STATISTICAL PROPERTIES OF URBAN WCDMA CHANNEL FOR MOBILE POSITIONING APPLICATIONS

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1 June 2, 25 3:36 NOKIA meas v8 IJWOC International Journal on Wireless & Optical Communications c World Scientific Publishing Company STATISTICAL PROPERTIES OF URBAN WCDMA CHANNEL FOR MOBILE POSITIONING APPLICATIONS Elena Simona Lohan, Abdelmonaem Lakhzouri, and Markku Renfors Institute of Communications Engineering, Tampere University of Technology P.O. Box 553, FIN-33, Finland, {elena-simona.lohan, abdelmonaem.lakhzouri, markku.renfors}@tut.fi. Introduction The goal of this paper is to report the results of a comprehensive statistical analysis of the urban wireless channels, based on WCDMA field-measurements data. The applications of our study are in the area of WCDMA-based mobile phone positioning. The target here is the analysis of the Line-of-Sight (LOS) and Non Line-of-Sight (NLOS) situations and of the statistical distributions of their parameters, such as the delays and amplitudes. The distribution of the first arriving path is tested against several theoretical distributions, such as Rayleigh, Rician, and Nakagami-m distributions. The estimated delay of the first arriving path is compared to the LOS delay estimated via GPS, in order to detect NLOS situations. The estimation of the mobile speed, based on field-measurements data is also carried out and compared to the speed estimation based on the GPS link. The measurements were conducted in urban environment, downtown Helsinki. Keywords: LOS identification, mobile positioning, multipath channel modeling, WCDMA. The mobile radio channel is a propagation medium that is characterized by different phenomena like reflection, diffraction, scattering, and absorption. In many cases, it may happen that the Line Of Sight (LOS) signal is followed by closely spaced Non-LOS (NLOS) components, which may affect adversely the accuracy of LOS delay estimation. Depending on the geometry of the environment, such as urban, suburban, or rural, the LOS signal presence may vary from one environment to another. The LOS component is a crucial element in any mobile positioning procedure. In the 3G systems [], [5], which are our concern here, the Observed Time Difference of Arrival - Idle Period Down Link (OTDOA-IPDL) and Cell Identity methods have been selected in order to allow more involvement of the mobile station in the localization procedure. The mobile station needs to estimate quite accurately the time of arrival simultaneously from different Base Stations (BS), and the NLOS situations should be detected, in order to increase the reliability of the position estimates. Therefore, understanding the characteristics of the mobile channel in the real-world environments, is of utmost importance. The aim of this paper is to report the results of wideband propagation

2 June 2, 25 3:36 NOKIA meas v8 IJWOC 2 E.S. Lohan, A. Lakhzouri, M. Renfors measurements in terms of some statistical models of an urban WCDMA channel in the context of mobile phone positioning applications. The focus is on the analysis of the first arriving path, which might be either a LOS or a NLOS component. The motivation of our study comes from the lack of current literature dealing with channel modeling based on real field-measurement data for WCDMA systems. Typically, NLOS cases are assumed to be rare enough, and the amplitude distribution of the first path is mostly assumed to be Rician or Rayleigh. We show here that in urban environments, the first arriving path is most likely to be a NLOS path, and that the Rician and Rayleigh distributions are not always the most adequate models for the path amplitude variations, but, most of the times, the Nakagami-m distribution should be considered. We also introduce two simple methods for estimating the mobile speed: one is based on the signal autocorrelation function (ACF) and the other one is based on the Doppler Spectrum (DS). We discuss the advantages and drawbacks of each method and we compare these estimates with the speed estimates obtained via the Navstar Global positioning System (GPS). The rest of this paper will be organized as follow: in Section 2 the experimental procedure is described. Then, the main results of our analysis are given in Section 3: the statistical analysis of the fading coefficient of the first arriving path, the comparison of the delay of the first arriving path with the LOS delay estimated via GPS, and the analysis of the number of multipaths which are likely to occur in urban environments. Section 4 will be devoted to several different methods for speed estimation. Finally, conclusions are drawn in Section Experimental procedure The measurements were conducted in the center of Helsinki city, via several trajectories, where both microcell and macrocell sites were measured. The classification into macrocell or microcell environments was done according to the BS position and the resulting maximum cell radius. For example, in macrocell environments, the BS is placed above the average rooftop height and the maximum cell radius is about 35 km. For microcell environments, the BS is placed below the average rooftop height and the maximum cell radius is about 2 km. The target speed was 4 km/h in macrocell (i.e., vehicular speed) and 3 km/h in microcell (i.e., pedestrian speed). Because the wavelength was roughly 5cm, this speed ensures, there are always more than 2 samples per wavelength, i.e. the Nyquist criterion is met and the fading can be reconstructed if necessary. The test routes consisted mainly of street canyons, which were traveled by car in the macrocell measurements and, respectively, by trolley in the microcell measurements. The measurements were carried out by Nokia and provided to the authors in the form of Channel Impulse Responses (CIR), as described below. The measurements were obtained via a channel sounder, that is a device to measure radio channels by sending repeatedly a known signal which is then received and processed, in order to estimate the CIR in the time domain. During the measurements, the receiver of the sounder (Rx) was placed at the base station site. The transmitter (Tx) was moving and the Tx antenna was a modified GSM handset antenna. The signal was transmitted simultaneously at two RF frequencies using two transmitters. This allowed the measurement of Uplink (UL) and Downlink (DL) channels simultaneously (however, since we did not notice any significant difference between UL and DL results, in what follows, we will not discuss separately the two cases). The carrier frequency in UL measurements was f c =.935 GHz and in DL measurements it was f c = 2.25 GHz, in accordance with 3GPP standards []. In order to know the geometry of the measured radio channel at a certain time, the position and time were also determined by using the Global Positioning System (GPS).

3 June 2, 25 3:36 NOKIA meas v8 IJWOC Statistical Properties of Urban WCDMA Channel for Mobile Positioning Applications 3 During the measurements, the handset was placed beside a head model and tilted to correspond to a natural usage position of the phone. In most routes, the head model was mounted on the roof of the van or on a trolley. The van was moving at the speed of the traffic, approximately 25-4 km/h. The trolley measurements were done at the speed of a pedestrian user, which was approximately 3 km/h. The measurements were conducted during two days, 2 and 4 of June 2, denoted hereinafter by 26 and 46, respectively. The measurements were done in the Hesperia region, downtown Helsinki. The measurements consisted of different trajectories. The trajectories were different from one day to another, even if the same trajectory number will be used in what follows (i.e., trajectory of day 26 is not the same as the trajectory of day 46). The duration of a trajectory may vary from one trajectory to another. The sampling frequency f s was taken to be equal to N s f c, where f c = 5 MHz is the (wideband) chip frequency and N s = 4 is the oversampling factor. Each trajectory was divided into measurement cycles, one cycle having a duration of 3.65 msec. Each cycle contains impulse responses of duration 58 samples. 3. Results on fading channel characteristics For the purpose of checking the statistics of the channel coefficients, the first arriving path was estimated via two methods: it was either taken to correspond to the first local maximum applied directly on the envelope of the CIR (First Local Peak algorithm), or taken to correspond to the first local maximum of the envelope of the complex Teager-Kaiser (TK) operator applied to the CIR (TK algorithm). We recall that TK is a nonlinear quadratic operator whose expression, when applied to a complex discrete signal, is given in [3], [4], [9]. The use of TK operator was motivated by the good resolution properties of TK operator, reported in various delay estimation algorithms [3], [9], together with the aim of obtaining more reliable results, i.e., via two distinct algorithms. Therefore, the first arriving peak is detected (with one of the above algorithms), and its coefficient α n and delay τ n are stored for further statistical analysis. For each trajectory of index i, a set of N (i) T CIR were stored (since the trajectories may have different lengths, the number of points stored for each trajectory, N (i) T, may be different from one trajectory to another). In Fig. we show an illustration of the estimation of the delay and amplitude of the first arriving path for two snapshots of trajectory 3, day 26. The variation of the normalized received signal amplitude was computed for different trajectories (the normalization was done with respect to the global peak of the amplitude of the CIR). An illustrative example is shown in Fig. 2 for one trajectory for each day of the measurements. We notice that the first arriving peak does not always have the highest amplitude (i.e., here db), and that it might be even 2 db weaker than the global maximum. We also notice that TK estimator sometimes tends to under-estimate the signal power compared to the first local peak algorithm (e.g., for day 26). The very low signal level for day 26 might also be due to various sources of noise. From this point of view, the measurements from day 46 seem to be less noisy, as seen in the lower plot of Fig. 2 (where we also notice that First Peak and TK algorithms estimate similar signal powers most of the times, i.e., the two curves are overlapping). 3.. Path amplitude distribution Finding the first-arriving-path amplitude distribution is very important both from the point of view of the channel modeling and for the possibility of detection between LOS and NLOS situations, based on this distribution, e.g., as proposed in [7]. The estimated Probability Density Function (PDF) of

4 June 2, 25 3:36 NOKIA meas v8 IJWOC 4 E.S. Lohan, A. Lakhzouri, M. Renfors Day 26, trajectory 3, time instant= ms Amplitude of CIR Est. st path via st peak algo: 9 µ s Est. st path via TK algo: 9 µ s Ampl. of CIR Ampl. of TK of CIR Delay [µ s ] Day 26, trajectory 3, time instant=9.5 ms Amplitude of CIR Est. st path via st peak algo: 9.3 µ s Est. st path via TK algo: 9 µ s Ampl. of CIR Ampl. of TK of CIR Delay [µ s ] Fig.. Illustration of the first peak detection via two algorithms: First Local Peak algorithm and TK algorithm; two snapshots of CIR. 5 Amplitude variations, day 26 First Local Peak TK 5 Amplitude variations, day 46 Normalized ampl. of the first path [db] Normalized ampl. of the first path [db] First Local Peak TK time [s] time [s] Fig. 2. Examples of the normalized received amplitude of the first peak for two trajectories. Left: measurement in macrocell sites, day 26. Right: measurement in microcell sites, day 46. the first arriving path was compared to some reference PDFs. The distributions mostly used in the literature are Rayleigh, Rician, and Nakagami-m PDFs, defined according to the first and second order moments of α n as follows: Rayleigh PDF p Rayl ( ): p Rayl (x) = x ( ) b 2 exp x2 2b 2, ()

5 June 2, 25 3:36 NOKIA meas v8 IJWOC Statistical Properties of Urban WCDMA Channel for Mobile Positioning Applications 5 where b = E( α n 2 ) 2/π is the Rayleigh parameter. Rician PDF p Rice ( ): p Rice (x) = x ( ) ( σ 2 exp x2 2σ 2 K x ) 2K I, (2) σ where K is the Rician factor, estimated from the first and second moments of the measured data as: K = µ2 I + µ2 Q σ 2, (3) where µ I is the mean of the real part (I=real( α n )) of the complex coefficients corresponding to the estimated first peak, µ Q is the mean of the imaginary part (Q=imag( α n )) of these coefficients, σ 2 = (σ 2 I + σ2 Q )/2 is the variance of the underlying complex Gaussian process, and I ( ) is the modified Bessel function of the first kind defined as: I (t) 2π exp(tcosv)dv = 2π + m= ( ) t 2m 2 (m!) 2 (4) If the Rician factor is very small (close to ), it is very likely that we have Rayleigh distribution and no LOS component might be detected; otherwise, we might have LOS cases [7]. Nakagami-m PDF p Naka m ( ): p Naka m (x) = 2mm x 2m P m Γ(m) exp ( mx 2 P ), (5) where m is the Nakagami m factor, estimated as follows: ( ) 2 E( α n 2 ) m = (E ( α n 2 E( α n 2 ) )) 2, (6) with Γ( ) being the Gamma function and E( α n 2 ) is the envelope power. We consider that N independent values {x i } i=,...,n are available for the estimation of the channel distribution whenever the positioning is needed. This assumption about the sample independence should be usually checked. Here, we use the fact that the coherence time (in seconds) ( t) coh of a fading channel is of the order of ( t) coh /(2f D ) [2], where f D is the maximum Doppler spread, f D = (v/c)f c, v is the speed of the van or trolley, c is the speed of light and f c is the carrier frequency (here, f c =.935 GHz for UL and f c = 2.25 GHz for DL). In Table, we show the uplink and downlink coherence time for various mobile speed. Table. Uplink and downlink coherence time. Speed 3 km/h km/h 2 km/h 4 km/h 5 km/h Uplink, f c =.935 GHz ( t) coh 93 msec 27.9 msec 4 msec 7 msec 5 msec Downlink, f c = 2.25 GHz ( t) coh 84.7 msec 25.4 msec 2.7 msec 6.4 msec 5. msec

6 June 2, 25 3:36 NOKIA meas v8 IJWOC 6 E.S. Lohan, A. Lakhzouri, M. Renfors It follows that, in macrocell environments, the successive measurements, which are spaced at 3.65 ms, may be seen as almost uncorrelated. However, in microcell environments a high number of points will be needed in the statistics, in order to get significant results. In the measurement data analysis, we will use the same N T = N (i) T = coefficients for all the trajectories (i being the trajectory index). This means that the number of independent points used in the statistics is N (i) = N (i) T /( t) coh, and it depends on the mobile speeds, which will be estimated in Section 4. We tested the hypothesis that for each trajectory i, the measured PDF, P meas ( ), is close to a known reference PDF, P ref ( ) (e.g. Rayleigh, Rician, Nakagami-m): P meas P ref. (7) From eq. (7) two alternative states H and H can be formulated as []: { H : P meas (a l ) = P ref (a l ) for l N (i) H : P meas (a l ) P ref (a l ) for some l (8) Then, the N events A l = {a l < x a l }, l =,..., N (i), are defined such that a and a N are the smallest and the largest estimates of the channel coefficient, respectively and all the a l are equally spaced. The number of successes of A l is denoted by k l (i.e., the number of samples in the interval (a l, a l ]). Under the hypothesis H, the probability of having P meas (a l ) = P ref (a l ) is defined as where, al a l P meas (x l )dx l P (A l ) = al a l P ref (x l )dx l. (9) Thus, to test the hypothesis in eq. (7), we form the Pearson s Test Statistic (P T S) [] P T S = m k l= Two criteria for the curve fitting are possible: (k l N (i) T p ) 2 N (i) T p, () p = (a l a l )P (A l ). () Chi-square test: the hypothesis H is accepted if the P T S value satisfies P T S < χ λ (m k ), where χ λ (m k ) is taken from the standard chi-square tables corresponding to the confidence level λ and to the degree of freedom (m k ) []. For example, by choosing a confidence level of 95% (λ =.95) and degree of freedom 2, the threshold χ.5 () = Minimum PTS: Here the PTS for each reference PDF (i.e., Rayleigh, Rice,...etc.,) is first evaluated. Then the hypothesis H is accepted for the minimum value of P T S The average probabilities that data is drawn from a Rayleigh, Rice, or Nakagami-m distribution (with estimated parameters, as in eqs. (), (3) and (6)) with 99.99% significance level are shown in the upper plots of Figs. 3 and 4 for the two measurement days, respectively. The lower plots of those figures show the best-fit distribution, in the sense of minimum PTS (the best fit means simply the closest distribution to the true data among the three tested distributions).

7 June 2, 25 3:36 NOKIA meas v8 IJWOC Statistical Properties of Urban WCDMA Channel for Mobile Positioning Applications 7.5 PTS statistic on N T = points, day 26 Rayleigh fitting Best fitting, in the sense of minimum PTS, N = points, day 26 T Rayleigh fitting.5 Fraction of fits Rice fitting Nakagami m fitting Fraction of fits Rice fitting Nakagami m fitting Fig. 3. Chi-square tests (left) and best fitting curves (right) for the trajectories of 26 (statistics are done on sliding pieces of 3.65 seconds each)..5 PTS statistic on N T = points, day 46 Rayleigh fitting Best fitting, in the sense of minimum PTS, N = points, day 46 T Rayleigh fitting.5 Fraction of fits Rice fitting Nakagami m fitting Fraction of fits Rice fitting Nakagami m fitting Fig. 4. Chi-square tests (left) and best fitting curves (right) for the trajectories of 46 (statistics are done on sliding pieces of 3.65 seconds each). We remark that we might have the best fit with Nakagami-m distribution with estimated m parameter (e.g., trajectory 5 of Fig. 4), but this distribution might be still far from the true distribution (i.e., chi-square test failed), therefore the best fit curves alone do not tell much, and they should be read together with the chi-square tests. For clarity reasons we show in what follows only the plots for the chi-square statistics obtained with the first local-peak algorithm (the TK algorithm gave quite similar results). We remark from the upper plots of Figs. 3 and 4 that usually, when we decide that Rayleigh distribution is true, we also decide that Rician distribution is true. This is not contradictory, because Rayleigh fading is a particular case of Rician fading, with Rician factor close to. Similarly, Nakagami-m distribution can be seen as the most general case, covering both Rayleigh and Rician situations.

8 June 2, 25 3:36 NOKIA meas v8 IJWOC 8 E.S. Lohan, A. Lakhzouri, M. Renfors 2 Day, 26 Day, 46 Rice and Nakagami factors [db] 2 Estimated Rician factor Estimated Nakagami m factor Rice and Nakagami factors [db] 2 3 Estimated Rician factor Estimated Nakagami m factor Fig. 5. Estimated Rician and Nakagami-m factors. Upper plot: day 26, lower plot: day 46. PDF, one piece of N T () = points, 26 PDF, one piece of N T (2) = points, Measured data Rayleigh Rice Nakagami m Measured data Rayleigh Rice Nakagami m.8. PDFs.6 PDFs Amplitude levels Amplitude levels Fig. 6. Examples of curve fitting: one piece of trajectory (upper) and of trajectory 2 (lower) of day 26. The average Rician and Nakagami-m factors are shown in Fig. 5 (they were computed according to eqs. (3) and (6)). Typically, a high Rician or Nakagami-m factor may signal the presence of LOS component [7]. However, we notice that these values are rather low, therefore, the presence of a LOS component in urban scenarios may be quite unlikely (this conclusion is later verified via the comparison with GPS estimates). The case with strong Rician factor from day 26, trajectory 7, is due to the fact that the mobile was in static condition (as it will be seen in Section 4). For illustration purposes, two examples of curve fitting are shown in Fig. 6. From the point of view of the best fitting curve (lower plots of Figs. 3 and 4), we notice that the most suitable distribution model is Nakagami-m distribution. We also notice from the upper plots of Figs. 3 and 4 and from the Rician factors of Fig. 5 that the Rician distribution with very low Rician factor is also modeling quite well the channel profile and it might be adopted in the theoretical models, having the advantage of an easier modeling and known theoretical ACF and Doppler spectrum Comparison with LOS delay estimated via GPS The GPS-based LOS delay estimate was also available from the measurement data and it could be used as a benchmark. Basically, the gap between the estimated delay of the first arriving path of the terrestrial data ( τ (i) ) and the LOS estimated via GPS (LOS GP S ) should be higher or equal to (if both transmitter and receiver clocks are synchronized, as in our case). We note that LOS GP S was estimated only once per second, while τ (i) delays were estimated once per cycle (i.e., we have

9 June 2, 25 3:36 NOKIA meas v8 IJWOC Statistical Properties of Urban WCDMA Channel for Mobile Positioning Applications 9 about /3.65 = 273 estimates per second). The curves τ (i) LOS GP S (minimum, mean, and maximum values, respectively) are shown in Fig. 7 for trajectory 3 of 26 and of 46 (similar curves were obtained for the other trajectories). The minimum, mean and maximum values were computed over s. Estimated NLOS delay, date 26 Estimated NLOS delay, date 46 Min NLOS error Mean NLOS error Max NLOS error st Peak LOS from GPS [µ s] 2 Min NLOS error Mean NLOS error Max NLOS error st Peak LOS from GPS [µ s] Time [ s] Time [ s] Fig. 7. NLOS delay estimation error from the comparison with GPS. Upper plots: day 26, trajectory 2. Lower plots: day 46, trajectory. st Peak LOS from GPS [µ s] Illustration of offset correction, date 46 Estimates of mean(τ i ) without offset correction Third order polynomial approximation on mean Estimates of mean(τ i ) with offset correction Time [s] Fig. 8. Illustration of the coarse offset correction, via third-order polynomial approximation. It is reasonable to assume that the negative minima (discontinuous points of the lower curves in Fig. 7), might occur because of the noise and to some possible residual offset between transmitter and receiver clocks. The curves in Fig. 7 are after the coarse correction of this offset. This coarse offset was estimated via third-order interpolation on the available τ (i) estimates, for minimum, mean and maximum values, respectively. An example of the trend estimate for the mean values is shown in Fig. 8. The coarse offset correction is estimated from the polynomial coefficients of this trend together with the average value of mean( τ (i) ). The offsets between the first arriving peak and the LOS estimated via GPS (as seen in Fig. 7) show clearly that LOS is typically not present in urban environments and the maximum LOS error

10 June 2, 25 3:36 NOKIA meas v8 IJWOC E.S. Lohan, A. Lakhzouri, M. Renfors can be as high as few µs. This observation is in agreement with the previous observations based on the data PDF and Rician/Nakagami-m factors. We did not find any clear LOS case from the analyzed urban data Number and spacing of multipaths The number of the fading paths in urban environments is also a significant factor in channel modeling. The identification of the multipath components was done as the following: from each impulse response of the channel, we detected all the local maxima, which are at most 7 db below the global maximum. Figs. 9 and show the number of paths and its distribution for two measurements dates. We noticed that the mean value of number of paths is around 5 and, in most of the cases, we do.4 Meas. 26, Traj Meas. 26, Traj. 5 5 Meas. 26 Probability Probability Meas. 26, Traj. 2 Probability Probability Meas. 26, Traj Min Mean Max Fig. 9. for day 26. Upper plot: The distribution of number of paths in 4 trajectories. Lower plot: the min, max, and mean of the estimated number of paths of all trajectories. not exceed 5 paths. We also noticed that the average maximum delay spread was.2 µs for day 26 and 8.6 µs for day 46. The average was done over all the available trajectories. Another important parameter for channel modelling and positioning purposes is the average spacing between successive paths. It was noticed that the average spacing between successive paths was.44 µs for both days (26 and 46). These values were obtained by looking at the local peaks of the envelope of CIR which are at most 7 db lower than the maximum peak (i.e., those peaks which are likely to correspond to a multipath component). The results were also verified using TK algorithm and we obtained similar results (i.e., an average maximum delay spread of.93 µs for day 26 and of 8.56 µs for day 46, and an average path spacing of.42 µs for day 26 and.38 µs for day 46). 4. Speed estimation We remark that mobile speed means here only the absolute value of the velocity vector. In what follows, we address also the problem of mobile speed estimation, via three alternative methods:

11 June 2, 25 3:36 NOKIA meas v8 IJWOC Statistical Properties of Urban WCDMA Channel for Mobile Positioning Applications.35 Meas. 46, Traj..7 Meas. 46, Traj Meas Probability Probability Min Mean Max Probability Meas. 46, Traj Probability Meas. 46, Traj Fig.. for day 46. Upper plot: The distribution of number of paths in 4 trajectories. Lower plot: the min, max, and mean of the estimated number of paths of all trajectories.. GPS-based estimation This method can be applied when GPS measurements, such as in our case, are available. The GPS position was measured once every second and stored together with the measurement data. Therefore, it is reasonable to assume that the mobile speed was constant during this small observation time and it can be estimated via: (x2 x ) v = 2 + (y 2 y ) 2, t with t = s, y, x are the mobile coordinates (in x-y plane) at time t (in meters), and y 2, x 2 are the mobile coordinates at time t 2 (in meters). 2. ACF-based estimation There are various Doppler-spread estimation methods based on the covariance approximation methods [4], [3], [2], [8]. We selected here the ACF-based speed estimation method of [4]. Speed estimation is based on the approximation of the channel coefficient ACF with Jakes ideal ACF. In Rayleigh and Rician fading channels the normalized ACF of the real (as well as imaginary) part of a fading multipath component is well-known from [4] and can be written further for k =,, 2,... as: ( ) 2πf D k t cos(θ ) φ ideal,rice (k t, θ ) = K + J (2πf D k t) + K K + e, (2) where K is the Rician factor given by eq. (3), t is the time spacing between consecutive samples of the channel (here, t = 3.65 ms), J ( ) is the zero-order Bessel function of the first kind, f D is the maximum Doppler spread, and θ is the angle between first arriving path component and the mobile direction (since this angle is not known beforehand, it is assumed to be uniformly distributed in [, 2π]). The ACF-based maximum Doppler spread estimator tries to approximate the ideal ACF with the normalized sample correlation estimator r h (k t): [ f D, θ ] = arg min f D,θ N samples k= ( φ ideal,rice (k t, θ ) φ meas (k t)) 2, (3)

12 June 2, 25 3:36 NOKIA meas v8 IJWOC 2 E.S. Lohan, A. Lakhzouri, M. Renfors where N samples is the number of samples used in the approximation and it is a parameter of the model (there is a tradeoff between the noise and the accuracy of the estimation when increasing the number of samples; in our estimates, we found that N samples = offers a good tradeoff), and φ meas (k t) is the ACF function of the real (or imaginary) part of α n with lag k t. For better estimation, we considered the average between the speed estimates based on the real part of the fading coefficients and those based on the imaginary part of fading coefficients. We remark that the general expression of the ACF in Nakagami-m fading channel is not known, and therefore the ACF-based estimator is not likely to exhibit good results in Nakagami-m fading channels. 3. Doppler-spectrum-based estimation There are several methods based on the spectrum of the estimated channel coefficients [4], [], [6]. The Doppler spectrum is the Fourier transform of the fading coefficients α n. For example, the ideal Doppler spectrum for Rayleigh fading coefficients is given by the Clarke function: 3 S ideal,rayleigh (f) = 2πf D ( f ). 2 f D In practice, some other power spectral densities might be expected, such as asymmetric Clarke power spectrum or Laplacian power spectrum. Examples of Doppler spectra based on measurement data are shown in Fig., where the comparison with the ideal Clarke spectra is also included. Doppler spectrum.5 Doppler spectrum, day 46, trajectory Estimated Doppler Spectrum Ideal Clarke spectrum Doppler spectrum Frequency (Hz).5 Estimated Doppler Spectrum Ideal Clarke spectrum Frequency (Hz) Fig.. Example of Doppler spectra for two pieces of trajectory, day 46. As we can notice from Fig., the Doppler spectra may be highly asymmetric and embedded in noise. Therefore, we introduce here the following method in order to determine the maximum Doppler spread from the Doppler spectra: () Find the frequency f D corresponding to the maximum peak in the range of negative frequen-

13 June 2, 25 3:36 NOKIA meas v8 IJWOC Statistical Properties of Urban WCDMA Channel for Mobile Positioning Applications 3 cies, and the frequency f D2 corresponding to the maximum peak in the range of positive frequencies. (2) If the ratio of the two peaks corresponding to the two frequencies above is either less than 2 or higher than /2 (i.e., the spectrum is rather symmetrical), the estimate of f D is obtained as the average between the two frequencies: f D = f D +f D2 2, otherwise (i.e., we have a highly asymmetric spectrum), f D is the maximum (in absolute value) between the two: f D = max( f D, f D2 ). The advantage of this method is that it can be used for any type of fading and it is not limited to Rayleigh and Rician-fading situations as the ACF-based method. In what follows we compare these three methods based on the set of the measurement data. Four representative cases of the estimation results are shown in Fig. 2. As seen in the upper plot of Fig. 2, the mobile was in a stationary condition for trajectory 7 of 26 date (according to GPS data), which is in conformity with our previous observations. We also notice that the speed estimates for day 26 are typically noisier than for day 46, in accordance with the previous observations. We also notice that both ACF-based and DS-based estimates tend to be very close to GPS estimates if the data has a Rayleigh/Rician distribution (e.g., all the trajectory of 46 and some parts of the trajectory of 46, as seen in the two lowest plots of Fig. 2), but they also may underestimate the true mobile speed if the distribution is Nakagami-m or unknown (e.g., the uppermost plot of Fig. 2 and the last part of trajectory in the lowest plot of 2). The spurious peak in GPS estimates in Fig. 2 is signalling that the GPS estimates were also prone to some measurement errors Estimated speed, date 26, trajectory Estimated speed, date 26, trajectory Estimated Speed via GPS Estimated Speed via Doppler spectrum Estimated Speed via ACF 3 Mobile Speed (km/h).5 Estimated Speed via GPS Estimated Speed via Doppler spectrum Estimated Speed via ACF Mobile Speed (km/h) Time [seconds] Time [seconds] Estimated speed, date 46, trajectory Estimated Speed via GPS Estimated Speed via Doppler spectrum Estimated Speed via ACF Estimated speed, date 46, trajectory Estimated Speed via GPS Estimated Speed via Doppler spectrum Estimated Speed via ACF Mobile Speed (km/h) Time [seconds] Mobile Speed (km/h) Time [seconds] Fig. 2. Speed estimators for two trajectories of day 26 (upper plots) and for two trajectories of day 46 (lower plots). For the trajectory 7 of the measurement date 26 (upper left plot), the mobile is stationary, and, thus, the estimated speed via GPS is zero (and thus it is overlapping with the x-axis).

14 June 2, 25 3:36 NOKIA meas v8 IJWOC 4 E.S. Lohan, A. Lakhzouri, M. Renfors The root mean square error (RMSE) for each trajectory of each day is shown in Fig. 3. The error is computed as the difference between ACF-based estimates and the GPS estimates, and between DS-based estimated and GPS-based estimates, respectively. We show here both estimates via First Peak algorithm and via TK algorithm, respectively. We notice that the two algorithms have similar results. We also notice that DS-based estimates are, on average, slightly better than ACF-based estimates, which is due to the fact that DS-based estimators do not depend on the Rayleigh/Rician fading assumption. The median RMSE value is about 4 km/h for 26 (when the measurements were noisier than for 46 case) and 6 km/h for 46. On the other hand, there are some situations where ACF-estimates are much better than DS estimates (e.g., trajectory of 46). This is explained by the fact that DS-based estimates are less robust to the noise than ACF-based estimates. There are only few situations when the RMSE error is very high and these usually corresponds to the cases where the chi-square tests fail to match with any of the tested distribution (Rayleigh/Rice/Nakagami-m), as shown in the upper plots of Figs. 3 and 4 (e.g., trajectory 5 of 46). There are however some situations which were determined to be Rayleigh or Rician trajectories, but which have very high RMSE, such as trajectory 2 of 46. In such situations, the high RMSE values can be partially explained by the presence of measurement errors in GPS data. There are also some situations, such as trajectory 6 of 26, which were not determined to be Rayleigh or Rician situations, but for which the RMSE error computed via ACF-based and DS-based models is very small. 2 RMSE for speed estimates (reference is the GPS estimate), 26 RMSE for speed estimates (reference is the GPS estimate), 46 2 DS based, First Peak DS based, TK ACF based, First Peak ACF based, TK RMSE [km/h] DS based, First Peak DS based, TK ACF based, First Peak ACF based, TK RMSE [km/h] Fig. 3. RMSE for speed estimation via ACF and DS-based algorithms, with respect to GPS estimates, day 26 (left) and day 46 (right). The speed-estimation plots also show that, via relatively simple algorithms (such as ACFbased estimation), we can make reliable decisions whether the mobile is in a low-speed scenario or whether if it is in a high-speed scenario. This information may be very helpful for positioning and navigation as well as for other receiver algorithms.

15 June 2, 25 3:36 NOKIA meas v8 IJWOC REFERENCES 5 5. Conclusions In this paper we have analyzed the statistical properties of an urban wireless channel for the purpose of WCDMA mobile positioning. The main focus was on the first arriving multipath component, which can be either LOS or NLOS path. For positioning purposes, the NLOS situations should be detected, in order to cope with the NLOS error. We studied here the statistical distribution of the amplitude of the first arriving path and we saw that this distribution typically matches with Nakagami-m fading or Rician fading with very low Rician factors. We also saw that the first arriving path is almost always a NLOS path with an error in the range of. to.2 µs. It is reasonable to assume that the LOS cases would have a much stronger Rician factor than NLOS cases. However, from the measurement data analysis, we noticed that a strong Rician factor alone cannot be used as an indicator of LOS cases, because it may also occur due to stationary receiver/transmitter. The measurement data also showed us that, in urban environment we have many multipath components, with an average of 5 paths. It was also shown that in average the the maximum delay spread was in the range µs. Furthermore, we analyzed three simple speed-estimation methods and we saw that we are able to obtain reliable results regarding whether the mobile is moving at a low speed or a high speed (with RMSE errors typically smaller than 5 km/h), even if the statistical distribution of the first path amplitude does not match the Rician or Rayleigh distributions. Our study can be used for further modelling of generalized channel profiles (such as Nakagami-m fading) for the purpose of WCDMA studies (positioning, channel estimation, etc.) in urban scenarios. The methods presented here for speed estimation can also be included in the receiver blocks, in order to allow for various purposes, such as better positioning, better handover decisions, adaptive modulation, channel estimation algorithms, etc. Acknowledgements This work was carried out in the project WCDMA Channel Estimation for Positioning, funded by Nokia. The source for the field measurements was Nokia, which is gratefully acknowledged. References [] 3GPP. Physical layer-general description. Technical Report TS 25.2 V3.., available via web, at (active in Nov 24), 999. [2] M.D. Austin and G.L. Stuber. Velocity adaptive handoff algorithms for mcrocellular systems. IEEE Trans. on Vehicular Technology, 43(3):549 56, 994. [3] R. Hamila. Synchronization and Multipath Delay Estimation Algorithms for Digital Receives. PhD thesis, Tampere University of Technology, Tampere, Finland, June 22. [4] J. F. Kaiser. On a simple algorithm to calculate the energy of a signal. In Proc. of IEEE ICASSP, pages , Albuquerque, New Mexico, 99. [5] K. Kalliojarvi. Terminal positioning in wcdma. In Proc. of EUSIPCO 2, pages , 2. [6] T. Klaput and M. Niediwiecki. A novel approach to estimation of doppler frequencies of a time-varying communication channel. In In Proc. of IEEE American Control Conference,, volume 4, pages , 22. [7] A. Lakhzouri, E. S. Lohan, R. Hamila, and M. Renfors. Extended Kalman filter channel

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