Estimators of the indoor channel for GPS-based pseudolite signal

Alexandru Rusu- Casandra, Ion Marghescu Faculty of Electronics, Telecomm. and Information Tech.

University Politehnica of Bucharest Bucharest, Romania

rusu.alex[at]yahoo[dot]com, marion[at]comm.pub[dot]ro

Elena Simona Lohan Department of Comm. Eng.

Tampere University of Technology Tampere, Finland

elena-simona.lohan[at]tut[dot]fi

Abstract— Satellite-based positioning is nowadays experiencing an exponential growth of the consumer segment demand and the Global Positioning System (GPS) is the main provider of this service. While GPS performs very well in outdoor conditions, many people still cannot be located when they are in indoor environment. The characteristics of the indoor propagation are still not well understood and the question whether the GPS signals are good enough for indoor positioning is still open. One of the challenges related to indoor positioning is to find suitable statistical models of the indoor propagation that give further insight on multipath behavior and fading distributions. The main limitations of the GPS use indoors are the low signal power and the presence of multipaths, which may affect significantly the signal acquisition and tracking accuracy. Indoors, there is also a high likelihood of non-line of sight signal propagation (i.e. when no line of sight signal is available, due to various obstructions in the propagation wave). The indoor signals are also likely to be much weaker than the outdoor signals, due to the propagation through building materials. In numerous situations, it is presumed that with the installation of pseudolites, indoor navigation can prove better performance. In this paper we analyze the indoor channel propagation using GPS pseudolites, based on the measurement data collected in measurement scenarios.

Keywords- Global Positioning System (GPS); indoor propagation channel; multipath; pseudolites.

I. INTRODUCTION The GPS constellation consists of nominally 24 satellites

(currently 32 satellites are operational). The requirements set by various communications authorities from the European Union and the United States of America, concerning the location information provided with an emergency call made from mobile phones, heightened the interest of the researchers for the development of better wireless positioning systems, especially in indoor environments. Pseudolites (i.e., pseudo-satellites), placed on Earth's surface, especially indoors, are a relatively new technology with great potential for a wide range of positioning and navigation applications. They can be used either as augmentation of space-based positioning systems or as independent systems for indoor positioning, capable of showing better performance [1]. That is why the pseudolite-to-indoor propagation and its fading statistics have also great importance. There are several studies that attempted to develop channel models for GPS-indoor channel, such as [2] and [3].

This paper deals with the complex issue of indoor propagation channel characterization in multipath and low CNR environment. The article presents an analysis of experimental data for the GPS-based-pseudolite channel, obtained in indoor measurement campaigns carried out at the Tampere University of Technology (TUT) in cooperation with some industrial partners. The aim of the paper is to analyze the indoor signal fading characteristics and to give further insight on the real indoor-to-indoor pseudolite signal propagation. We have focused our research on the GPS Coarse Acquisition (C/A) signal because it is the most used civilian navigation signal.

The outline of this paper is explained next. In Section II, the experimental settings and measurement environments are described. Data processing and analysis is described in Section III. In Section IV several probability distribution functions regarding the channel parameters are compared against known theoretical distributions. Section V gives the conclusions.

II. DESCRIPTION OF THE MEASUREMENT CAMPAIGNS Several indoor GPS pseudolite measurement campaigns

were carried out at TUT by the Signal Processing for Wireless Positioning Group in cooperation with some industrial partners in 2005 and 2009. The equipment used in the measurement campaign consists of:

• a Space Systems Finland C/A signal transmitter (the pseudo-satellite or pseudolite), which produces GPS signal with the same characteristics as that emitted by a GPS satellite (carrier, PRN code); in order to facilitate detection, all the navigational data bits have been set to '1';

• two identical uN9018 GPS receivers produced by Atheros (previously called uNav Microelectronics) with the following specifications: designed for L1 signal, 12 channels, warm start 35 s;

• two antennas;

• two computers controlling the pseudolite and the receivers;

• a 30 m radio-frequency (RF) connecting cable.

This work has been supported by: the Lifelong Learning Programmethrough an Erasmus study grant; the Sectoral Operational Programme HumanResources Development 2007-2013 of the Romanian Ministry of Labour,Family and Social Protection through the Financial AgreementPOSDRU/88/1.5/S/61178. This work has also been supported partly by the Academy of Finland. The measurements used in here were done with the helpof Atheros and Space Systems Finland, both from Finland.

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Figure 1. Block diagram of the experimental setup

Fig. 1 explains how the equipment was set up for the experiment: the pseudolite generates the same C/A signal through two outputs; one is connected to a directional antenna, and the other is connected via a cable to one of the receivers, which records the received signal and saves it in a file. This is the reference measurement data, characterizing the single-path static channel. It is not affected by indoor propagation. The wireless signal from the antenna of the pseudolite is received by the second receiver through an antenna and is recorded in another file. This is the wireless measurement data, which is affected by indoor propagation because it was received via a multipath fading channel. Both receivers are located on a hand-pushed cart, which is moved through indoor environment during the measurement scenario, in order to simulate the movement of the human GPS user, while the pseudolite emits from a fixed position. Fig. 2 illustrates the route of the cart in a typical measurement scenario. Interference from the GPS constellation has been avoided by using a Pseudo Random Number (PRN) code which is not assigned to any of the operational satellites.

III. PROCESSING THE MEASUREMENT DATA The purpose of recording both the reference and the

wireless signal is that, after demodulation, the characteristics of the wireless signal can be compared with those of the reference signal and thus the properties of the indoor channel can be

Figure 2. Typical route during a measurement scenario

identified. Because the reference and wireless data are stored in two separate files, without any temporal connection one with another, the two measurements cannot be compared because they are not synchronized. To obtain precise time synchronization, the exact time when each data record has begun is saved in a separate file. The accuracy of this procedure, called ''synchronization stamp'', is crucial for the further results obtained after the processing stage because any misalignment occurred during the reading of the two files will corrupt any possible conclusions. The actual data that is recorded in both files is the binary data stream outputted by the RF front end of each of the receivers. The sampling rate used in the measurement scenarios is fs = 16.367 MHz. We used the synchronization stamp method, illustrated in Fig. 3, to simultaneously process the reference and wireless data files. The position of the time stamp gives the offset in samples that are to be jumped from the beginning of both files. In the next step, we estimated the Doppler frequency shift by sweeping the [-2, 2] kHz interval with a 20 Hz accuracy. For each possible value a time frequency mesh similar to the one depicted in Fig. 4 has been computed. The absolute maximum of each mesh is analyzed and at the end of the sweep the mesh with the highest spike is selected. This corresponds to the correct Doppler frequency shift. We continued the processing stage, using Matlab models of the acquisition and tracking blocks of a GPS receiver created by previous members of the research group, slightly modified in order to adapt them to the new measurement data, but the obtained results were unsatisfactory.

Figure 3. Schematic representation of synchronization stamp method

Figure 4. Time frequency mesh for the reference signal

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Figure 5. Plots of auto-correlation functions for the reference signal (upper plot) and the wireless signal (lower plot)

The partial conclusion was that, due to various frequency and phase drifts in the reference and wireless signals, an exact synchronization is difficult to be achieved. As seen in Fig. 5, the shape of the Auto-Correlation Function (ACF) which was obtained for the wireless signal is very noisy and no clear spike is present.

IV. COMPARATIVE RESULTS

A. Amplitude of received signal The relevant output of the Matlab blocks consists of two

bidimensional matrices, IDI and IDQ, representing the outputs of the I and Q prompt correlations. These outputs are obtained from the integrate-and-dump blocks of the code tracking delay lock loop. The length in miliseconds (30000 ms) of the Matlab simulation gives the number of rows of each matrix, while the number of columns is obtained from the number of correlators used in the tracking loop. Because the correlation window covers the [-1,1] chip interval, with 0.05 chip step, there are 41 correlators. For each of the wireless (multipath fading channel) and cable (single-path static reference channel) signals, we have two corresponding matrices. Furthermore, matrix A is obtained from IDI and IDQ. Each element of A can be defined as following:

A(m,n) = IDI(m,n)2 + IDQ(m,n)2 (1)

where (m,n) correspond to the location (row, column) of

the element (m = 1,2,...,30000 ms; n = 1,2,...,41correlators). For each milisecond of the Matlab simulation time, the corresponding row of matrix A can be plotted and thus the auto-correlation function window is obtained for that particular milisecond. One similar plot is illustrated in Fig. 6. Because correlator number 21 corresponds to zero chip lag (on time signal replica), the peak of the auto-correlation function for the reference signal is located in the center of the window. The form of the peak corresponding to the wireless signal is delayed and shaped according to the indoor propagation conditions. Fig. 7 illustrates a plot obtained after 2000 ms of simulation time of data obtained during one scenario.

Figure 6. Plot of the modeled output of the tracking block

Figure 7. Plot of the output of the tracking block after m=2000ms of Matlab simulation of the data.

The shapes of the plot of reference data shows a close similarity to the triangular shape presented in Fig. 6. We can see that the shape of the wireless data is not similar to the expected triangle. Thus, it can be concluded that the tracking loop has lost its lock after the first two seconds of the wireless data simulation.

B. Channel estimators In order to obtain more information about the

characteristics of the indoor channel, two estimators have been extracted from matrix A: phase φ and delay τ. The time delay error τ is defined as:

τ(m) = column index of max( A(m,n)|n=1...41 )[chips] (2)

where (m,n) correspond to the location (row, column) of the current element. τ represents the delay of the maximum peak of the ACF, relative to zero chip lag (correlator number 21). Fig. 8 shows the histograms of this estimator and of the difference between wireless τ and reference τ. It can be seen that reference τ has almost all the values close to zero, meaning that there are no late replicas of the signal, because of the single-path static reference channel

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Figure 9. Histogram of estimator φ

It can also be observed that the most fitted distribution to model the wireless τ delay error is the uniform distribution, with spikes at the edges of the histogram.

The phase φ is defined as:

(3)

Fig. 9 shows the histograms of this estimator during the measurement scenario. It can be observed that the most fitted distribution to model wireless φ is the uniform distribution in the interval [-π/2, π/2], as expected, because the superposition of several Gaussian complex processes is likely to give a uniform distribution of the phase and a Rayleigh or Rician distribution of the amplitude [4].

V. CONCLUSIONS

The main problem this paper has dealt with is the complex issue of indoor propagation channel characterization in multipath and low CNR environment. A significant part of the research work presented in this paper consisted in processing and analyzing the data obtained during measurement campaigns carried out in typical office environments. This step

has utilized a Matlab model for the tracking of measured GPS pseudolite signals, both via cable (single-path static channel) and via wireless (multipath fading channel) propagation.

The analysis based on the data from the measurement scenario has brought forward an estimation of several probability distribution functions regarding the channel parameters, based on baseband samples. These findings can be summarized as following:

• estimator reference τ time delay error has almost all the values close to zero for the first scenario (Gaussian distribution centered on zero), meaning that there are no late replicas of the signal, because of the single-path static reference channel. The most fitted distribution to model the estimator wireless τ time delay error is the uniform distribution;

• the most fitted distribution to model the estimator wireless φ phase is also the uniform distribution;

After comparing these results with the initial goals of our research, we can affirm that such synchronization problems between the reference data file and the wireless data file were not expected and that the noise level in wireless data proved much higher than anticipated. Also it can be said that the Matlab model is still not fully optimized for the measurement data. Considering the results that were obtained, continuation of the research work can be done in the following directions:

• improving the synchronization method for the reference and wireless data files;

• optimizing the tracking loops and developing improved noise reduction methods in the Matlab model;

• improving the methods used for recording the data files in measurement campaigns.

Our research work has focused on the propagation of the GPS C/A signal. However, this work can be extended on the long term as analyzing also the Galileo civil signals, as L1F and E5. Also a comparison between the measured data and simulated data would be beneficial for the further validation of the channel model.

REFERENCES [1] N. Islam, CNR estimation and indoor channel modeling of GPS signals,

MSc Thesis, TUT, 2008 [2] A. Lakhhzouri, E. S. Lohan, I. Saastamoinen and M. Renfors,

‘’Interference and indoor channel propagation modeling based on GPS satellite signal measurements’’, TUT, Finland, 2005

[3] N. Islam, E. S. Lohan, A Lakhzouri, E Pajala, H. Laitinen and M. Renfors, ''Indoor fading distributions for GPS-based pseudolite signals'', IWSSC 2007

[4] T. Rappaport, Wireless Communications: Principles and Practice, Prentice Hall, United Kingdom, 2001

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