8/6/2019 Propagation Char. of Electric Field

1/5

PROPAGATION CHARACTERISTICS OF HORIZONTALL Y ANDVERTICALLY POLARIZED ELECTRIC FIELDS IN AN INDOORENVIRONMENT: SIMPLE MODEL AND RESULTSPersefoniKyritsi,Donald C. oxDavid Packard Electrical Engineering Building350 Serra Mall, Stanford UniversityStanford, CA 94305-95 15

Abstract- In this paper we will present measurement resultsthat demonstrate the different propagation characteristics ofthe vertical and horizontal polarizations and their cross-correlation coupling under line-of-sight and non-line-of-sight conditions. We will also present a simplified model forthe propagation environment that uses an approach similarto the method of images, and achieves results that match themeasurements.I. INTRODUCTION

Assume an indoors wireless system and let for examplethe transmitter antenna be a vertically polarized dipole.Depolarization is defined as coupling, due to the interactionwith the environment, into a state of polarization orthogonalto the original state of polarization, so that some of thepower incident at the receiver may be carried by ahorizontally polarized wave. Such coupling occurs as aresult of oblique reflections from the walls as well as due toscattering from indoor clutter, such as furniture. Reflectionoff horizontal and vertical surfaces such as the floors, theceiling, or the walls would otherwise preserve thetransmitted polarization.The propagation of polarized electric field has beenextensively studied in the context of polarization diversityfor portable communications systems [11. Polarizationdiversity is a technique that mitigates deep fading due torandom handset orientation and multi-path propagation.A different context within which the effect of electricfield polarization has been studied is the area of computer-based tools for propagation prediction [2]-[3]. The purposeof such tools is to avoid over-designing indoors wirelesssystems, or performing costly site-specific measurementsand still provide sufficient propagation prediction. Thesetools estimate the average signal strength over an area a fewwavelengths across. They are also used to calculate theaverage interference power from adjacent co-channel base-stations. Polarization of the electric field is considered inthese tools to assess depolarization losses.The field of multiple element communications systemshas renewed the interest in the propagation characteristics ofhorizontally and vertically polarized electric fields. Suchsystems have been developed to maximize the achievabledata rates for wireless applications. Their spectral efficiency

0-7 803-700 5 -8101B10.000 2001 IEEE 1422

depends on the average received power as well as thedecorrelation properties of the equivalent sub-channels. Theissue of polarization is pertinent because polarizationcoupling tends to result in a lower average received power(most of the energy stays in the same polarization), but itresults in a higher sub-channel decorrelation.11. METHOD F IMAGES FORWAVEGUIDES

The method of images is commonly used to analyzeelectromagnetic problems in the presence of perfectlyconducting boundaries.A . Point Source Abov e Infinite Pelfectly Condu cting Plane

Assume a perfectly conducting plane that extendsinfinitely on the plane y=O, and a point source at a location(0, d, 0), d>O. We want to calculate the electric field at anypoint (x,y,z) in the positive y half-space (we know that theelectric field is zero at any point in the negative y half-space). An equivalent representation is to assume the imageof the original source at the point (0, -d, 0) and to neglectthe perfectly conducting surface. The electric field can thenbe calculated as the sum of the electric fields of the originalsource and its image. If the source is vertically polarized,then the reflection coefficient off the conductor is 1 and theimage has the same sign as the original. If the source ishorizontally polarized, then the reflection coefficient off theconductor is -1, and the image has the opposite sign. Thesesign adjustments are necessary for the satisfaction of theboundary conditions on the plane y=O.If the boundary is NOT perfectly conducting but ratherthe surface of a dielectric material, then the above approachcan be used as an approximation of the true physical picture.If R is the reflection coefficient off the surface, then thetransmitted signal from the image will be scaled by R.B. Point Source Between Tw o Infinite PeflectlyConducting Planes

Again assume a point source at a location (0, d, 0)between two infinite perfectly conducting planes y=-a andy=a (Idlea). An equivalent picture would be to assume noperfectly conducting boundaries and an infinite string ofimage sources at locations (0 ,2na+(-l)"d, 0), for n integer.

8/6/2019 Propagation Char. of Electric Field

2/5

Again if the reflection coefficient is R, then the signal fromthe nth mage will be scaled by RI.In the lossless case, one would have to consider aninfinite number of images. In the lossy case, the strength ofthe images decreases with distance and one need onlyconsider a limited number thereof.C . Point Source in a Waveguide

Assume an infinite waveguide, parallel to the z axiswith perfectly conducting boundaries at the planes x=+a,y=+b, as in Fig. 1. Assume a point source at a location(d,,d,,O) (Id,l

8/6/2019 Propagation Char. of Electric Field

3/5

8/6/2019 Propagation Char. of Electric Field

4/5

-60

-70

.s -80

-90

E%zLPI

-100

Horizontalpolarization(//walls)

Vertical(I alls)polarization

Ee3c.-LHa

RX RY.\/=. - E , cos e,,/m2E , cos e,,/= e . - cos e,4 e . +COS ei

1

-1

-100 '10' 1o2 IO' 1o2D ist ance (R) D ist ance (R)V t o H V t o V

-100 IIO' 1o2 1o3D ist ance (R) D ist ance (R)Fig. 6: Power dependence on distance in the labsIndeed even graphically we notice that power falls off as

d There is a loss of about 15dB incurred by going into thelabs and losing the strong line-of-sight component relativeto the hallway. We observe that the cross-polarizationcoupling in the labs is much higher (-3dB). Finally thesystem behavior is similar for all antenna orientations.VI. COMPARISONITHTHEORY

We considered two sets of elements. The first setcontained only vertically polarized elements on both thetransmitter and the receiver sides (the mildly shadedelements in figure 2). The second set contained onlyhorizontally polarized elements (the more shaded elementsin figure 2). This will enable some spatial averaging, butwill avoid the computational complexity of including allantenna elements.For each set of antennas, we considered distancesbetween loft and 250 ft, with a step size of loft. The fieldfrom each transmitter to each receiver was calculated as thesum of the fields from its images. This is equivalent tocoherent addition as opposed to incoherent addition of thesignals that would only sum the powers. The power wasthen averaged over all combinations.In order to account for the fact that the method of imagescannot describe complex structures such as the intersectingcorridor, we present the results for distances greater than50ft. Also in order to normalize for the transmit power, thesimulated and the measured data were set to the same valueat a distance of 60ft. This will allow us to study the roll-offbehavior independently of the absolute power levels.Fig. 7 shows the results of our comparison. We observethat indeed the method of images captures the polarizationeffect that was experimentally observed. The power roll-offis faster for the horizontally polarized waves (polarizationparallel to the walls). We also observe that it overestimatesthe roll-off factor a.

1425

8/6/2019 Propagation Char. of Electric Field

5/5

1 I 1- easured H toH 1 I35 -.-. M. of Images H toHMeasured V to V

I I I J50 la, 150 200 250

Distance in feet-65

Fig. 7: Comparisonof themeasurements to the Method of ImagesThe discrepancies are due to the larger step size in thecalculation with the method of images, the imperfectknowledge of the dielectric properties of the material of thewalls, and the inherent limitations of the method of images.The floor and the ceiling are assumed to be perfectlyconducting, which they are not. They are also assumed to beperfectly smooth, which they also are not. Imperfectionswould increase back-scattering and cross-polarizationcoupling. It is also assumed that the ceiling is at a constantheight, however the position of the reflecting surfacesvaries. As for the walls, we have ignored the existence ofdoors and openings that allow coupling into the rooms.Finally this very simple model cannot capture the effect ofcross-polarization coupling.

VII. CONCLUSIONSIn this paper, we presented measurement results thatdemonstrate the different propagation characteristics of thevertical and horizontal polarizations.The measurements showed that power falls off faster forhorizontally polarized waves under strong line-of-sightconditions in a hallway, whereas this is not so when theline-of-sight component is not dominant. The explanationfor this phenomenon is the following: in a hallway the floorand the ceiling can be treated as perfectly conductingsurfaces, whereas the walls are more closely approximatedas dielectric materials. Under those conditions horizontally

polarized waves (polarization parallel to the walls) undergo

a Brewster angle phenomenon and penetrate the walls withlittle reflection back into the hall. Vertically polarized wavesdo not suffer a similar effect and remain constrained in thehall way.The cross-polarization levels under strong line-of-sightconditions are around -15 dB. In the labs however the cross-polarization is -3dB, and the two polarizations displaysimilar power roll-off behaviors.We verified these experimental results by introducing asimple model using the method of images. This mode,because of its abstraction, fails to capture the cross-polarization effects. It deviates for the measurements since itis not an accurate ray-tracing tool, specific for thisenvironment. However it successfully captures the differentpower roll-off behavior for the horizontal and the verticalpolarized signals.REFERENCES

[11 S.A. Bergmann, H.W. Arnold, Polarization diversity inportable communications environment, ElectronicLetters, May 22 , 1986, Vol. 22 , No. 11, pp. 609-610.[2] D.Chizhik, J. Ling, R.A. Valenzuela, The effect ofelectric field polarization on indoor propagation,International Conference on Universal PersonalCommunications 98 (ICUPC 98), 1998, pp.459-462.

31 R.A. Valenzuela, D. Chizhik, J. Ling, Measured andpredicted correlation between local average power andsmall scale fading in indoor wireless communicationschannels, IEEE Vehicular Technology Conference,Ottawa, May 1998.41 D. Cox, R. Murray, H. Arnold, A. Norris, M.Wazowicz, Cross-polarization coupling measured for800MHz radio transmission in and around houses andlarge buildings, IEEE Trans. on Antennas andPropagation, Vol. AP-34, No.1, Jan. 1989, pp. 83-87.[5] D.M.J. Devasirvatham, Time delay spread and signallevel measurements of 850 MHz radio waves inbuilding environments, E E E Trans. on Antennas andPropagation, Vol. 34, No.11, November 1986.[6] D.M.J. Devasirvatham, A comparison of delay spreadand signal level measurements within two dissimilaroffice buildings, IEEE Trans. on Antennas andPropagation, Vol. 35, No.3, March 1987, pp. 319-324.[7] R.R. Murray, H.W. Arnold, D.C. Cox, 815 h4HzRadio attenuation measured within a commercialbuilding, Symp. Digest IEEE Antennas andPropagation Symposium, Philadelphia, PA, June 9- 13,1986, pp. 209-212.

I426