COMPARISON OF HIGH RESOLUTION CHANNEL PARAMETER MEASUREMENTS WITH RAY TRACING SIMULATIONS IN A MULTIPATH ENVIRONMENT

Transcription

1 IN PROC. OF THE 3RD EUROPEAN PERSONAL MOBILE COMMUNICATIONS CONFERENCE (EPMCC 99), (PARIS, FRANCE), PP , MARCH COMPARISON OF HIGH RESOLUTION CHANNEL PARAMETER MEASUREMENTS WITH RAY TRACING SIMULATIONS IN A MULTIPATH ENVIRONMENT Ralf Heddergott, Pascal Truffer, Martin Tschudin Communication Technology Laboratory ETH Zürich, CH-8092 Zürich, Switzerland fralf,truffer,tschuding@nari.ee.ethz.ch Michael Nold Department of Information Technology University of Ulm, D Ulm, Germany michael.nold@e-technik.uni-ulm.de Abstract: A wideband indoor channel sounder operating at 24 GHz with a delay resolution of 2 ns and an estimation scheme based on the space-alternating generalized expectation-maximization (SAGE) algorithm is used for obtaining high resolution estimates of the parameters characterizing the impinging waves, i. e. their propagation delay, incidence azimuth, incidence elevation, and complex amplitude. We present a channel measurement of an extreme multipath scenario. The parameter estimates are compared with those obtained by ray tracing simulations. The accuracy of the latter is assessed by comparing the measured and simulated power delay profile. 1. Introduction Efficient wireless indoor transmission represents a key technology to pave the way toward the realization of universal personal telecommunication (UPT). During the next decade a rapid development of new powerful indoor radio systems can be expected. Correspondingly, a profound knowledge of the radio channel is indispensable. The information required for the elaboration of channel models can solely be obtained from experimental investigations by means of measurements combined with a suitable data processing algorithm, which allow a resolution of the electromagnetic wave propagation with respect to both the delay and incidence direction. The wideband channel sounder ECHO 24 (ETH Channel Sounder operating at 24 GHz) permits the determination of the complex channel impulse response (CIR) with a delay resolution of 2 ns. Spatial information results from placing the receiving antenna at the locations of a virtual antenna array. Resolution with respect to the propagation delay and incidence direction is achieved by processing the received signals on the basis of the space-alternating generalized expectation-maximization (SAGE) algorithm [1]. The SAGE algorithm has been applied for joint delay and azimuth estimation in time-invariant environments [2] as well as for joint delay, azimuth, and Doppler frequency estimation in time-variant environments [3]. In [4], a SAGE scheme for joint delay-azimuth-elevation estimation suitable for indoor environments has been presented. The estimation accuracy has been evaluated by means of Monte-Carlo simulations. Furthermore, the reliability of ECHO 24 and the signal processing with the SAGE algorithm has been assessed by measuring a pre-defined incidence constellation consisting of a direct and two reflected waves. In this paper we present measurements carried out in an extreme multipath scenario. A radio frequency shielded room (RFSR) has been chosen as measurement site. Inside the RFSR, the walls are smooth so that only specular reflections occur. Moreover, the scenario can easily be modeled by applying wave propagation tools. The following performance criteria are applied: Firstly, the delay, azimuth, and elevation estimates obtained with the SAGE algorithm are compared to the parameters obtained by ray tracing simulations [5], [6]. Secondly, the convergence rate of the SAGE algorithm as well as the number of iteration cycles which are required for convergence are assessed by monitoring the sequence of loglikelihood values. Finally, the power delay profile (PDP) computed from the antenna output signals measured at the locations of the virtual antenna array is compared to the PDP re-calculated by using the parameters estimated by the SAGE algorithm. The comparison of the measured PDP and the calculated PDP from the parameters obtained in the ray tracing simulation permits the performance evaluation of the wave propagation model. The paper is organized as follows. A short description of the ECHO 24 channel sounder and the SAGE scheme used for delay, azimuth, and elevation estimation is given in Sec. 2. In Sec. 3 we describe the wave propagation model used for obtaining reference values of the channel parameters. The measurement of the multipath scenario including the discussion of the results is presented in Sec. 4. Sec. 5 contains an assessment of the accuracy of the wave propagation model by comparing the PDP calculated from the simulated parameters to the measured PDP. 2. High Resolution Measurement Technique 2.1. Measurement System ECHO 24 The channel sounder ECHO 24 permits the determination of highly time-variant complex CIRs by means of a correlation method, where the transmitter (Tx) and the receiver (Rx) can be separated by distances up to 50 m. It transmits the signal u c (t) =< u(t) e 2fct at a carrier frequency f c = 24 GHz, where< fg denotes the real part and u(t)

2 IN PROC. OF THE 3RD EUROPEAN PERSONAL MOBILE COMMUNICATIONS CONFERENCE (EPMCC 99), (PARIS, FRANCE), PP , MARCH a periodically repeated pseudo-noise (PN) code signal of length N c = 1023 and chip duration T c = 2ns. Thus, the period time is T a = N c T c = 2:046 s. To achieve a coherent demodulation, the Tx and the Rx have to be synchronized properly. In the upper part of the SHF range neither the use of atomic standards nor a connection with modern semirigid coaxial cables is possible because of frequency shift and attenuation problems, respectively. Moreover, the handling of stiff coaxial cables is rather cumbersome. Hence, a fiber optic antenna feeding concept has been developed which permits simple heterodyne detection and flexible low attenuation fiber links [7]. The measurement system is depicted in Fig. 1. It consists of the Tx module, the Rx module, and the control unit. Due to the fiber optic antenna feeding the control unit can be placed outside of the RFSR. The Tx and Rx module can be seen inside the RFSR in the back and the front, respectively. Both modules are equipped with a wideband =4 monopole antenna. The Rx antenna is moved along the M sensors of a virtual antenna array located at r 1 ;:::;r M 2 R 3 with respect to the antenna arrays center of gravity by means of a stepping motor driven positioning device for three dimensions. At the m-th position of the virtual antenna array, the signal y c m (t) =< y m (t) e 2fct is received by the Rx antenna. Real and imaginary parts of the baseband signal y m (t) are returned to the control unit by means of two standard coaxial cables where they are sampled for data acquisition purposes. The subsequent high resolution data processing is done off-line. The SAGE algorithm has been implemented on ECHO 24 in order to check some of the measurements instantly. A detailed description of the measuring system can be found in [8]. Fig. 1. Photo of the RFSR and ECHO The SAGE Algorithm The output Y (t), [Y 1 (t);:::;y M (t)] T of the virtual antenna array can be modeled as 1 Y (t) = LX `=1 s(t; `) +N (t) ; (1) 1 Y (t) denotes a stochastic process, while y(t) refers to its measured realization. where L represents the number of different multipath signals s(t; `), and where the vector `, [`;`;#`;`] contains the parameters of the `-th multipath signal, i.e. the propagation delay `, the incidence azimuth `, the incidence elevation #` and the complex amplitude `. The additive noise vector N (t) is assumed to be a zeromean, temporally and spatially white noise process with covariance matrix N 0 I M,whereI M refers to a unit matrix of dimension M. Note that the `-th multipath signal s(t; `) =`f (`;#`)c(`;#`) u(t, `) is a delayed, scaled, and phase-shifted version of the sounding signal u(t) employed by ECHO 24 2,wherec(; #) and f (; #) denote the steering vector of the antenna array and the complex field pattern of the receiving antenna, respectively. The problem at hand is the resolution of the L multipath components s(t; `), which are overlapping in delay and space, by estimation of the parameter vectors `, ` =1;:::;L. An optimal solution in the Maximum- Likelihood (ML) sense is given by the global maximum ^ ML (y) of the loglikelihood function of, [ 1 ;:::; L ] given an observation Y (t) =y(t) [9]: Z n o (; y), 1 2 < [s(t 0 ; )] H y(t 0 ) dt 0 N 0, Z ks(t 0 ; )k 2 dt 0 : (2) The calculation of ^ ML (y) for large L is computationally expensive due to the high dimension of and due to the nonlinearity of the underlying optimization problem. The SAGE algorithm [1] is an iterative way of finding ^ ML (y). Its application to the resolution of electromagnetic waves is described in [2] while [4] presents a scheme for delay-azimuth-elevation estimation. Two different steps are employed in the SAGE algorithm: Firstly, the complete data ^x` t; ^ 0, y(t), L X `0 =1 `0 6= ` s t; ^ 0`0 is determined, which can be viewed as a noisy estimate of the `-th waves signal contribution. Secondly, a ML estimation of the parameters describing ^x` t; ^ 0 is carried out by applying a coordinate-wise updating procedure [4]. The sequential calculation of these two steps for all L waves counts for one iteration cycle of the SAGE scheme. It is important to note that the sequence of SAGE estimates inserted in (2) yields a non-decreasing sequence of loglikelihood values. In order to provide the SAGE algorithm with good initial values we employ an initialization scheme based on successive interference cancellation [4]. 3. Wave Propagation Model The wave propagation model [5], [6], which was developed at the Department of Information Technology at the University of Ulm, permits the calculation of the incidence delays, azimuths, elevations, and complex amplitudes as well 2 The baseband sounding signal u(t) embodies the impulse response of the measurement system. It can be determined by a calibration measurement, where the Tx output and the Rx input is connected by a short cable. (3)

3 IN PROC. OF THE 3RD EUROPEAN PERSONAL MOBILE COMMUNICATIONS CONFERENCE (EPMCC 99), (PARIS, FRANCE), PP , MARCH as the channel impulse response at the Rx antenna location. For sufficient small wavelength-to-object size-ratios, geometrical optics and the theory of diffraction can be applied [10]. Tx and Rx are regarded as point sources, and the propagation of electromagnetic waves is described by straight lines called rays. The environment is represented by arbitrarily placeable rectangular objects. The electromagnetic properties of each object are described by a single material parameter. Any fine structure, such as small objects, surface roughness etc., is disregarded. The propagation paths are constructed considering the laws of reflection, diffraction and refraction by applying ray tracing techniques such as the virtual imaging method or the variation method [11]. For keeping the computational complexity small, multiple diffraction or diffraction combined with subsequent reflections is not considered. At each object the electric field corresponding to a ray is calculated fully polarimetrically. The diffraction loss follows by using the uniform theory of diffraction (UTD). Free-space attenuation and atmospheric attenuation is also considered. At the Rx location, the complex impulse response results from the superposition of all impinging waves taking the far-field antenna pattern into account. 4. Measurements tennas have been determined with a theodolite. The cables connecting the Tx and Rx module to the ECHO 24 control unit could not be led out with the door completely closed. Therefore, the door opening has been covered by an iron shield during the measurements Ray Tracing Simulation The virtual imaging method is used to compute the delays, azimuths, and elevations of the incident waves for the geometrical dimensions given in Fig. 2. The RFSR is modeled as a cuboid. To determine the locations of the virtual Tx images, first a pair of parallel walls is considered with the Tx located between them, as shown in Fig. 3. It can be seen that all virtual images of the Tx, resulting from multiple reflections on the walls, are located on a straight line through the Tx orthogonal to the walls. Then, the combination of perpendicular pairs of reflecting walls in three dimensions yields the cuboidal lattice structure of the virtual Tx image locations, which is shown in Fig. 4. The propagation path lengths and incidence directions result from the connecting lines between the Rx location and the locations of the virtual Tx images, respectively. The delays are obtained by division of the propagation path lengths by the velocity of light. The delays and azimuths of the 3458 waves occurring in the range = 0:::100 ns computed with the virtual imaging method are depicted in Fig. 5. Note that with increasing delay the angular separation decreases while the number of incident waves occurring in a delay interval [; + ) increases. Thus, the propagation scenario becomes more diffuse Measurement Site The RFSR is shown in Fig. 1. The interior walls are made of zinc-plated iron shields. The geometrical dimensions of the RFSR as well as the positions of the Tx antenna and the coordinate system of the Rx antenna array are sketched in Fig. 2. The positions of the edges and the Tx and Rx anh=2.42 m 3.68 m Tx 1.62 m Tx h=1.47 m Wall #1 Wall #2 Fig. 3. Locations of virtual images of the Tx for a pair of parallel reflecting walls m x Rx y h=1.42 m z 2.66 m 1.31 m 3.66 m Tx Rx Fig. 2. Sketch of the RFSR. Fig. 4. Cuboidal lattice structure of the virtual Tx image locations for a single reflection in each dimension. The solid-line cuboid shows the RFSR boundaries.

4 Azimuth [ ] IN PROC. OF THE 3RD EUROPEAN PERSONAL MOBILE COMMUNICATIONS CONFERENCE (EPMCC 99), (PARIS, FRANCE), PP , MARCH Delay [ns] Virtual imaging method Estimation (SAGE) " Fig. 5. Delays and azimuths of the propagation scenario in the RFSR calculated with the virtual imaging method and estimated with the SAGE algorithm from measured signals Measurement Results From the received signals of a 3-dimensional uniform cross array comprising M = 33 sensors, the complex amplitudes, delays, incidence azimuths, and incidence elevations of L = 150 impinging waves have been estimated by the SAGE algorithm. The quantization precision is T c =4 = 0:5ns for the delay estimates and 0:25 for both the azimuth and the elevation estimates. The range for the delay estimates was restricted to = 0:::110 ns. Including the initialization, the SAGE scheme performed 25 iteration cycles until convergence has been achieved 3. The estimated delays and azimuths are depicted in Fig. 5. A good match 4 with the ray tracing data could be found for 41 estimated waves. The delay and incidence direction of the direct wave has been estimated exactly within the quantization precision of the parameter estimates. Deviations between simulated and estimated parameters appear especially with increasing delay. This behavior occurs due to the lower angular separation and the lower power of the incident waves. From Monte-Carlo simulations [4] it is known that in this case the mean-squared estimation error increases. Moreover, errors in the determination of the RFSR geometry may cumulate at high reflection orders. Errors also might occur due to the equipment in the RFSR. The convergence behavior of the SAGE algorithm is illustrated in Fig. 6, where the sequence of loglikelihood values 3 Convergence has been achieved when no change occurred in any of the L quantized delay, azimuth, and elevation estimates in one iteration cycle compared to the previous one. 4 A good match between the simulated and estimated parameters of a wave is achieved when the absolute error is lower than 2nsand 3 for the delay and for both the azimuth and the elevation, respectively. computed with (2) is depicted versus the number of iteration cycles 5. Note that the sequence is non-decreasing, as stated in Sec. 2. The loglikelihood values strongly increase within the first iteration cycles, and have almost converged after 5 cycles. After the initialization cycle approximately 97% of the final loglikelihood value have been reached. This emphasizes the accuracy of the successive interference cancellation scheme used for the initialization. The power delay profile has been computed from the measured signal vector by averaging the squared magnitude of all 33 sensor output signals correlated with the sequence u(t). Furthermore, the PDP has been reconstructed using the parameter estimates obtained by the SAGE algorithm. The profiles embody the response of the measurement system. Both profiles are reported in Fig. 7 for comparison. A remarkably slow decay of the measured PDP arises due to the severe multipath propagation. Note that only a small fraction of the very high number of impinging waves in the real scenario has been captured by estimating 150 impinging waves. The match between the measured and reconstructed PDP is fairly good for delays in the range 0 <50 ns, while the fit is less accurate for > 50 ns. This arises due to the fact that the SAGE algorithm preferably estimates the strongest waves and, due to the high number of incident waves, the reconstruction is more difficult as the delay increases. However, the relatively good fit of the reconstructed PDP to the measured PDP shows that the SAGE algorithm returns meaningful estimates in the sense that for a given number L of waves to be estimated the received signal y(t) is approximated by the signal s(t; ^) in an optimum fashion. 5 The noise power spectral density N0 has been set to one.

5 (^; y) IN PROC. OF THE 3RD EUROPEAN PERSONAL MOBILE COMMUNICATIONS CONFERENCE (EPMCC 99), (PARIS, FRANCE), PP , MARCH x Measured PDP Reconstruction (SAGE) Power [db] Number of iteration cycles Fig. 6. Sequence of loglikelihood values versus the number of iteration cycles. 5. Reconstruction of the Power Delay Profile by Ray Tracing Simulation The quality-of-fit between the ray tracing simulation and the real scenario is assessed by comparing the measured PDP for a single antenna located in the antenna arrays center of gravity to the corresponding re-calculated PDP from the simulated parameters. The latter has been obtained as follows. First, the course of the rays has been constructed with the help of the virtual imaging method up to a maximum reflection order of 12. This procedure yields 2625 simulated rays. Then, the electromagnetic field at the Rx antenna location corresponding to each ray has been computed fully polarimetrically, considering free-space attenuation. Furthermore, the far-field patterns of the Tx and Rx antennas have been taken into account. Finally, the received signal at the correlator output has been computed as the superposition of delayed, attenuated, and phaseshifted versions of the autocorrelation function R uu ( ) of the sounding signal u(t) employed by ECHO 24. Taking the squared magnitude yields the simulated PDP. The measured and simulated PDP is compared in Fig. 8. Due to the maximum reflection order of 12, all simulated rays have a delay less than 151 ns. Furthermore, the cuboidal lattice structure of virtual Tx images explained in Sec. 4.2 is complete only for = 0 :::74 ns, while for = 74 :::151 ns there exist far more propagation paths than those captured by the ray tracing simulation. The coarse shape of the PDP, which is determined by the power of the impinging waves, is reconstructed given that all paths that are geometrically possible were simulated. Due to errors in the modeling of the RFSR geometry, the phases of the impinging waves cannot be determined exactly. Therefore, the fine-structure of the simulated PDP does not match the measurements. 6. Conclusions The wideband channel sounder ECHO 24 described in this paper permits the measurement of the complex channel impulse response at a carrier frequency of 24 GHz with a time resolution of 2 ns. A virtual antenna array is used for obtaining spatial information of the electromagnetic field. The SAGE algorithm has been applied to jointly estimate Delay [ns] Fig. 7. Power delay profile (PDP) computed from the measured signals and reconstructed from the parameters estimated by the SAGE algorithm. Power [db] Measured PDP Reconstruction (ray tracing) Delay [ns] Fig. 8. Power delay profile (PDP) computed from the measured signals and reconstructed from the parameters obtained in the ray tracing simulation. the delays, incidence azimuths, incidence elevations, and complex amplitudes of the impinging waves. A measurement of an extreme multipath scenario has been carried out. The parameters of the impinging waves have been calculated by ray tracing simulation using the virtual imaging method. A match could be found for a part of the estimated and simulated parameter set. At high propagation delays the number of incident waves increases while their angular separation and their power decreases. In this situation a high resolution scheme is no longer capable of resolving all impinging waves accurately. However, a comparison of the power delay profile (PDP) obtained from the measured signals to the PDP computed from the estimated channel parameters shows that the SAGE algorithm returns meaningful estimates. A comparison of the measured PDP and the PDP recalculated from the parameters obtained in the ray tracing simulation shows that the coarse shape of the measured PDP, which is determined by the power of the impinging waves, can be reconstructed by ray-tracing simulations, while the fine-structure, which depends on the phases of the impinging waves, cannot.

6 IN PROC. OF THE 3RD EUROPEAN PERSONAL MOBILE COMMUNICATIONS CONFERENCE (EPMCC 99), (PARIS, FRANCE), PP , MARCH Acknowledgements The authors would like to thank Heinrich Maag from the Electronics Laboratory, ETH Zürich, for providing the radio frequency shielded room, and Hermann Bösch from the Institute of Hydrology, ETH Zürich, for conducting the theodolite measurements. Finally, we want to express our gratitude to Prof. P. E. Leuthold, Director of the Communication Technology Laboratory, ETH Zürich, and Prof. J. Lindner, Head of the Department of Information Technology, University of Ulm, for their encouragement and support of this research. References [1] J. A. Fessler and A. O. Hero, Space-alternating generalized expectation-maximization algorithm, IEEE Trans. on Signal Processing, vol. 42, pp , Oct [2] B. H. Fleury, D. Dahlhaus, R. Heddergott, and M. Tschudin, Wideband angle of arrival estimation using the SAGE algorithm, in Proc. of the IEEE Fourth Int. Symp. on Spread Spectrum Techniques and Applications (ISSSTA 96), (Mainz, Germany), pp , Sept [3] K. Pedersen, B. Fleury, and P. Mogensen, High resolution of electromagnetic waves in time-varying radio channels, in Proc. of the 8th IEEE Int. Symp. on Personal, Indoor and Mobile Radio Communications (PIMRC 97), (Helsinki, Finland), pp , Sept [4] M. Tschudin, R. Heddergott, and P. Truffer, Validation of a high resolution measurement technique for estimating the parameters of impinging waves in indoor environments, in Proc. of the 9th IEEE Int. Symp. on Personal, Indoor and Mobile Radio Communications (PIMRC 98), (Boston, Mass), pp , September [5] T. Huschka, Untersuchungen zum Funkkanal innerhalb von Gebäuden. PhD thesis, University of Ulm, Ulm, Germany, [6] T. Huschka and M. Nold, Modellierung des Indoor- Funkkanals bei 60 GHz, in European Microwave Conference (MIOP 97), (Sindelfingen, Germany), pp , April [7] J. O Reilly, P. Lane, R. Heidemann, and R. Hofstetter, Optical generation of very narrow linewidth millimeter wave signals, Electronics Letters, vol. 30, pp , Jan [8] P. Truffer, Wideband channel sounder with optical antenna feeding, in Proc. of Workshop on Mobile Millimeter Communications, (Dresden, Germany), pp , May [9] H. V. Poor, An Introduction to Signal Detection and Estimation. New York, NY: Springer-Verlag, [10] M. Born and E. Wolf, Principles of Optics. Oxford: Pergamon Press, 6th ed., [11] T. Huschka, Ray tracing models for indoor environments and their computational complexity, in Proc. of the 5th IEEE Int. Symp. on Personal, Indoor and Mobile Radio Communications (PIMRC 94), (The Hague, Netherlands), pp , Sept