሻǣ ൌ σ௅ିଵ has ௟ୀ଴ ߙ௟ ߜሺ‫ ݐ‬െ ߬௟ ሻ coefficients ߙ௟ and delays ߬௟ , obeying ߬௟ ൏ ߬௟ାଵ .The timing offset ߬଴ refers to the first arrival time. To isolate ߬଴ , we define ߬௟ǡ଴ ؔ ߬௟ െ ߬଴ as the relative time delay of each channel tap, where ߬௅ିଵǡ଴ is channel delay spread. To avoid inter-symbol interference (ISI),୤ is selected to satisfy the following condition: ܶ௙ ൒ ቀܿே೑ ିଵ െ ܿ଴ ቁ ܶ௖ ൅ ߬௅ିଵǡ଴ ൅ ܶ௣ [2]. The received pulse within each frame is ‫݌‬௥ ሺ‫ݐ‬ሻǣ ൌ σ௅ିଵ ௟ୀ଴ ߙ௟ ‫݌‬ሺ‫ ݐ‬െ ߬௟ǡ଴ ሻ; The waveform in the output of the receiver antenna is:

൅൝

ඥԪ௦ ‫ݏ‬ሾ݊ െ ݊௦ െ ͳሿ‫݌‬ோ ൫‫ ݐ‬൅ ܶ௦ െ ݊௙ ܶ௙ െ ߳൯ǣ‫ א ݐ‬ൣͲǡ ݊௙ ܶ௙ ൅ ߳൯ሺͷሻ ඥԪ௦ ‫ݏ‬ሾ݊ െ ݊௦ ሿ‫݌‬ோ ൫‫ ݐ‬െ ݊௙ ܶ௙ െ ߳൯  ‫ א ݐ ׷‬ൣ݊௙ ܶ௙ ൅ ߳ǡ ܶ௦ ൯Ǥ

where ‫ݔ‬ሺ‫ݐ‬ሻ is the received segment of duration ܶ௦ . Next step is to achieve the cross-correlation between adjacent segments for generating ܴ௫ǡ௫ , as below: ்ೞ

ܴ௫ǡ௫ ሾ݊ሿ ൌ න ‫ݔ‬ሺ‫ ݐ‬൅ ݊ܶ௦ ሻ‫ݔ‬ሺ‫ ݐ‬൅ ሺ݊ ൅ ͳሻܶ௦ ሻ ݀‫ݐ‬ǡሺ͸ሻ ଴

்ೞ

ൌ ߱ ෕ሾ݊ሿ ൅ ‫ ܣ‬න ‫݌‬ோଶ ൫‫ ݐ‬൅ ܶ௦ െ ݊௙ ܶ௙ െ ߳൯ ݀‫ݐ‬





‫ݎ‬ሺ‫ݐ‬ሻ ൌ ඥԪ௦ ෍ ‫ݏ‬ሾ݇ሿ‫݌‬ோ ሺ‫ ݐ‬െ ݇ܶ௦ െ ߬଴ ሻ ൅ ‫ݓ‬ሺ‫ݐ‬ሻǡሺʹሻ

where ‫݌‬ோ ሺ‫ݐ‬ሻ is the received waveform of each symbol ே೑ ିଵ

௅ିଵ



ൌ ߱ ෕ሾ݊ሿ ൅ ‫ ܣ‬න

™Š‡”‡ǣ ൜

௟ୀ଴

and ‫ݓ‬ሺ‫ݐ‬ሻ represents zero-mean additive white Gaussian noise (AGWN). The timing offset ߬଴ could be represented by: ߬଴ ൌ ݊௦ ܶ௦ ൅ ݊௙ ܶ௙ ൅ ߳, where ݊௦ ൌ ‫߬ہ‬଴ Ȁܶ௦ ‫ ۂ‬൒ Ͳ denotes the symbol-level timing offset, ݊௙ ൌ උሺ߬଴ െ ݊௦ ܶ௦ ሻȀܶ௙ ඏ ‫א‬ ൣͲǡ ܰ௙ െ ͳ൧ the frame-level offset, and ߳ ൌ ൫߬଴ ݉‫ܶ݀݋‬௙ ൯ ‫א‬ ሾͲǡ ܶ௙ ሻ the pulse-level offset [2]. By substituting ߬଴ in (2), the received signal can be expressed by: ஶ

‫ݎ‬ሺ‫ݐ‬ሻ ൌ ඥԪ௦ ෍ ‫ݏ‬ሾ݇ሿ‫݌‬ோ ൫‫ ݐ‬െ ݇ܶ௦ െ ݊௦ ܶ௦ െ ݊௙ ܶ௙ െ ߳൯ ൅ ‫ݓ‬ሺ‫ݐ‬ሻǤሺͶሻ ௞ୀ଴

In the next section, we will present timing recovery structure, which can be decomposed into two subtasks: A) symbol-level acquisition “find ݊௦ ”; and B) fine synchronization “estimate݊௙ and ߳”.

்ೞ

்ೞ ି௡೑ ்೑ ିఢ

‫݌‬ோ ሺ‫ݐ‬ሻǣ ൌ ෍ ‫݌‬௥ ൫‫ ݐ‬െ ݆ܶ௙ െ ܿ௝ ܶ௖ ൯ ൌ ෍ ߙ௟ ‫ ்݌‬൫‫ ݐ‬െ ߬௟ǡ଴ ൯ ǡሺ͵ሻ ௝ୀ଴

்ೞ

൅ ‫ ܤ‬න ‫݌‬ோଶ ൫‫ ݐ‬െ ݊௙ ܶ௙ െ ߳൯ ݀‫ݐ‬ǡ

௞ୀ଴

‫݌‬ோଶ ሺ‫ݐ‬ሻ ݀‫ ݐ‬൅ ‫ ܤ‬න

்ೞ ି௡೑ ்೑ ିఢ



‫݌‬ோଶ ሺ‫ݐ‬ሻ ݀‫ݐ‬Ǥ

‫ ܣ‬ൌ Ԫ௦ ‫ݏ‬ሾ݊ െ ݊௦ െ ͳሿǤ ‫ݏ‬ሾ݊ െ ݊௦ ሿ ‫ ܤ‬ൌ Ԫ௦ ‫ݏ‬ሾ݊ െ ݊௦ ሿǤ ‫ݏ‬ሾ݊ െ ݊௦ ൅ ͳሿ

For simplify, TH spreading codes are not employed, the possible values of A and B are exhibited in Table 1. The sampled noise ߱ ෕ሾ݊ሿ is composed of three terms, two of them are the result of correlation between the symbol and the noise, and the third term is between shifted noises [7]. With the presence of ‫ܯ‬ଵ training symbols, the successive received symbols have the same values. In this case, by looking on the Table I and taking the corresponding value of ‫ ܣ‬and ‫ܤ‬, then substituting them in (6),ܴ௫ǡ௫ ሾ݊ሿ becomes ܴ௫ǡ௫ ሾ݊ሿ ൌ ் Ԫ௦ ‫׬‬଴ ೞ ܲோଶ ሺ‫ݐ‬ሻ  ൅ ߱ ෕ሾ݊ሿ. Therefore, the optimal ݊ො௦ can be estimated via a line search to maximize the objective function ‫ܬ‬ሺ݊‫ ݏ‬ሻ [2], as below: ݊ො௦ ൌ

݉ܽ‫ܬ ݔ‬ሺ݊௦ ሻǡ ݊௦ ‫א‬ሾͲǡǦ‫ ͳܯ‬ሿ ௡ೞ ାெభ ିଵ

ͳ ‫ܬ‬ሺ݊௦ ሻ ൌ ቌ ෍ ‫ ͳܯ‬െ ͳ



ܴ௫ǡ௫ ሾ݊ሿቍ Ǥሺ͹ሻ

௡ୀ௡ೞ

Figure 1. TH-UWB signal with PAM modulation, TH codes=[0, 1,0].

The presence of ‫ݎ‬ሺ‫ݐ‬ሻ in the receiver is declared when ‫ܬ‬ሺ݊ො௦ ሻ ൒ ߟ, where ߟ is a threshold set by the desired probability of false alarm (FA). We could see in (7) and (6) that, when we increase the size of training symbols (‫ܯ‬ଵ ሻ, that will help integrate the additive noise effects, and thus improve

synchronization performance but that comes at the price of reduced bandwidth and power efficiency. As a result, this method can be applied to a UWB receiver even in the presence of TH codes or Inter-Frame Interference (IFI), because the two dirty adjacent segments contain the same TH codes and IFI properties regardless of the unknown channel characters (e.g. unknown time offset), but in the condition of the absence of ISI. Moreover, this method exploits the rich multipath diversity provided by UWB channels, and doesn’t generate clean correlation template at the receiver. This reduces complexity with high detection accuracy. After signal detection and symbol-level offset estimation, the new time offset is confined within one symbol duration ߬଴ ൌ ݂݊ ݂ܶ െ ߳ ‫ א‬ሾͲǡ ܶ௦ ሻ. B. Fine Syncronization In this section, we will focus on estimating ߬଴ ൌ ݊௙ ܶ௙ െ ߳ based on dirty template algorithms in both data aided DA and non-data aided NDA modes. The original TDT method proposed in [2], is resumed by: In the absence of ISI, the estimation of time offset error (TOE) can be achieved for DA and NDA modes, depending on the cross-correlation between the pairs of successive received segments of duration ܶ௦ , as shown below: ಾమ మ ିଵ

ሺଶ௡ାଵሻ்ೞ

ʹ ߬Ƹ ଴ ൌ ܽ‫ݔܽ݉݃ݎ‬ ෍ ቌ න ‫ܯ‬ଶ ݉ ௡ୀ଴ ଶ௡்ೞ

‫ݔ‬ሺ‫ ݐ‬൅ ݉ο௧ ሻǤ ‫ݔ‬ሺ‫ ݐ‬൅ ܶ௦



൅ ݉ο௧ ሻ݀‫ݐ‬ቍ  ሺͺሻ where ‫ܯ‬ଶ is the size of the successive received segments, used for accomplishing the TDT operation, ݉ο௧ ‫ א‬ሾͲǡ ܶ௦ ሻ; ο௧ represents the size of the increment, and ݉ denotes the number of increments. Since the synchronization accuracy can be improved by reducing ο௧ (reducing in this turn, the error floor, which we describe in the simulations section), but in the price of fast estimation timing. Practically, in DA mode, the form of training symbols used for achieving fast acquisition is as follows: െͳǡ ‫ݏ‬ሾ݇ሿ ൌ ൜ ൅ͳǡ

݂݅ሺ݇‘†Ͷሻ ൌ Ͳǡ ‫ݎ݋‬ǡ ͳ ǣ ݇ ‫ א‬ሾͲǡ ‫ܯ‬ଶ െ ͳሿǤሺͻሻ ݂݅ሺ݇‘†Ͷሻ ൌ ʹǡ ‫ݎ݋‬ǡ ͵

We can explain TDT in (8) by another way, when we do the cross-correlation between signals with its sliding replica, we obtain the unique maximum point at ߬଴ ൌ Ͳ. The TDT use the same principle to achieve the synchronization. However, we may notice, in the UWB transmitted model, the presence of gaps among the received symbole and its dirty template. And these gaps may cause in (8) to exhibit multiple maxima points around its peak (optimal point), so the estimation error of the timing synchronization may increase [2]. To avoid this problem, we modify the structure of the cross-correlation operation by adding the suitable window filter. In this case, the timing estimation in (8) can be achieved, as follows:

TABLE I. ࢙ሾ࢑ െ ૚ሿ ࢙ሾ࢑ሿ ࢙ሾ࢑ ൅ ૚ሿ

࡭ ࡮

POSSIBLE VALUES OF ‫ ܣ‬AND ‫ ܤ‬IN (6)

+1 +1 -1

+1 -1 -1

-1 -1 +1

-1 +1 +1

+1 +1 +1

-1 -1 -1

+1 -1 +1

-1 +1 -1

൅Ԫ௦

െԪ௦

൅Ԫ௦

െԪ௦

൅Ԫ௦

൅Ԫ௦

െԪ௦

െԪ௦

െԪ௦

൅Ԫ௦

െԪ௦

൅Ԫ௦

൅Ԫ௦

൅Ԫ௦

െԪ௦

െԪ௦

ெమ Τଶିଵ

்ೞ ʹ ߬Ƹ ଴ ൌ  ܽ‫ݔܽ݉݃ݎ‬  ෍ ቆන ‫ݔ‬ሺ‫ ݐ‬൅ ʹ݊ܶ௦ ൅ ‫ݐ‬௦ ሻǤ ‫ݔ‬ሺ‫ ݐ‬൅ ሺʹ݊ ൅ ͳሻܶ௦ ‫ܯ‬ଶ ଴ ݉ ௡ୀ଴ ଶ

൅ ‫ݐ‬௦ ሻ Ǥ ܹሺ‫ݐ‬ሻ݀‫ݐ‬ቇ ሺͳͲሻ

where the window ܹሺ‫ݐ‬ሻ contains the information of spreading TH codes, as shown below: ே೑ ିଵ

ͳ‫ Ͳ݅ݏ‬൑ ‫ ݐ‬൑ ܶ௣ ൅ ߬‫ܮ‬െͳǡͲ ሺͳͳሻ ܹሺ‫ݐ‬ሻ ൌ ෍ ܿ௝ ‫݌‬൫‫ ݐ‬െ ݆ܶ௙ ൯ Ǣ ‫݌‬ሺ‫ݐ‬ሻ ൌ ൜ Ͳ‫݁ݏ݅ݓݎ݄݁ݐ݋‬Ǥ ௝ୀ଴

As the time of channel delay spread ߬௅ିଵǡ଴ is unknown. So we suppose that, the window wide is approximately equal to ܶ௖ . This suggestion may reduce the energy capture from the cross-correlation, and without any impact on the estimation accuracy. In other word, the cross-correlation between the window ܹሺ‫ݐ‬ሻ and the sliding product of the successive symbol-long received segments reaches its maximum if and only if these received segments are scaled versions of each other, which is achieved uniquely at the correct timing ݉ο௧ ൎ ߬Ͳ , and this maximum point is unique. In particular, the window ܹሺ‫ݐ‬ሻ simplifies the implementation of timing operation, because we don’t need to take all sampled points of the symbol to calculate the cross-correlation, the sample points inside the windows are sufficient. Moreover, this method can reduce multiple users interference MUI, by using orthogonal TH codes for the different users. IV.

SIMULATIONS

In this section, we will evaluate the performance of the proposed dirty template synchronizer with simulations. We select the pulse ‫݌‬ሺ‫ݐ‬ሻ as the third derivative of the Gaussian function with unit energy and duration ܶ௣ ൎ ͳns. Each symbol contains ܰ௙ ൌ ͵Ͳ frames, each with duration ܶ௙ ൌ ͳͲͲns. The simulations are performed in a Saleh-Valenzuela channel [9]. The parameters of this channel are chosen with (1/೷, 1/Ȝ, ī, Ȗ) = (2, 0.5, 30, 5) ns. The maximum channel delay spread of the channel is about 99ns.We compare the performance of the dirty template synchronizer between NDA and DA modes. In all simulations, the fine timing level is performed, we supposed that signal detection has been carried out and that ݊௦ has been identified successfully. We generate ɒ଴ randomly from a uniform distribution over ሾͲǡ ܶ௦ ሻ. We employ TH spreading codes of period ܰ௙ , which is generated from a uniform distribution over ሾͲǡ ܰ௖ െ ͳሿ, with ܰ௖ ൌ ͻ, and ܶ௖ ൌ ͳͲns.

Figure 2. Normalized MSE vs. SNR per pulse for data aided TDT

Figure 3. Normalized MSE vs. SNR per pulse for non-data aided TDT

Fig. 2 and Fig.3 show the comparison of mean square error (MSE) performance of DA and NDA modes with dirty templates for various values of ‫ܯ‬ଶ . In these figures, the MSE results are normalized by ܶ௦ ଶ , and plotted versus the signal-tonoise ratio (SNR) per pulse. The simulations confirm that, the DA mode has high MSE performance, and it could be used with small training pattern size such as ‫ܯ‬ଶ ൌ Ͷ, that helps to reduce the number of operations performed at the receiver as well as the synchronization time. Where the NDA technique requires ‫ܯ‬ଶ ൌ ͳ͸ to operate. On the other side, NDA provides a more efficient use of bandwidth. In general, as ‫ܯ‬ଶ increases the normalized MSE decreases. Increasing SNR also helps to reduce the MSE. In Fig. 2, 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 (ο୲ ) or by applying a tracking phase.

without time-hopping (TH), where inter-symbol interference (ISI) is absent.

V.

CONCLUSION

In this paper, we present a dirty template algorithms used for achieving rapid, accurate and low-complexity timing acquisition, which constitutes a major challenge in enabling the unique benefits of UWB transmissions. Timing synchronization with DT technique relies on searching a peak in the output of the correlation between the received signal and a dirty template. In addition, we develop the fine synchronization level. In the original TDT algorithm, we may find 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 filter. This window contains information of the TH codes. This modified approach guarantees that we obtain a single maximal peak at the outside of the estimator and that improve the estimation error performance. Both the theoretical analysis and simulation results show the estimation performances of DA and NDA modes of the proposed DT method, and confirm that for the same size of correlation sequence pattern, the DA mode has the high performance and fast timing, compared to NDA mode, but that is in the price of the bandwidth efficiency. In particular, the described technique can be applied to UWB systems with or

In the future research, we plan to develop fine tracking algorithms, using an Adaptive Early-Late locked loop [10][11][12]. REFERENCES [1]

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