OF
C.
David Packard Electrical Engineering Building
350 Serra Mall, Stanford University
Stanford, CA 94305-95 15
Abstract- In this paper we will present measurement results that demonstrate the different propagation characteristics of the 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 for the propagation environment that uses an approach similar to the method of images, and achieves results that match the measurements.
I. INTRODUCTION
Assume an indoors wireless system and let for example the transmitter antenna be a vertically polarized dipole.
Depolarization is defined as coupling, due to the interaction with the environment, into a state of polarization orthogonal to the original state of polarization, so that some of the power incident at the receiver may be carried by a horizontally polarized wave. Such coupling occurs as a result of oblique reflections from the walls as well as due to scattering from indoor clutter, such as furniture. Reflection off horizontal and vertical surfaces such as the floors, the ceiling, or the walls would otherwise preserve the transmitted polarization.
The propagation of polarized electric field has been extensively studied in the context of polarization diversity for portable communications systems [ 11. Polarization diversity is a technique that mitigates deep fading due to random handset orientation and multi-path propagation.
A different context within which the effect of electric field polarization has been studied is the area of computer- based tools for propagation prediction [2]-[3]. The purpose of such tools is to avoid over-designing indoors wireless systems, or performing costly site-specific measurements and still provide sufficient propagation prediction. These tools estimate the average signal strength over an area a few wavelengths across. They are also used to calculate the average interference power from adjacent co-channel base- stations. Polarization of the electric field is considered in these tools to assess depolarization losses.
The field of multiple element communications systems has renewed the interest in the propagation characteristics of horizontally and vertically polarized electric fields. Such systems have been developed to maximize the achievable data rates for wireless applications. Their spectral efficiency depends on the average received power as well as the decorrelation properties of the equivalent sub-channels. The issue of polarization is pertinent because polarization coupling tends to result in a lower average received power
(most of the energy stays in the same polarization), but it results in a higher sub-channel decorrelation.
11. OF IMAGES FOR WAVEGUIDES
The method of images is commonly used to analyze electromagnetic problems in the presence of perfectly conducting boundaries.
A . Point Source Above Infinite Pelfectly Conducting Plane
Assume a perfectly conducting plane that extends infinitely 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 any point (x,y,z) in the positive y half-space (we know that the electric field is zero at any point in the negative y half- space). An equivalent representation is to assume the image of the original source at the point (0, -d, 0) and to neglect the perfectly conducting surface. The electric field can then be calculated as the sum of the electric fields of the original source and its image. If the source is vertically polarized, then the reflection coefficient off the conductor is 1 and the image has the same sign as the original. If the source is horizontally polarized, then the reflection coefficient off the conductor is -1, and the image has the opposite sign. These sign adjustments are necessary for the satisfaction of the boundary conditions on the plane y=O.
If the boundary is NOT perfectly conducting but rather the surface of a dielectric material, then the above approach can be used as an approximation of the true physical picture.
If R is the reflection coefficient off the surface, then the transmitted signal from the image will be scaled by R.
B. Point Source Between
Conducting Planes
Two Infinite Peflectly
Again assume a point source at a location (0, d, 0) between two infinite perfectly conducting planes y=-a and y=a (Idlea). An equivalent picture would be to assume no perfectly conducting boundaries and an infinite string of image sources at locations (0, 2na+(-l)"d, 0), for n integer.
0-7 803-7005 -810 1 0 200 1 IEEE 1422

Again if the reflection coefficient is R, then the signal from the nth image will be scaled by RI”’.
In the lossless case, one would have to consider an infinite number of images. In the lossy case, the strength of the images decreases with distance and one need only consider a limited number thereof.
C. Point Source in a Waveguide
A8
P
MLLWAY
I
,
Fig. 2: Building layout
Assume an infinite waveguide, parallel to the z axis with 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<a,
I d, I<b). Removing the boundaries would create an infinite grid of images on the z=O plane at locations (2na+(- l)”d,, 2mb+(- l)md,, 0), n,m integers.
If R, is the reflection coefficient off the waveguide walls at x=+a, and R, the reflection coefficient off the walls at y=fb, then the signal from the image (n, m) should be scaled by R l ’ R y ‘ .
The roles of vertical and horizontal polarization depend on the surface of reference. The polarization for example that is ‘vertical’ with respect to the boundaries x=+a is
‘horizontal’ with respect to the boundaries y=+b.
If we approximate the hallway of a building as a waveguide, then the walls are better represented as dielectric materials while the floor and the ceiling are commonly better represented by high dielectric constant or conducting surfaces (reinforced concrete and corrugated steel being common building materials). In that case the vertical and horizontal polarization propagation characteristics are not identical. For the floor and the ceiling the reflection for both polarizations is high. However, the two polarizations have different reflection coefficients for reflections off the wall surfaces. The horizontally polarized waves (polarization parallel with respect to some walls) undergo a Brewster angle phenomenon, and penetrate the walls without any reflection at all. At angles near the Brewster angle, the reflection is not zero but still greatly reduced. No such effects are present for the vertical polarization
(perpendicular to the walls). Therefore one would expect lower received power for the horizontal polarization in the waveguide than for the vertical one. This simple model does not account for cross-polarization coupling.
B I B - + -
B I B
l L t
B I B
- + -
B I B
- + - -
‘ I ’
Fig. 1: Point source in an infinite waveguide
111.
The measurements were taken on the second floor of the
Lucent Crawford Hill Laboratory, a building that houses approximately 150 people. The hallway measurements were taken in the building’s main corridor, which is straight, 390- ft long, 6 feet wide and lined with offices (typically 10xlOft) on one side and laboratories (typically 12x24ft) on the other.
No measurements were taken in the second corridor that intersects the first one in a ‘T’ shape. Inside walls are built of wood and wallboard; outside walls are largely glass.
Ceilings and floors are made of reinforced concrete over steel plates. The average hallway height is 10 ft.
Both the transmitter and the receiver array were placed at a height of 6 feet. The transmitter array was placed 82.5 ft from the eastern end of the hallway and 2ft from the northern wall of the hallway, pointing west. The receiver was wheeled to the desired position along the hallway at- distances 3ft-246ft from the transmitter at 3 ft. In the labs, the receiver was again wheeled to the desired position, which was 8 ft north of the east-west line defined by the transmitter (Fig. 1).
The elements were folded cavity backed slot antennas mounted on 2’x2’ panels. These have a hemispherical gain pattern and measurements were taken for the east and west orientation in the hallway and all four cardinal orientations in the labs. 12 transmitters and 15 receivers were used, arranged in a square grid. The separation between adjacent elements was 8cm (a half wavelength) and the antennas were arranged with alternating polarizations as in Fig. 3 (H: horizontal, V: vertical).
The transmitted power was set to 9.2 dbm and was equally divided on all the transmitters. The frequency of operation was 1.95GHz, and the signal bandwidth was
30kHz.
TRANSMlTTER SIDE RECEIVER SIDE
Fig. 3: Antenna layout
1423

Previous measurements taken in the same building have shown that the delay spread is in the order of lp [ 5 ] , so for the purpose of this experiment we can assume the channel gain from each transmitter to each receiver to be a complex scalar (flat fading).
The transmitted signals are fully co-channel, that is they occupy the same frequency band. In order to calculate the channel complex gains, the system had incorporated a training phase that was k 2 0 symbols long. During this phase, each antenna transmitted a row of a MxL Fourier matrix (orthogonal rows), appropriately scaled to the transmit power. At the receivers the channel estimate was computed by applying the pseudo-inverse of the transmitted training matrix to the received training matrix (since the transmitted matrix was Fourier, its pseudo-inverse was simply the Hermitian transpose of the original matrix, so no pre-computation of the pseudo-inverse was required).
Synchronization was provided by a cable connecting the transmitter and the receiver arrays.
Let Tij be the channel complex gain between transmitter j and receiver i. The purpose of this study is to investigate the distance dependence of the received power as a function of the transmitter and receiver polarization. In order to achieve some spatial averaging, we will average over all transmit- receive pairs of the polarization in question. Let HT, HR be the sets of horizontally polarized transmitters and receivers respectively, and VT, VR be the sets of vertically polarized transmitters and receivers respectively. So for example when we study the cross-polarization coupling from a horizontally polarized transmitter to a vertically polarized receiver we will average the channel gain over the set HV =
{(i,j), i e V ~ , j € H T l . rv.
MEASUREMENT IN THE HALLWAY
Our results agree with the results presented in [7], as
shown in Fig. 4.
different frequency (815MHz/ 1.95GHz) and to the different antenna heights (loft/ 6 ft) in the two experiments.
-40
E
-45 c
-55
-60
-80
I
Average power roll-off with distance
HH 0.0162; 0.0178
I
;
I
50
I
100
I
150
Distance in feel
I
200
Fig. 5 Power dependence on distance in the hallway
250
A hallway can be modeled as a lossy waveguide where a e-& power roll-off law would apply. We fit a curve of the form e
-d
in Fig. 5.
We observe a steep power drop at about 40 ft. This is where power is coupled into the intersecting corridor. As expected, the loss factor is higher for the horizontal polarization. This effect becomes more pronounced if we concentrate on the distances larger than 50ft
neglect the effect of the inter-secting corridor. The cross- polarization loss is -15dB and the power roll-off factor is roughly the same for both cross-polarizations (0.019 ft-').
V.
An added parameter in the labs is the orientation of the antenna array. We fit curves of the form dad measured data. In table I, we present the values for the parameters a and y that we found and the corresponding errors. Clearly, E+<&, in a lab, and the average received power is better approximated as a d' function of distance, as one would expect in a rich scattering environment.
TABLE I ni.t.nc.
I" b.1
Fig. 4. Comparison with previous measurements
1424

-60
-70
E
%!
.s -80
L
PI z a
-90
-100
10'
-100
'
IO' 1 o2
Distance (R)
V t o H
1 o2
Distance (R)
V t o V
E e3
L
H a
-100 I
IO' 1 o2
Distance (R)
1 o3
Fig. 6: Power dependence on distance in the labs
Distance (R)
Indeed even graphically we notice that power falls off as d'. There is a loss of about 15dB incurred by going into the labs and losing the strong line-of-sight component relative to the hallway. We observe that the cross-polarization coupling in the labs is much higher (-3dB). Finally the system behavior is similar for all antenna orientations.
Horizontal polarization
(//walls)
Vertical polarization
VI.
RX
1
-1
We considered two sets of elements. The first set contained only vertically polarized elements on both the transmitter and the receiver sides (the mildly shaded elements in figure 2). The second set contained only horizontally polarized elements (the more shaded elements in figure 2). This will enable some spatial averaging, but will avoid the computational complexity of including all antenna elements.
For each set of antennas, we considered distances between loft and 250 ft, with a step size of loft. The field from each transmitter to each receiver was calculated as the sum of the fields from its images. This is equivalent to coherent addition as opposed to incoherent addition of the signals that would only sum the powers. The power was then averaged over all combinations.
In order to account for the fact that the method of images cannot describe complex structures such as the intersecting corridor, we present the results for distances greater than
50ft. Also in order to normalize for the transmit power, the simulated and the measured data were set to the same value at a distance of 60ft. This will allow us to study the roll-off behavior independently of the absolute power levels.
RY that indeed the method of images captures the polarization
.\/=
,/m2
Fig. 7 shows the results of our comparison. We observe is faster for the horizontally polarized waves (polarization parallel to the walls). We also observe that it overestimates the roll-off factor a.
-
,/=
4 e . - cos e, e.
+COS e i
1425

-35
1 I
1
-
H toH
-.-.
M. of Images H toH
Measured V to V
1
I
-65‘
50
I la,
I
150
Distance in feet
I
200
J
250
Fig. 7: Comparison of the measurements to the Method of Images
The discrepancies are due to the larger step size in the calculation with the method of images, the imperfect knowledge of the dielectric properties of the material of the walls, and the inherent limitations of the method of images.
The floor and the ceiling are assumed to be perfectly conducting, which they are not. They are also assumed to be perfectly smooth, which they also are not. Imperfections would increase back-scattering and cross-polarization coupling. It is also assumed that the ceiling is at a constant height, however the position of the reflecting surfaces varies. As for the walls, we have ignored the existence of doors and openings that allow coupling into the rooms.
Finally this very simple model cannot capture the effect of cross-polarization coupling.
VII. CONCLUSIONS
In this paper, we presented measurement results that demonstrate the different propagation characteristics of the vertical and horizontal polarizations.
The measurements showed that power falls off faster for horizontally polarized waves under strong line-of-sight conditions in a hallway, whereas this is not so when the line-of-sight component is not dominant. The explanation for this phenomenon is the following: in a hallway the floor and the ceiling can be treated as perfectly conducting surfaces, whereas the walls are more closely approximated as dielectric materials. Under those conditions horizontally polarized waves (polarization parallel to the walls) undergo a Brewster angle phenomenon and penetrate the walls with little reflection back into the hall. Vertically polarized waves do not suffer a similar effect and remain constrained in the hall way.
The cross-polarization levels under strong line-of-sight conditions are around -15 dB. In the labs however the cross- polarization is -3dB, and the two polarizations display similar power roll-off behaviors.
We verified these experimental results by introducing a simple 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 it is not an accurate ray-tracing tool, specific for this environment. However it successfully captures the different power roll-off behavior for the horizontal and the vertical polarized signals.
REFERENCES
[ 11 S.A. Bergmann, H.W. Arnold, “Polarization diversity in portable communications environment”, Electronic
Letters, May 22, 1986, Vol. 22, No. 11, pp. 609-610.
[2] D.Chizhik, J. Ling, R.A. Valenzuela,
“
The effect of electric field polarization on indoor propagation”,
International Conference on Universal Personal
Communications ’98 (ICUPC ’98), 1998, pp.459-462.
31 R.A. Valenzuela, D. Chizhik, J. Ling, “Measured and predicted correlation between local average power and small scale fading in indoor wireless communications channels”, IEEE Vehicular Technology Conference,
Ottawa, May 1998.
41 D. Cox, R. Murray, H. Arnold, A. Norris, M.
Wazowicz, “Cross-polarization coupling measured for
800MHz radio transmission in and around houses and large buildings”, IEEE Trans. on Antennas and
Propagation, Vol. AP-34, No.1, Jan. 1989, pp. 83-87.
[5] D.M.J. Devasirvatham, “Time delay spread and signal level measurements of 850 MHz radio waves in building environments”, E E E Trans. on Antennas and
Propagation, Vol. 34, No.11, November 1986.
[6] D.M.J. Devasirvatham,
“
A comparison of delay spread and signal level measurements within two dissimilar office buildings”, IEEE Trans. on Antennas and
Propagation, Vol. 35, No.3, March 1987, pp. 319-324.
[7] R.R. Murray, H.W. Arnold, D.C. Cox, “815 h4Hz
Radio attenuation measured within a commercial building”, Symp. Digest IEEE Antennas and
Propagation Symposium, Philadelphia, PA, June 9- 13,
1986, pp. 209-212.
I426