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This paper studies a new positioning beacon for railway transport using Ultra Wideband (UWB) radio and Time Reversal (TR) techniques. UWB radio has the potential to offer a good level of performance in terms of localization accuracy. Time Reversal channel pre-filtering facilitates signal detection and also helps increasing the received energy in the targeted area. In this paper, we evaluate the characteristics of TR technique in terms of temporal focusing. The theoretical and simulation results for Power Delay Profile, equivalent channel model and focusing gain of TR-UWB are given. We analyze the contribution of Time Reversal associated with UWB technology to enhance the localization resolution. The IEEE 802.15.3achannel models are used to evaluate the performance of this system. In terms of localization error, the theoretical and simulation results show that TR-UWB technique delivers improved performance over the UWB localization approach.

Guided urban automated transportation systems are progressing significantly nowadays, highlighting many benefits. User’s security and accessibility to these guided transport systems constitute a major issue dealt with many teams. In order to obtain an efficient and safe control and command system of the trains, it is essential to ensure an adequate exchange of information between vehicles and infrastructure and to determine accurately and constantly the absolute localization of the train.

The track to train data exchange is usually called CBTC for Communication Based Train Control. It can use many different radio techniques [

In this paper, we propose a new solution allows to increase the positioning performances in terms of localization errors and to reduce the cost of track maintenance operations, thus constituting a new beacon realization. This new solution is based on the Ultra Wideband ImpulseRadio technology (UWB-IR) associated to the Time Reversal (TR) technique.

Otherwise, the combination of these techniques could be applied in various areas of the localization, such as the detection and localization of persons-through barriers or to find victims of accidents, especially in the mountains or in mines [

In this context, the proposed association between UWB and TR techniques for the precise localization of trains is illustrated in

This study evaluates the temporal focusing performance of the time reversal (TR) method using the IEEE 802.15.3a channel models. For these evaluations, theoretical and simulation methods are used. Since the railway localization problem can be considered as a one dimension (1D) problem, we analyse the contribution of TR on the quality of localization in 1D.

This work also aims to verify whether the combination of UWB and TR techniques allows obtaining the decimetre required localization level of precision necessary to the railway application.

This paper is organized as follows: the second part presents the UWB and TR techniques. The third part presents the propagation channel modeling using the IEEE 802.15.3a channel models. The fourth section provides the analytical results of the TR-UWB system in terms of temporal focusing including focusing gain and Power Delay Profiles. The fifth section provides a comparative study between analytical and simulation results of the TR-UWB system in terms of temporal focusing. The sixth section presents the principle of TR-UWB localization

and the performance of the proposed solution in terms of localization error. Finally, the conclusion summarizes the results and suggests future work.

UWB radio is typically defined as a wireless transmission scheme with a bandwidth over 500 MHz, or occupying 20% or more of the carrier frequency. There are different UWB approaches. In our study, we use an Impulse Radio UWB-IR system. This model involves the transmission of very short pulses occupying a very wide spectrum (

A direct benefit of UWB concerns the use of low-cost, small size radio interface circuits [

UWB radio technology also offers some potential for railway applications [

● It provides potentially high transmission data-rate, using a very large bandwidth;

● It offers high resolution train location because of the fine temporal resolution of the transmitted pulses;

● It adds ability to detect obstacles (radar) due to the impulsive nature of the signals. This capability is essential to detect obstacles in front of the train;

● Availability and robustness to multi-path are inherent to the large frequency bandwidth.

Localization in indoor environments such as tunnels is the subject of two major sources of error, the first being the lack of line of sight between the transmitter and the receiver and the second being the excessive presence of multipath. With the introduction of UWB in wireless communications, it seemed that this technology can provide improvements. However the studies have also raised some major problems like the complexity of the signal processing at the reception. Acquisition of UWB signals is critical, and its fundamental limits [7,8].

In order to solve all the problems facing the UWB, several studies have been conducted associating UWB and time reversal technique [

Classically, Time Reversal has been applied to acoustics and underwater systems [10,11]. It is closely related to retro-directive array in microwave [12,13] and phase conjugation in optics. More recently, it has also been studied for broadband especially for UWB communications [

We propose to use the properties of time reversal [

The principle of the proposed TR-UWB system uses three steps. Firstly, we select the signal we want to transmit. In our case, it is the second derivative of the Gaussian function; it is an ultra short pulse. Secondly, the channel impulse response is measured between the transmitter (Tx) and the receiver (Rx) and the channel state information is loaded into Tx. Thirdly, the selected signal and the impulse response are reversed in time and transmitted by Tx in the propagation channel, up to Rx. This TR-UWB principle, represented in _{rt}(t), the received signal with TR at the receiver. Their expressions are given by:

where represents the convolution operation and n(t) is the Gaussian noise.

From Equation (2), we deduce the equivalent impulse response heq(t) which corresponds to the autocorrelation function of the channel [

The autocorrelation function is used to evaluate two main characteristics associated to time reversal, i.e., the temporal focusing and the spatial focusing. These characteristics are very beneficial to the UWB system [17, 18]. To study the temporal focusing, we evaluate the Focusing Gain (FG), which is defined as the ratio of the strongest peak in TR received to the strongest peak received by a conventional UWB system [

Higher FG could potentially translate into higher communication range and higher precision of localization for a localization system as compared to a classical UWB system.

In this part, we describe the IEEE 802.15.3a channel model. The objective of using this channel model is to characterize the channel impulse response [20,21]. The time reversal would benefit from the complexity of the propagation environment. If the environment is increasingly complex, best will be the focus of energy [

The IEEE 802.15.3a model was developed from around 10 contributions, all referring to distinct experimental measurements, performed in indoor residential or office environments [23,24].

In order to reflect the phenomenon of ray clustering that was observed in several measurement campaigns, the model is based on the Saleh-Valenzuela formalism. Parameters are provided to characterize the clusters and ray arrival rates (Λ and λ), as well as the interand intraluster exponential decay constants (Г and γ). Four sets of parameters are provided to model the four following channel types:

● The channel model CM 1 corresponds to a distance of 0 - 4 m in a LOS situation;

● The channel model CM 2 corresponds to a distance of 0 - 4 m in an NLOS situation;

● The channel model CM 3 corresponds to a distance of 4 - 10 m in an NLOS situation;

● The channel model CM 4 corresponds to an NLOS situation with a large delay spread τ_{rms} = 25 ns.

For our study we use the three first scenarios CM1, CM2 and CM3. CM4, generated to fit a large 25-ns RMS delay spread was considered not relevant to our application. Some important characteristics of these scenarios based upon a 167-ps sampling time are shown in

This comprehensive model is a reference for the study of UWB systems. It can be applied in indoor environments and short range conditions. We use these models for performance evaluation in terms of temporal focusing and error localization.

In this section, we develop an analytical study of the temporal focusing of time reversal. The study of the temporal focusing is based on the characterization of the propagation channel. For each considered channel model (CM1, CM2, CM3), we determine the equivalent impulse response, the Power Delay Profile and Focusing Gain.

Throughout the study, we denote by:

- s(t): transmitted pulse (derivative Gaussian pulse);

- h(t): Channel Impulse Response CIR;

- h*(–t): conjugated and reversed CIR.

The analytical study in the case of the IEEE 802.15.3a model is done using the statistical moments of interferences that affect the performance of a TR-UWB receiver [

For this channel model, we can define CIR by:

The expected value of the equivalent CIR is: [

Using the Auto-Correlation Function (ACF) for prototype pulse defined by Equation (7):

The Equation (6) becomes:

Computing the average energy of the CIR in a generic time window given:

where is the random set of multipath components within W and referred to Average Power Delay Profile (APDP).

A continuous-time in W is given by a variance of the CIR energy function [

where is the kurtosis delay profile.

Using the equivalence (9) in (8), we obtain:

We observe, for therefore

.

The Average Power Delay Profile P_{g}(t) is described by a model with exponential decay which is characterized by the average received energy E_{g} and the rms delay spread τ_{rms} of the channel.

For determining R_{g}(t) we choose a uniform Poisson arrival process with an arrival rate of ray/s and Nakagami m distributed ray amplitude a simplified version of the Saleh-Valenzuela channel model is [

In this case the Power Delay Profile for the equivalent CIR is given by:

It becomes:

(15)

The equivalences (11a) and (15) are developed in Appendix, and their final expressions are given by the Equations (11b) and (16):

The focusing gain presented in (4) can be written in this case as:

with

The correlation function peak is located at zero time shift, therefore:

where

Then, (17) becomes:

In this section, we compare the simulation and the analytical results in UWB and TR-UWB cases using IEEE 802.15.3a channel models. Thereafter, we study the contribution of Time Reversal in UWB in terms of temporal focusing.

Tables 2 gives general input parameters for analytical and simulation steps.

We performed a comparative study of the m value appearing in the Nakagami distribution and we considered the four following cases [

m = 0.5: corresponding to a Gaussian situation;

m = 1: is the Rayleigh law, i.e. deep fading;

m = 1.5: corresponding to a severe fading;

m = 4: corresponding to a low fading.

This study showed that the value of m has a negligible impact on system performance TR-UWB. We agreed to choose the value m = 1.5 in the remainder of our studies.

Figures 6(a)-(f) show analytical and simulation results for TR-UWB system, in case of IEEE 802.15.3a channel models. The average over 1000 runs of channels is performed for each channel model (CM1, CM2 and CM3). These results correspond to the equivalent channel impulse response and Power Delay Profile for transmitted a second Gaussian derivative pulse. We can observe then, the simulation results are close to analytical results.

By expanding by simulation the study interval, we can now compare PDP-UWB and PDP-TR-UWB for the 3 considered channel models. Figures 7-9 provide a comparison between PDP_{UWB} and PDP_{TR-UWB}. Considering PDP_{TR}, we obtain a very effective temporal focusing as well as an increase of the amplitude of the power over PDP_{UWB} alone. This translates into the values of FG presented in

From CM1 to CM3 FG increases, due in particular to the stronger multipath. Indeed, TR takes advantage of the complexity of the channel.

This would be very beneficial for the purpose of locating in confined environments such as tunnels.

In this section, we carry on this study by evaluating the localization error. We still consider the two preceding UWB alone and TR-UWB techniques. The goal is to estimate the contribution of TR to the location in terms of localization error, as a function of the propagation environment position of a mobile in a 2D plane. To locate the mobile, each base station sends its own signal (recorded and reversed in time in the case of TR). The UWB signals are modulated by an antipodal modulation and coded by a Gold code [29,30], one code per base station. Processing is performed at the mobile (R_{x}) to determine its position relative to the base stations. The localization error is given by the difference between the calculated position and the actual position of the mobile.

The mobile receives the signals from each base station and performs an adequate signal processing to determine its position, relative to the base stations. Using the TDOA technique, the signal received at the mobile is processed to retrieve the position of the latter [_{1}, S_{2} and S_{3} represent the three base stations of known coordinates, M is the mobile to be located. The difference distance between mobile and the i^{th} base station is given by Equation (32):

where, (x, y) are the unknown coordinates of mobile position, (X_{i}, Y_{i}) are the coordinates of the base stations. Considering as a reference station S_{1} (the reference station is the nearest station of the mobile, in the studied case), the difference distance between reference station S_{1} and other stations is given by:

(23)

where, c is the celerity of light, d_{i}_{,1} is the TDOA estimate between reference station and the i^{th} station.^{ }Calculating the differences in distance allows us to define a system of nonlinear equation of hyperbolas (Equation (24)), resolvable by Chan’s method [

For a three base station system, Chan’s method produces two TDOA to determine the coordinates (x, y) of mobile:

(25)

where:

Our comparison is based on the computation of the Root Mean Square Error of localization between the conventional UWB system and the proposed TR-UWB system. An Additive White Gaussian Noise (AWGN) is also injected in the CM1, CM2 and CM3 models. A large number of iterations are used (1000 iterations).

whereas it is only 1.12 cm for TR-UWB system. This remark also applies to CM1 and CM2.

Different SNR versus were also tested.

In this contribution, we presented results obtained working on the association of time reversal and UWB impulse radio for a localization application. The IEEE 802.15.3a channel models are used to perform these studies. The analytical and simulation results have shown that this particular combination can reduce the error localization thanks to the focusing characteristics of time reversal. In future work, we will study different waveforms and modulation types to identify the most appropriate ones. This study will also be conducted with other channel models as well as different single transmitter and multiple transmitter configurations. To validate the analytical and simulation results, experimentations will be soon conducted in an anechoic chamber and a real environment.

This appendix computes the equivalence (18) that is given by:

(26)

Substituting and expanding all the products. We obtain by noticing that

:

This equation is then composed of three terms named I, II and III:

Knowing that:

Then (28) becomes:

Using the property the second term II becomes:

By following the change of variable: we get:

and

According to [

Therefore, referring to (4), (31) becomes:

where

It also defines that: is the autocorrelation energy of pulse, then II becomes:

The third tem III gives:

Also, arguing with the short support of, we can approximate the inner integral by

Where is the pulse auto-correlation function and is a normalized time-compressed auto-correlation function of, (). Therefore III can be written as:

Using this development, (27) becomes:

Substituting (12) and (13) in (11a) and (15) for observation interval we obtain: