Polarization Characteristics of Multiple-Input Multiple-Output Channels

Transcription

1 Polarization Characteristics of Multiple-Input Multiple-Output Channels Lei Jiang, Lars Thiele, Armin Brylka, Stephan Jaeckel and Volker Jungnickel Fraunhofer Institute for Telecommunications, Heinrich-Hertz-Institut Einsteinufer 37, D Berlin,Germany Abstract-In this paper, we investigate the polarization characteristics of the multiple-input multiple-output (MIMO) channels. The cross polarization discrimination (XPD) is found to change over time, while its variation in frequency domain is relatively small. The probability density function (PDF) of the XPD follows a Gaussian distribution. Analysis and measurement results show that the polarization preserves better in the line of sight (LOS) scenario. In the case of non line of sight (NLOS) scenario, the polarization of the signals is destroyed due to multiple reflections, diffractions or scattering. The difference between the XPDs of the vertically polarized and horizontally transmission highly depends on the specific propagation environment between the transmitter and the receiver. Comparison of the capacity in different scenarios further shows that the polarization diversity gain is less in NLOS scenarios compared with that in LOS scenarios. ios. In addition, the channel capacity is also compared for co-polarized and cross-polarized MIMO channels in LOS and NLOS scenarios. II. MEASUREMENT SETUP I. INTRODUCTION The multiple-input multiple-output (MIMO) system has been shown to dramatically increase the capacity of the wireless system and it draws increasing attentions in recent years [1], []. An important condition for MIMO channels to achieve high capacity is that the environment provides sufficient multipath components. By exploiting the multipath components, the MIMO link results in a high rank channel with improved capacity. Recently, cross-polarized antennas have been used in the MIMO communication system to obtain polarization diversity gain in addition to the spatial diversity gain compared with MIMO channel using co-polarized antennas. Thus it is of great interest to investigate the polarization characteristics of the MIMO channels. [3]-[6] performed the measurement for indoor propagation environments and studied the polarization effects in such scenario. [7], [8] investigated the channel properties for outdoor environment. [7] developed simple models to estimate the dependence of the cross polarization discrimination (XPD) as a function of excess loss and distance. [8] studied the polarization characteristics of the ultra wideband propagation channels. In this paper, we aim at analyzing the characteristics of the MIMO channel based on outdoor measurements. Simple propagation model for MIMO channel with cross-polarized antennas will be given, and the factors that affect the XPDs will be analyzed. Based on the measurement at.53ghz for outdoor propagation environments, the XPD of propagation channels will be investigated for different propagation scenar /08/$ IEEE Fig. 1. Transmit and receive antennas. Measurements were made on the campus of Technical University Berlin (TUB) at.53 GHz with the RUSK HyEff channel sounder in a 0 MHz band. The base station is a uniform linear array (ULA) with cross-polarized patch antenna elements on it as shown in the top of Fig. 1. The four patches in each column are coupled to narrow the vertical beam width and hence obtain higher antenna gain. The left-most and rightmost columns of antennas are grounded via 50 n resistor to minimize the edge effects. Therefore, altogether 8 columns of cross-polarized antennas at >.../ spacing, Le., 16 transmit antennas are used as active elements. A +44 dbm power amplifier with a 1 x 16 high power switch is used for the multiple antennas. The effective transmit power is +37 dbm per antenna, due to the 4 db insertion loss of the switch and -3 db antenna efficiency.

2 - Sinfj(Jp co~y) ADA CO~,~ADD ]. cos p COS tt-)aoa cos Cf/AOD Ns -jkl i L -TG~,P ifi(cpi) sin L TciLC ifi(cpi) cos i=l Ns -jkl i i=l 1, (Jp,i COS'l/JAOA,i COS'l/JAOD,i 1, (Jp,i COS"pAOA,i The noise figure of the HyEff receiver is.5 db. Low-loss feeder cables are used to reduce receiver noise. Altogether, the link margin is improved by almost 0 db compared to [9]. This allows a sufficient SNR for evaluating the MIMO capacity. All antennas are made of similar patch elements with two points of delivery feeding horizontal and vertical polarization. Cross-polarization coupling is smaller than -0 db, measured back-to-back between two patched. The 3 db antenna aperture is about 90 0 both in azimuth and elevation.the receivers are built in two forms. One is a cylinder with 8 cross-polarized patches antennas on the surface arranged in a row. The other is a cylindrical antenna made of two 1-patch elements arranged in two rows. On top a cube antenna is mounted as shown in the lower part of Fig. 1. (4) cos "paod,i (5) in the bottom right of Fig. 1. The receiver is placed at about m above the ground level. Short measurement tracks of 10 m inside campus area and long tracks with a total length of approximately 4.5 kin outside the campus area were recorded. III. CROSS-POLARIZATION DISCRIMINATION XPD is defined as the ratio of co-polarized average received signal power to the cross-polarized average received power. It is given by XPD = E{l h vvi } v XPD H E{lhHVI } = E{lhHHI } E{lh vh j} (1) () The XPD quantifies the separation between two transmission channels due to different polarization orientations [7]. From the definition we can see that the XPD depends on the channel, hence it depends on the propagation environments. A simple x cross-polarized MIMO channel can be written as in [10] (3) Fig.. Locations of the base station and terminal antennas. The base station was placed on the rooftop of the buildings indicated as BSx in Fig., where BS 1 is on Heinrich-HertzInstitut (HHI), BS is on Deutsche Telekom (DTAG) and BS3 is on the main building the TUB. The receiver sites marked with Rx use the cylindrical antenna as shown in the bottom left of Fig. 1. Those marked with Tx use the antenna shown where the channel matrix for the LOS scenario is obtained as in (4), where D is the LOS distance between the transmit and receive antennas, k is the wave number, ()p is the polarization mismatch angle between the transmitter and the receiver (e.g. ()p == 0 for co-polarized transmit and receive antennas, ()p == 1f / for cross-polarized transmit and receive antennas), o denotes the element wise multiplication. G~'~ (.) take into account the vertically and horizontally polarized transmit and receive antenna beam patterns. WAOA and WAOD denote the angle of arrival (AOA) at the receiver and angle of departure (AOD) at the transmitter. The channel matrix for NLOS is shown in (5). fi(</>i) represents the total amplitude and phase changes due to the reflection, diffraction and scattering during the whole propagation path. Ii and (}p,i denote the path length and polarization rotation angle for each path respectively. The received signal is the summation of N s multipath components undergoing reflection, diffraction or scattering. As N s is large

3 enough, the channel may be approximated by the Rayleigh channel. p!'los is the total received power, hvv, hhh, hvh and hhv are identical independent distribution (ij.d) complex Gaussian random variables. Therefore, the XPD for the x MIMO channel yields XPD v == e- jkd v v ~ ro 1 --yr-gr('l/jaoa)gt('tpaod)cos()p + V K+fVPrhvv Ie-;;v l Gji('ljJAOA)G~('l/!AOD) XPD NLOS = Ih vv l V I hhvl (8) Similar results can be obtained for horizontally polarized signal as below XPDiiOS = IGji('ljJAOA) I: cot 0 p IGk(VJAOA) I XPD NLOS = h I hhl H Ih v hl sinop + JK~l vp;hhvl (6) where P r is the total received power at the receiver. It can be approximated that in strong LOS scenario where the Ricean K factor K» 1 XPDtOS = IG~Cl/)AOA)I: cot 0 p (7) IGjf(VJAOA) I While in NLOS scenario where K approaches 0, (9) (10) From the equations above we can see that the XPDs in LOS scenario depend on the receive antenna patterns and the polarization mismatch angle between the transmit antenna and the receive antenna. In the NLOS case, they highly depend on the propagation environment. In the following parts, we will validate our statements by measurement results. A. The Distribution of the XPD The cumulative distribution function (CDF) of the XPD in db is plotted in Fig. 3 for three different environments as indicated in the figures. We average over all antenna elements. It can be observed that the XPD v and XPDH are almost the same in strong LOS scenario. This can be explained from (7) and (9), as long as the antenna pattern of the vertically and horizontally polarized antennas are the same, the XPD v and XPDH are equal. This has also been reported in [11], with the omni-directional antenna pattern, the vertically and horizontally polarized microwave signals yield the same performance. In our measurement, although the antennas are not omni-directional, the vertically and horizontally polarized antenna patterns are similar, and hence they have the same XPD in LOS scenario. In some cases when the single reflected or diffracted rays also contribute an innegligible part to the total received signal, the XPD v and XPDH may be different. 8o :flosl{= I~:zE~~J XPD (db) LL o 0.5. () OL :::::: l...-_ l-_----j XPD (db) ~ 0.5. NLOS: () ol.-_..._~iiiiiiiii:: ~_~.:...:.=..:...:...I:.. i J -4 - Fig. 3. XPDv and XPDH in different propagation environments. However, different from [11], we observe difference between the XPD v and XPDH in other propagation scenarios. As the K factor decreases, the multipath components contribute more to the total received signal. The effect of depolarization due to the multiple reflections, diffractions and scattering becomes more obvious. The depolarization effect depends on the propagation environments, e.g. the orientation and geometrical shape of the scatterers, the relative permittivity and conductivity of the scatterers' surface etc. [1]. This usually results in an uncertain degree of depolarization of the vertically and horizontally polarized signal. From the second and third subplots of Fig. 3 we can observe that, XPD v is usually larger than XPDH, which is in agreement with the well-known statement that vertically polarized signal is preferable during the propagation [3]. In the pure NLOS scenario, it may also happen that XPD v and XPDH remain the same. Scenario 1 in the third plot of Fig. 3 is the normal NLOS propagation environment with rich scatterers, while scenario is analogous to a canyon-like propagation environment. From (8) and (10) we know that, the degree of depolarization highly depends on the specific propagation environment between the transmitter and receiver. In a certain scenario, the XPDH is even higher than XPDv. In Fig. 3 we can also see that the XPD is very high in the LOS scenario, which means that less power is coupled. As the contribution of the LOS components becomes less, the XPD decreases. In the NLOS scenario, the XPD is the lowest, thus more power is coupled. Generally, the XPD decreases with decreasing K factor. The relationship between them will be investigated in our future work. B. Gaussian Distribution Fit It is reported in [8] that the Gaussian distribution fits best for the empirical distribution of the XPD with vertical transmission for indoor LOS scenario. In our measurement, similar results have been discovered for outdoor environments. Measured data and the fitted Gaussian distribution are shown in Fig. 4. It can be seen that, no matter in the LOS or 10

4 4000 losscenario los scenario 'I' \, \"/""~_I... I'~'I-""I/\~...I",...,,',\/,,/\.II '_/'y' " 13 0 L..----'---'---.L '---1'--O_ '-_~---':-----J Bandwidth (MHz) o XPDH(dB) NlOSscenario '..." " NlOSscenario 00L..----'---'---..L '---1'--O_...L I._--l ::== Bandwidth (MHz) ~L..-_~ XPDV(dB) Fig. 5. The XPDs vs channel bandwidth. Fig. 4. The Gaussian distribution fit for the XPDs for strong LOS and NLOS scenarios. found to vary considerably from 3.1 GHz to 10.6 GHz in indoor LOS scenario. NLOS scenario, both XPDv and XPDH fit the the Gaussian distribution very well. Hence we can model the distribution of the XPD as XPD rv N(f-t, a). The best fit mean values and standard deviations of the XPDs using least squares fitting are given in Table I. TABLE I J-L AND a FOR XPD 9L L----L.---'---...L.--..L..---L l' L---1::Ia.----l Snapsho1s XPD Mean (J-L) Standard deviation (a) XPDf, S 14.7 db.6 db XPDJi.D S 15.3 db 3.1 db XPD~LOS.7 db 1. db XPDZLO S.5 db 1.6 db OL L----L.---'---...L.--..L..---L l' L----l Snapshots It is shown in [13] that the measured mean XPD in the literature ranges from 0 db to 18 db depending on the propagation environment. Our measurement results fall in this range. The mean XPD in strong LOS scenario is about 15 db, and in pure NLOS scenario, the value is around 3 db. The typical value of the standard deviation is reported to be 3-8 db. In our measurement, the standard deviations are smaller compared with the reported value. Furthermore, we find that the standard deviation for the selected LOS scenario is larger than that for the selected NLOS scenario. C. Time and Frequency Dependency In order to study the frequency dependency of the XPD, we averaged the XPD over time and antenna elements. The XPDs versus the channel bandwidth is given in Fig. 5. It can be seen that the XPDs vary slightly over the whole band, with a very small variation range. This indicates that the mean XPD is not highly frequency dependent in a 0 MHz bandwidth despite the propagation environments, while in [8] the mean XPD is Fig. 6. The XPDs vs snapshots. The averaged XPD over frequency and antenna elements against the time is plotted in Fig. 6. Fromthe figure we observe that the XPD changes with time, like the fast fading channel. In this figure, the results are given from a short measurement track of 10 m, hence the value of XPD shows only small changes caused by the similar propagation conditions. For the long track measurement, the XPDs will vary over time in a much larger range, according to the scenario where the measurements were made. Further effort will be put to that in our future work. IV. CHANNEL CAPACITY The channel capacity is calculated by

5 where Nt and N r are the numbers of transmit and receive antennas, respectively. Po is the total transmit power and a is the noise power at the receiver. goilos]../.<l:~://,. IZ, ~ go:nlos_l~~/eu '... i~ Fig Ii~t~ o Capacity for co-polarized and cross-polarized channels. Fig.7 shows the capacity of the co-polarized and crosspolarized MIMO channels. For comparison, we choose similar antenna configurations for both two receive antennas in Fig. 1. VV or HH stands for the case that transmit and receive antennas have the same polarization, VH or HV stands for case that the transmit and receive antennas have different polarizations. We can see from the figure that, the polarization preserves better in the LOS scenario, hence the VV channel and HH channel performs much better than the VH and HV channel. The polarization diversity gain is the highest in such scenarios. The performance difference is more than 10 bps/hz. As the contribution of multiple components increases, the performance gain of VV and HH channel compared with VH and HV channel becomes less. The capacity gain of the VV and HH channel is less than 4 bpslhz in the mixture of LOS and NLOS scenario compared with the VH and HV channels as shown in the second plot of Fig. 7. In NLOS scenario, it becomes further less. It can also be observed that most of the time, the HV channel is the worst of all, i.e. vertically polarized transmit antenna with horizontally polarized receive antennas. The VV channel performs best in general, which indicates that the vertical polarization preserves better than the horizontal polarization during the propagation. V. CONCLUSION In this paper, we investigated the polarization characteristics of the MIMO channel with cross-polarized antennas. Analysis and measurement results show that the polarization preserves better in the LOS scenario. The PDFs of XPD v and XPDH follow a Gaussian distribution in both LOS and NLOS scenarios. The mean XPD is about 15 db in LOS scenario and 3 db in NLOS scenario. Measurement results show that the XPDv and XPDH vary with time, since the channel XPD depends on the propagation environment. However variations are relatively small in frequency domain over a 0 MHz bandwidth. In the NLOS scenario, the polarization of the signals is destroyed due to multiple reflections, diffractions or scattering. The difference between the XPD v and XPDH highly depends on the specific propagation environment between the transmitter and the receiver. Comparison of the capacity further shows that the performance gain of VV and HH channel over VH and HV channel is less in NLOS scenario compared with that in LOS scenario. ACKNOWLEDGMENT The authors would like to thank the German Ministry for Education and Research (BMBF) for the support in the projects 3GeT and EASY-C. The authors would also like to thank Udo Kriiger, Thomas Wirth, Yosia Hadisusanto, Matthias Mehlhose, Stefan Schiffermiiller and Kai Bomer for preparing and performing the measurement. Efforts from Gerd Sommerkom and Steffen Warziigel are also gratefully appreciated. REFERENCES [1] M. A. Jensen and J. W. Wallace, "A review of antennas and propagation for MIMO wireless communicationss (invited paper)," IEEE Trans. Antennas Propagat., vol. 5, pp , Nov [] G. F. Foschini and M. J. Gans, "On limits of wireless communication in a fading environment when using multiple antennas," Wireless Pers. Commun., vol. 6, no. 3, pp , [3] P. Kyritsi, D. C. Cox, R. A. Valenzuela, and P. W. Wolniansky, "Effect of antenna polarization on the capacity of a multiple element system in an indoor environment," IEEE J. Select. Areas Commun., vol. 0, pp , Aug. 00. [4] X. Zhao, S. Geng, L. Vuokko, J. Kivinen, and P. Vainikainen, "Polarization behaviors at, 5 and 60 GHz for indoor mobile communications," IEEE 1. Select. Areas Commun., vol. 7, pp , Nov [5] J. W. Wallace, M. A. Jensen, A. L. Swindlehurst, and B. D. Jeffs, "Experimental characterization of the MIMO wireless channel: Data acquisition and analysis," IEEE Trans. Wireless Commun., vol., pp , Mar [6] V. R. Anreddy and M. A. Ingram, "Capacity of measured Ricean and Rayleigh indoor MIMO channels at.4 GHz with polarization and spatial diversity," in Proc. IEEE WCNC, vol., pp , 006. [7] P. Soma, D. S. Baum, V. Erceg, R. Krishnamoorthy, and A. 1. Paulraj, "Analysis and modeling of multiple-input multiple-output (MIMO) radio channel based on outdoor measurements conducted at.5 GHz for fixed BWA applications," in Proc. IEEE Int. Conf. Commun., vol. 1, pp. 7-76, 00. [8] W. Q. Malik, "Polarimetric characterization of ultrawideband propagation channels," IEEE Trans. Antennas Propagat., vol. 56, pp , Feb [9] V. Jungnickel, V. Pohl, H. Nguyen, U. Kiiger, T. Haustein, and C. von Helmolt, "High capacity antennas for MIM0 radio systems," in Proc. 5th WPMC, vol., pp , 00. [10] L. Jiang, L. Thiele, and V. Jungnickel, "On the modelling of polarized MIMO channel," in Proc. Europ. Wireless 007, (Paris), Apr.I [Online]. Available: [11] H. Asplund, J.-E. Berg, F. Harrysson, 1. Medbo, and M. Riback, "Propagation characteristics of polarized radio waves in cellular communications," in Proc. IEEE Veh. Tech. Conf., pp , 30 Sept.-3 Oct [1] C. Oestges, V. Erceg, and A. J. Paulraj, "A physical scattering model for MIM0 macrocellular broadband wireless channels," IEEE J. Select. Areas Commun., vol. 1, pp , June 003. [13] M. Shafi, M. Zhang, A. L. Moustakas, P. J. Smith, A. F. Molisch, F. Tufvesson, and S. H. Simon, "Polarized MIMO channels in 3-D: Models, measurements and mutual information," IEEE J. Select. Areas Commun., vol. 4, pp , Mar. 006.