Synchronization, TOA and Position Estimation - IEEE Xplore

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Paul Cheong, Alberto Rabbachin, Jean-Philippe Montillet, Kegen Yu and Ian Oppermann. Centrefor ... Direct method (DM) and Davidon-Fletcher-Powell.
Synchronization, TOA

and

for Low-complexity

Position Estimation

LDR UWB

Devices

Paul Cheong, Alberto Rabbachin, Jean-Philippe Montillet, Kegen Yu and Ian Oppermann Centre for Wireless Communications, University of Oulu, Finland. paul. cheonggee. oulufi Various position estimation algorithms exist and are categorized into iterative and non-iterative. The selection of algorithm depends partly on the computational budget per tag and the accuracy requirement. The accuracy of the position estimation in turn depends on the number and quality of the TOA estimates, which can be utilized in the calculation for a given node. Our analysis in this paper will focus on a lower complexity, non-iterative technique, direct method (DM) [9][10], and a higher complexity iterative technique, Davidon-Fletcher-Powell (DFP) [9]-[12]. These techniques are implemented in a centralized network with fixed access nodes. The paper is structured as follow: Section II gives a description of the synchronization process, section III describes the TOA estimation process, section IV briefly defines the two position estimation algorithms, section V provides the results for TOA and position estimation and finally the conclusion is given in section VI.

Abstract- The paper provides an evaluation of a noncoherent tWB system, which is suitable for low complexity, cost and data rate tWB wireless sensor networks with positioning capability. Synchronization and time of arrival (TOA) estimation is performed using a non-coherent energy collection method. Coarse and fine synchronization are performed to identify the energy clusters and refine the energy collection window respectively. The effect of the integration window size is evaluated for both TOA estimation and position estimation. Direct method (DM) and Davidon-Fletcher-Powell (DFP) algorithms are implemented for position estimation. The result shows the possibility of attaining sub-meter performance using a low complexity and cost device.

I. INTRODUCTION

T here are various methods of synchronization in the context of UWB systems. Wireless communication devices need to be synchronized to be able to communicate. The process of synchronization between two or more wireless communication devices is therefore an essential and important procedure to ensure a reliable signal acquisition and link. In the context of IR-UWB system, much emphasis has to be put on the issue of synchronization due to the time sensitive nature of UWB pulse. In order to keep the complexity and cost low, we concentrate our efforts on noncoherent receivers. Time of arrival (TOA) estimation is together with received signal strength intensity (RSSI) and angle of arrival estimation (AOA), among the most common position sensing techniques. TOA estimation gives to the receiver the estimation of the delay of the signal due to the propagation. This delay defines the distance between the transmitter and the receiver. TOA estimation technique seems to be the most capable to exploit the high time resolution, given by the large bandwidth of UWB signal. TOA estimation is usually performed by a cross-correlation procedure that correlates the received signal with a local generated replica of the received signal. The very short impulse duration and the distorted received waveform make correlation receiver difficult and costly to implement. Especially for UWB wireless sensor networks, a non-coherent receiver solution such as transmitted reference and energy collection seem to be more appealing than coherent solution. Non-coherent receivers such as energy collection [3]-[5] and transmitted reference [6]-[8] have been recently proposed for low complexity and low cost UWB solutions.

II. SYNCHRONIZATION

Synchronization can be divided into a few different phases, such as receiver synchronization, clock tracking, etc. In the context of IR-UWB system, much emphasis has to be put on the issue of synchronization due to the time sensitive nature of UWB pulse. These pulses are placed in different precise location to convey different information and therefore are time crucial. A system based on non-coherent receiver is defined as a system where the signal phase (in the case of IR-UWB, this reduces to the polarity of the signal) is not necessary for demodulation. That means that non-coherent systems cannot handle any form of Phase Shift Keying (PSK) modulation. Energy

Detection Module \ WA

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Fig. 1. Block diagram of a non-coherent receiver based on energy detection module.

At the receiving end of the UWB communication system, the receiver synchronization process determines the optimal position in time, where the RF front-end should be placed. In the case of non-coherent systems, the receiver is based on energy detection. The synchronization process will also determine where the fingers of the rake shall be placed, to ensure optimum energy collection. 480

Synchronization is also important for ranging where delay estimation is done. The precision of the synchronization of the first path will enable a more accurate delay estimation. This synchronization proposal will address receiver synchronization for both data and ranging scenarios. The receiver synchronization process can be divided into two sub-processes: 1) Coarse Synchronization is implemented to obtain the estimated position or area of the energy clusters of the received signal without knowing the position of the peak of the particular cluster. This is done by placing series of integration windows within the pulse repetition period (PRP). The energy collected by the window will be compared with a threshold and windows with energy greater than the threshold will be further synchronized with the next sub-process of fine synchronization. 2) Fine Synchronization is implemented to the integration windows selected during the coarse synchronization process. The objective of this sub-process is to locate the peak energy and enable maximum energy collection for the particular integration window.

smaller window size and better resolution. The window size can simply be changed by adjusting the trigger edges of the clock. The window size of the N integration windows are identical and Wc = SIN. Energy will be collected by the N integration windows within the sampling frame. These collected energy will be compared with a threshold which will be determined by the overall energy collected throughout the sampling frame, S, which in this case is the PRP. Fig. 3 illustrates an example of the selection of integration windows among the series of N integration windows.

A. Basic Assumptions The modulation techniques featured in our case are either OOK or PPM. No Time-hopping is implemented in any case. The preamble used for synchronization has to be designed to ensure that there is a pulse in each PRP. Particularly in the case where OOK is used but on the other hand, if the preamble consists of only ones, it can cause spectral lines, which is undesirable. The clock is assumed to be perfectly synchronized between the transmitter and the receiver and that there is no clock drift between the clocks of both devices. This can also be relaxed if admitted that this synchronization is repeated often. The PRP is known and fixed for all scenarios. Due to hardware constraints, the number of integration windows is fixed at N but the size of the integration windows may vary. The sampling frame, S, consists of N number of integration windows of size W. The size of the sampling frame Ts should be equal to the PRP. The number of selected integration windows is limited to a value, K. The value of K is to be determined in the future, where it could affect the robustness of the process to interference. In the ranging case, the first cluster of energy is assumed to contain the first path.

The selection process will identify the integration windows with energy above the threshold and select these windows for fine synchronization. ENS > EThreshold where NS is the selected integration window, ENS is the energy collected in NS, and EThreshold is the determined energy threshold for cluster detection.

B. Coarse Synchronization Coarse synchronization is the detection of energy cluster in a received signal by means of placing a series of N integration windows with a window size of Wc. Fig. 2 illustrates the concept of coarse synchronization with Ts = PRP and Ts = N x WC, N integration windows and window size Wc. Wc is dependent on the number of integration window, N, and the sampling frame size, Ts. The number of integration window, N is fixed. The reason behind this is that if the number of integration windows is made variable, it will incur an increase in hardware complexity. Therefore, to fully utilize the available hardware resources, the window size is made variable so that these integrators can be used for data energy collection and ranging purposes by placing these N integrators into these coarse synchronization window, with 481

PRP

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Ts= N X Wr

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Fig. 2. Coarse Synchronization with N integration windows of window size, Wc

PRP

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( Energy > Threshold)

Fig. 3. An example of the selection of integration windows for coarse synchronization in the presence of a cluster channel

These windows will be positioned where the energy clusters are located. Noise in the signal will affect the determination of the threshold and therefore some form of noise estimation will improve the performance of the cluster detection. The threshold has to be carefully analyzed to reduce the number of false detections and missed detections. As mentioned previously, the number of clusters (integration windows) selected should be limited to K. In the case where adjacent integration windows are above the threshold and selected, these integration windows will be combined and regarded as a single integration window as it will most probably belong to the same energy cluster (cluster 1) as illustrated in Fig. 3. The next process will be to perform fine synchronization of these windows, to enable the optimum collection of energy. For data retrieval, the main objective is to retrieve as much energy as possible from the clusters (integration windows), however, in the case of ranging, only the first cluster will be used for delay estimation. There are a few options on MAC allocation to enable synchronization for

data retrieval purpose and for ranging purpose. Nevertheless, the concept of coarse synchronization remains identical regardless of the purpose. C. Fine Synchronization The method proposed in this section can be used for fine synchronization as well as for ranging. The differences between using this concept for synchronization and ranging are as follow: * Ranging only require the knowledge of the first cluster, which is assumed to contain the first path required for delay estimation. * Synchronization requires the knowledge of as many clusters as possible, as maximum energy collection is preferred. Fine synchronization is performed by placing N windows within the coarsely synchronized windows. The process will refine the search for the starting point of the cluster. The hardware constraint affecting the synchronization accuracy and performance of this approach is the integration window size, which is dependent on the number of windows used as well as the clock resolution. Ranging and fine synchronization can be implemented at the same time, reducing the processing time. The explanation of this approach will be based on ranging but the concept can simply be implemented in the case of synchronization. III. TOA ESTIMATION

The main objective of ranging is to perform delay estimation of the first path. This process will be done after the coarse synchronization process. Coarse synchronization, as described previously, selects K number of windows, which represents the energy clusters. For ranging purpose, only the first cluster is essential where the assumed first path is located.

synchronization, which contributes to a synchronization error region of e,. This error region can also be interpreted into scenarios where only coarse synchronization is done. The energy collected by each integration window will be compared with a threshold, EdThre,hold, and the window with energy above the threshold (ENd> EdThreshold) will be selected as illustrated in Fig. 5(b). ENd is the energy collected in window Nd. The selected integration window will be declared the first path of the signal and will be used for delay estimation.

I ~

~~~~~~ Assumed First path

(Estimated TOA)

WC= NX W,

(a)

(b)

Fig. 5. (a) Fine Synchronization sub-process using N integration windows (b) Delay estimation by selecting the first window with energy greater than the threshold.

The precision of the delay estimation for ranging is dependent on the size and the number of integration windows and the degree of precision will affect the estimation of the time of arrival which will determine the accuracy of ranging and in turn affect the position estimation accuracy. 1217 1217 VV dI tdela 2r tdaVVd I

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IV. POSITION ESTIMATION

PRP

\Selected Integration \window for Delay Est. (Energy1 > Threshold & Energy 1 > Energy 2 & assumed first path)

Fig. 4. Coarse Synchronization for ranging purpose

Fig. 4 illustrates the integration window with the first energy cluster used for delay estimation. The integration window is selected on conditions that the energy collected is above the threshold and is larger than that of the other integration windows. The selected integration window will then proceed to the fine synchronization. Delay estimation is done with the same set of integrators that are used in the synchronization process. This will therefore reduce the need to incur further hardware complexity. The integration window with window size Wc is further sub-divided into N windows of size Wd as illustrated in Fig. 5(a). The ranging process is done with the assumption that the first path is in the first cluster. There will be imperfect

482

Two algorithms are emphasized in this section for the position estimation within a centralized network, where reference points are available in the form of base stations and fixed access nodes. One of the algorithms is the direct method (DM) [9]-[10], which directly solves a set of simultaneous equations based on the TOA/TDOA measurements. Therefore, exact solutions can be obtained for 2-D positioning with two fixed nodes using two TOA measurements (with known transmit time) or with three fixed nodes using three TDOA measurements. For 3-D positioning, four fixed nodes are needed to obtain exact solutions using TDOA measurements. This method has the lowest complexity compared to other algorithms and thus it is well suited for the scenarios where very low complexity is required. The other algorithm is the optimization-based quasi-Newton Davidon-Fletcher-Powell (DFP) algorithm [9]-[12], which is an iterative method. Since it is iterative and needs to determine the search direction during each iterate, this algorithm has much higher complexity compared to the non-iterative algorithms including the direct method. The position calculation processes for the two algorithms are briefly described in the flowcharts (Fig. 6). It is assumed that the positions of the anchor nodes are known and the anchor nodes are perfectly synchronized. The positions of sensor nodes of interest are to be estimated.

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Fig. 7. TOA error Distribution (5ns 20 integrators (a) without and (b) with peak method)

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Fig. 6. Flowcharts for position estimation algorithms (a) Direct Method and (b) DFP V. SIMULATIONS

A. TOA Estimation The TOA estimation is done after symbol synchronization is performed, which provides a time reference that is in the range of ±Tacc, around the effective starting point of the data bit Tb. The time window where the TOA search is implemented is defined as 2 Ta,c When TOA estimation is performed, a random point in the time window (2 x Tac - Tb) and Tb is taken. Starting from this point, the region defined by 2 Ta,c, is divided into N integration windows where the energy is obtained. In each Access node, the TOA estimation is performed considering different channel realization. The simulations are done utilizing the Saleh Valenzuela Channel Model 1 (CM1) as defined in IEEE 802.15.3a. A LOS channel model always has a path corresponding to the shortest arrival time of the pulse but the first path is not always the strongest one. Two different approaches have been considered in TOA estimation. In the first approach, the TOA estimation is based on a probability of false alarm threshold. This is defined as the probability to estimate the TOA on a point characterized by the presence of noise only. The first integrator output that overcomes the threshold is used for TOA estimation. This approach has a major drawback that setting the threshold too high to avoid false alarm will in turn lead to an increased probability of failure to detect the signal. For this reason, a Pfa=O.1 has been chosen, which means that several false alarm situations will occur and therefore severely effecting the TOA estimation as well as the positioning result. 483

In the second approach, the TOA is estimated by taking the peak value between the integrator outputs. Fig. 7(a) and Fig. 7(b) illustrate the distribution of the TOA error while performing TOA estimation with and without peak detection. (a)

(b)

Fig. 8. TOA error distribution (a) TaCc 10 ns, N= 10 integrators (b) TaCc 10 ns, N= 20 integrators

The second approach strongly reduces the false alarm but increases the probability of a positive TOA error due to the channel characteristics. Therefore, this approach is chosen and performed for the algorithms performance simulations

due to the above-mentioned reasons. The use of 10 or 20 integrators performed leads to a small TOA error. Fig. 8(a) and Fig. 8(b) illustrate the distribution for both cases and by simple observation, the distributions are similar. B. Position Estimation Position estimation was performed using two position calculation algorithms: Direct Method (DM) and DavidonFletcher-Powell (DFP). The results from the TOA estimation are used for position estimation evaluation. Two different integration window sizes were evaluated: iOns with 10 integration windows (1.Ons) and 5ns with 10 integration windows (0.5ns). The position estimation results are illustrated in Fig. 9 and Fig. 10. We observed that by reducing the integration window size, the performance improves for both DM and DFP. The DFP evaluated here is for a single iteration and it shows that DM performs better in this case. The increase in the number of base stations (BS) from 4 to 5 also improves the positioning performance. An accuracy of