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Measurement Investigation of Tap and Cluster Angular Spreads at 5.2 GHz Kai Yu, Qinghua Li, and Minnie Ho

Abstract—In this paper, we present indoor measurement results on the cluster angular spread (AS), the tap AS and its variation with different channel bandwidths. A frequency domain space alternating generalized expectation maximization (FD-SAGE) algorithm is employed to estimate the multipath components from the measured data. We then manually identify the clusters of the multipaths and calculate the tap and cluster ASs for each identified cluster. It is found that for the 100 MHz channels, the average tap AS is just few degrees less than the cluster AS and the difference diminishes for less channel bandwidth. Index Terms—Measured channel, channel modeling, angular spread, multipath component, antenna arrays.

I. INTRODUCTION

W

IRELESS local area networks (WLANs) equipped with multiple-input–multiple-output (MIMO) antenna arrays have attracted great interest for next generation high data rate communications. To facilitate the research and comparison of different MIMO techniques, accurate channel models for MIMO WLAN are of great significance. Recently, several measurement campaigns and modeling works for indoor MIMO radio channels have been conducted worldwide [1]–[3]. Within the IEEE 802.11 working group, MIMO WLAN channel models are developed by a special committee [4]. Both the Kronecker structure of the channel correlation matrix [1], [2] and the cluster modeling approach [5]–[8] are employed is approximated [4]. First, the channel correlation matrix as the Kronecker product of the transmit correlation matrix and the receive correlation matrix , where is the tap1 index. The above Kronecker structure has been verified from indoor measurements for MIMO channels with moderate array sizes [1], [2]. The transmit and receive correlation matrices and are then modeled separately using the cluster and are determined by the power model [4], where angular spectrums (PASs) and the associated angular spreads (ASs) seen from the transmitter and receiver respectively [9]. Manuscript received May 12, 2004; revised September 3, 2004. The work of K. Yu took place during his visit to the Smart Antennas Research Group, Stanford University, Stanford, CA, and was sponsored by Ericsson’s Research Foundation. Portions of this work were presented at the IEEE Vehicular Technology Conference, May 17-19, 2004, Milan, Italy. K. Yu is with the Signal Processing Group, Department of Signals, Sensors & Systems, Royal Institute of Technology (KTH), SE-100 44 Stockholm, Sweden (e-mail: [email protected]). Q. Li and M. Ho are with Intel Labs, Intel Corporation, Santa Clara, CA 95052 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TAP.2005.850721 1Here the channel’s impulse response is modeled by a tapped delay line model. One tap corresponds to one sampling time.

Note that the Kronecker structure becomes less accurate as the number of antennas increases [2], [10]. For such cases, the joint MIMO channel correlation matrix needs to be modeled with high complexity. The well-known cluster models [5]–[8] are based on the observation that multipath components (MPCs) arrive in groups. Let a cluster to be a group of MPCs that can be distinguished from the other MPCs in both time and angle. The PAS and its root mean square (RMS) cluster AS are widely used in characterizing the cluster. They provide an overall characterization of the cluster by aggregating the tap level information. In [6]–[8],2 it is reported that the PAS can be modeled by a Laplacian function with cluster AS 3.31 –37 . However, depending on the channel bandwidth, several taps can exist within one cluster and each tap includes a number of MPCs from that cluster. What is essential to many tapped delay line channel models such as [4] is and/or . the spatial correlation of each delay tap, i.e., Following [11], let the tap AS be the RMS AS of the delay tap (a mathematical definition will be given in Section IV-A) and it quantifies the channel dispersion in angle on the tap level. It is of great interest to study the tap AS and compare to the corresponding cluster AS, since the spatial correlation of each tap is controlled by the corresponding tap AS. It should be noted that the tap AS varies with channel bandwidth.3 Hence, it is also interesting to study the variation of tap AS with different bandwidths. This paper is organized as follows. Section II gives a brief description on the channel measurements conducted by the Intel Corporation. The frequency domain space alternating generalized expectation maximization (FD-SAGE) algorithm [12] is described in Section III. We then present the measurement results in Section IV. Finally, the conclusions are given in Section V. II. MEASUREMENT DESCRIPTION The measurements were carried out in a large office environment at Intel Corporation in Santa Clara, CA. Small cubicles are built in this environment using cloth partitions with metal frames. Typically, each cubicle contains some working desks and metal filing cabinets. There also exist a few conference rooms which are separated by plasterboard and metal studs. All the measurements were conducted on weekends. Test of the 2The results in [6] and [7] report that the distribution of the angle of arrival (AOA) is Laplacian. Using this fact and other results in [6], [7], it can be shown that the PAS can be matched by the same Laplacian function [11]. 3For example, the tap AS equals the cluster AS for a single tap channel, while it approaches 0 when the bandwidth is so large that at most one MPC falls in each tap.

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YU et al.: MEASUREMENT INVESTIGATION OF TAP AND CLUSTER ANGULAR

Fig. 1. Receive antenna cross.

channel stationarity showed that the variation of the environment was less than 1% during one complete measurement (i.e., one measured data set) [13]. During the measurements, the transmitter was positioned at 7 different locations, including cubicles and corridors at desktop ( -cm 91-cm) virtual height. At the receiver, a cross antenna array with 0.5 (1.27 cm) inter-element spacing was mounted underneath the ceiling, which has a 360 full range capture of MPCs as shown in Fig. 1. The distance between the transmitter and receiver was about 10–21 m. The measurements were conducted in the frequency domain with 1601 frequency points. The overall measured bandwidth was 1 GHz (5–6 GHz) and thus the frequency tone spacing is 625 KHz. In this paper, only part of the measured data were used to estimate the MPCs due to the following considerations. (i) Since plane waves are assumed in the estimation algorithm, all the scatterers must be located in the far-field region [14] to the receive array cross. Although this assumption can be removed by estimating the curvatures of the impinging waves, in order to lower the already high computational complexity, we decided to keep this assumption. Therefore only the data measured from ( cm 30.5 cm) sub-array cross at the center the of the original antenna cross were used to estimate the MPCs. Note that by doing so, we sacrificed the intrinsic resolution of the array. (ii) The attenuation of each individual MPC caused by air propagation, reflection, diffraction and scattering are frequency dependent for channels with large bandwidth comparing to the carrier frequency. The frequency dependence is difficult to be compensated in MPC estimation, and we assume that each MPC is frequency independent in this work. This means the overall channel bandwidth should be much smaller than the carrier frequency (narrowband assumption in RF engineering). Hence, in this paper, measured data with 400 MHz bandwidth (5.0–5.4 GHz) were employed. III. FD-SAGE ALGORITHM The space alternating generalized expectation maximization (SAGE)4 algorithm [16] is a popular method used in channel 4Although different opinions still exist on whether the results obtained from the SAGE algorithm (or other similar estimation algorithms) truly represent the reality [15], the SAGE algorithm is by far a very popular approach used to extract channel parameters.

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parameter estimation, since it can deliver high resolution estimates. By solving the maximum likelihood (ML) estimation problem iteratively, the SAGE algorithm lowers the high computational complexity required by the ML estimator. Since the measurements were conducted in the frequency domain, we employed the FD-SAGE algorithm [12] to estimate the MPCs. The successive interference cancellation (SIC) technique, which subtracts the estimated MPCs successively, was used in order to initialize the algorithm and detect the number of MPCs [12]. The grid steps used to search the angle of arrival (AOA) and time of arrival (TOA) were set to be 1 and 1 ns, respectively. We evaluate the performance of the FD-SAGE estimator following [16]. A synthetic environment was generated with the same measurement setups as described in Section II. Two MPCs with equal power were impinging at the receive array from 0 to 360 . The SNR was set as 20 dB. The difference between the AOAs of two MPCs was from 0 to 15 , and the TOAs of both ns. When two MPCs MPCs were generated from did not arrive simultaneously, the root-mean-square estimation errors (RMSEE’s) of the estimated AOAs were less than 0.25 , and the means of the estimation errors were close to zero which indicate that the estimator is unbiased. When two MPCs arrived simultaneously, the resolution of the FD-SAGE estimator degraded due to the limited array size. This is consistent to the results reported in [12], [16]. Note that the performance of the FD-SAGE algorithm also depends on the number of MPCs. In [17], a synthetic environment was generated with 32 MPCs arriving in several small groups. The MPCs were estimated accurately as long as they differ either in their AOAs or TOAs by a fraction of the intrinsic resolution. IV. MEASUREMENT RESULTS A. Definition of AS be the PAS and be the AOA of the arrived mulLet tipath component, the RMS AS can be calculated as the square root of the second central moment of the PAS [18]

(1)

where the mean AOA

is calculated as (2)

In this paper, three different ASs are studied, namely the cluster AS, the instantaneous tap AS and the average tap AS. When the PAS of a whole cluster is used in (1) and (2), we obtain the cluster AS. Instead, if we use the instantaneous PAS of an individual tap, we get the instantaneous tap AS. The average tap AS is obtained by first averaging the PAS of every individual tap within each cluster, and then calculating the AS from the obtained average PAS. Note that to average the PAS of each tap, each instantaneous PAS should be centered at its own mean AOA .

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Fig. 2.

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 53, NO. 7, JULY 2005

3-D multipath profile (data set 84). Fig. 4.

CDF of the instantaneous tap AS. TABLE I AVERAGE TAP AS AND CLUSTER AS (DATA SET 84)

Fig. 3. Image of the estimated MPCs in the delay-angular domain (data set 84).

using a horn antenna shows that about 49% of the impinging energy is reflected. The glass is likely being toughened or metal coated and therefore it is very reflective. By using Figs. 2 and 3, five clusters were manually identified. Similarly, four–five clusters were identified from each of the other data sets. For each identified cluster, we further calculated its cluster AS using (1) and (2). The results show that the corresponding cluster AS ranges 5.6 –36.5 for all measured data sets.

B. Cluster and Cluster AS Using the FD-SAGE algorithm, the MPCs were estimated from the measured data sets. In this paper, unless otherwise stated, we use the results obtained from data set 84 as an example. Fig. 2 shows the positions of the estimated MPCs for data set 84 in the delay-angular domain as well as their amplitudes. It can be seen from the figure that the MPCs arrive in several clusters. In order to further help identify the clusters, we used a two-dimensional (2-D) Hanning window [19] as a filter to smooth in the delay-angular domain so that the concentration of the estimated MPCs can be easily found. This is called weighted averaging [19] and is equivalent to 2-D low-pass filtering in the frequency domain. The 2-D Hanning window used here has lower sidelobes in the frequency domain comparing to the spatial averaging mask with equal weights [19]. Fig. 3 shows the image of the filtered MPCs with their amplitudes represented by the greyscale. It is observed that the MPCs look quite symmetric about the AOA 180 axis. This is due to the strong reflections from the large glass windows several meters behind the receive antenna cross. Test of the glass windows

C. Instantaneous and Average Tap ASS We first focus on investigating the tap AS of the channel model proposed in [4], which has 100 MHz bandwidth. Thus the time resolution is 10 ns. To find the tap AS for the channel with 10 ns time resolution, we collected all the MPCs for every 10 ns and put them in the same time bin. For each individual tap, the instantaneous PAS is obtained by simply computing the power of each individual MPC within the associated time bin. The instantaneous tap AS was then calculated as the square root of the second central moment of the instantaneous PAS. The cumulative distribution function (CDF) of the instantaneous tap AS obtained from all measured data sets is plotted in Fig. 4. It can be seen that the instantaneous tap AS is between 0 –43 . This shows that for some specific taps, the difference between the tap AS and the cluster AS can be large. We also found that such taps usually have fewer MPCs and less power. We further calculated the average tap AS and compared it to the cluster AS for each identified cluster. Table I lists the average tap AS and the cluster AS for data set 84. Similar data processings were conducted for the other data sets. Table II lists

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TABLE II AVERAGE TAP AS AND CLUSTER AS

TABLE III AVERAGE TAP AS (MEAN) WITH DIFFERENT BANDWIDTHS AND CLUSTER AS (MEAN)

the number of clusters being identified, the mean value of the average tap AS and the cluster AS for each measured data set. Note that the mean cluster AS found in the measured environment is 14.9 , which is comparable to the values reported in [6], [12]. The results clearly demonstrate that the average tap AS is a just few degrees less than the cluster AS for 100 MHz bandwidth channels. In order to study the variation of the tap AS with different channel bandwidths, the average tap AS was estimated for the channels with 10, 20, 50, and 100 MHz bandwidth respectively, using different time bins to collect the estimated MPCs. The results are listed in Table III together with the cluster AS. It is shown in Table III that the difference between the average tap AS and the cluster AS becomes even smaller with less channel bandwidth, and it becomes less than 1 for 10 MHz channel bandwidth. The above results show that the average tap AS is roughly equal to the cluster AS even for relatively large channel bandwidth studied in this paper. Furthermore, it indicates that within each cluster, the angular statistics is almost independent of the time delay. Therefore the cluster AS can be used to roughly describe the tap AS [4]. V. CONCLUSION We have investigated the tap AS and cluster AS based on the 5 GHz indoor wireless channel measurements. The FD-SAGE algorithm has been used to estimate MPCs and the clusters have been manually identified. Our investigation has shown that for each individual data set, four–five clusters can be identified with 5.6 –36.5 cluster AS. For 100 MHz channel, it has been found that the instantaneous tap AS ranges 0 –43 and the average tap AS is slightly less than the cluster AS. Furthermore, the difference between the average tap AS and the cluster AS diminishes as the channel bandwidth decreases.

ACKNOWLEDGMENT The authors thank Ericsson’s Research Foundation for financially supporting K. Yu’s research visit to the Smart Antennas Research Group, Stanford University, Stanford, CA, during which this work has been done. They also thank J. Lung, D. Cheung, C. Prettie, and E. Lin for the channel measurements. REFERENCES [1] K. I. Pedersen, J. B. Andersen, J. P. Kermoal, and P. Mogensen, “A stochastic multiple-input-multiple-output radio channel model for evaluation of space-time coding algorithms,” in Proc. IEEE Vehicular Technology Conf., vol. 2, Fall 2000, pp. 893–897. [2] K. Yu, M. Bengtsson, B. Ottersten, D. McNamara, P. Karlsson, and M. Beach, “Modeling of wideband MIMO radio channels based on NLOS indoor measurements,” IEEE Trans. Veh. Technol., vol. 53, no. 3, pp. 655–665, May 2004. [3] J. W. Wallace and M. A. Jensen, “Modeling the indoor MIMO wireless channel,” IEEE Trans. Antennas Propag., vol. 50, no. 5, pp. 591–599, May 2002. [4] V. Erceg et al.. (2004, Jan.) IEEE P802.11 wireless LANs: TGn channel models. IEEE 802.11-03/940r2 (Adopted) [Online]. Available: http://www.802wirelessworld.com [5] A. Saleh and R. Valenzuela, “A statistical model for indoor multipath propagation,” IEEE J. Sel. Areas Commun., vol. SAC-5, no. 2, pp. 128–137, Feb. 1987. [6] Q. Spencer, B. Jeffs, M. Jensen, and L. Swindlehurst, “Modeling the statistical time and angle of arrival characteristics of an indoor multipath channel,” IEEE J. Sel. Areas Commun., vol. 18, no. 3, pp. 347–360, Mar. 2000. [7] R. J.-M. Cramer, R. A. Scholtz, and M. Z. Win, “Evaluation of an ultrawide-band propagation channel,” IEEE Trans. Antennas Propag., vol. 50, no. 5, pp. 561–570, May 2002. [8] C. C. Chong, C. M. Tan, D. I. Laurenson, S. McLaughlin, M. A. Beach, and A. R. Nix, “A new statistical wideband spatio-temporal channel model for 5-GHz band WLAN systems,” IEEE J. Sel. Areas Commun., vol. 21, no. 2, pp. 139–150, Feb. 2003. [9] J. Salz and J. H. Winters, “Effect offading correlation on adaptive arrays in digital mobile radio,” IEEE Trans. Veh. Technol., vol. 43, no. 4, pp. 1049–1057, Nov. 1994.

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[10] H. Özcelik, M. Herdin, W. Weichselberger, J. Wallace, and E. Bonek, “Deficiencies of the “Kronecker” MIMO radio channel model,” Electron. Lett., vol. 39, no. 16, pp. 1209–1210, 2003. [11] K. I. Pedersen, P. E. Mogensen, and B. H. Fleury, “A stochastic model of the temporal and azimuthal dispersion seen at the base station in outdoor propagation environments,” IEEE Trans. Veh. Technol., vol. 49, no. 2, pp. 437–447, Mar. 2000. [12] C. C. Chong, D. I. Laurenson, C. M. Tan, S. McLaughlin, M. A. Beach, and A. R. Nix, “Joint detection-estimation of directional channel parameters using the 2-D frequency domain SAGE algorithm with serial interference cancellation,” in Proc. Int. Conf. Commun., vol. 2, 2002, pp. 906–910. [13] D. Cheung, C. Prettie, and J. Lung, “Angular spectra results for office environment,” in Proc. 13th Annu. Symp. Wireless Personal Communications. Blacksburg, VA, Jun. 2003. [14] H. Krim and M. Viberg, “Two decades of array signal processing research,” IEEE Signal Processing Mag., vol. 13, no. 4, pp. 67–94, Jul. 1996. [15] M. Bengtsson and B. Völcker, “On the estimation of azimuth distributions and azimuth spectra,” Proc. IEEE Vehicular Technology Conf., vol. 3, pp. 1612–1615, Oct. 2001. [16] B. H. Fleury, M. Tschudin, R. Heddergott, D. Dahlhaus, and K. I. Pedersen, “Channel parameter estimation in mobile radio environments using the SAGE algorithm,” IEEE J. Sel. Areas Commun., vol. 17, no. 3, pp. 434–450, Mar. 1999. [17] K. Yu, Q. Li, D. Cheung, and C. Prettie, “On the tap and cluster angular spreads of indoor WLAN channels,” in Proc. IEEE Vehicular Technology Conf., May 2004. [18] A. Paulraj, R. Nabar, and D. Gore, Introduction to Space-Time Wireless Communications. Cambridge, U.K.: Cambridge Univ. Press, May 2003. [19] A. K. Jain, Fundamentals of Digital Image Processing. Englewood Cliffs, NJ: Prentice-Hall, 1989.

Kai Yu received the B.Eng. degree from Shanghai University, Shanghai, China, in 1998 and the M.Sc. degree (with distinction) from the University of Liverpool, Liverpool, U.K., in 2000, both in electrical engineering. He received the Ph.D. degree from the Signal Processing Group, Royal Institute of Technology (KTH), Stockholm, Sweden, in 2005. From March to September 2003, he was a Visiting Researcher at the Smart Antennas Research Group, Stanford University, Stanford, CA. His current research interests include multiple-input–multiple-output (MIMO) channel modeling, MIMO channel prediction, array signal processing and multiple access techniques.

Qinghua Li received the Ph.D. degree in electrical engineering from Texas A&M University, College Station, in 2001. Previously, he worked for Ericsson and Nokia for short periods. In 2001, he joined Intel Labs, Intel Corporation, Santa Clara, CA, where he is a Researching developing high throughput techniques for IEEE 802.16e and 802.11n standards and Intel’s products. His research lies in the areas of wireless communications including MIMO, SDMA, UWB, MAC, indoor wireless channel modeling, CDMA, multiuser detection, and interference mitigation.

Minnie Ho received the B.S. degree from Princeton University, Princeton, NJ and the M.S. and Ph.D. degrees in communications from Stanford University, Stanford, CA. From 1994 to 1998, she was at Radix Technologies, where she was a Lead Algorithms Engineer for a wireless-local loop system with adaptive smart antennas. From 1998 to 2001, she managed a communication systems group at Fantasma Networks, one of the first UWB start-ups. In 2001, she joined Intel Labs, Intel Corporation, Santa Clara, CA, where she currently manages an advanced physical-layer research group which focuses on channel modeling, design and evaluation of smart-antenna systems, and system-level evaluation for cellular applications.