Polytechnic University
Raleigh and Ricean Fading Lab
Adapted from Polytechnic University lab by Henry L. Bertoni
I. INTRODUCTION
Propagation characteristics of radio signals in the UHF (300 MHz - 3 GHz) band place fundamental limits on the design and performance of wireless personal communications systems, such as cellular mobile radio (CMR), wireless LAN’s and Personal Communication Services (PCS). This experiment is intended to introduce students to the characteristics commonly found for narrow band CW excitation when the transmitter and receiver are located on the same floor inside a large office building.
A. Outdoor Propagation
During the development of CMR, knowledge of the channel was gained almost entirely through measurements, which defined the basic measurement methodology for narrow band signals. For the typical urban CMR propagation path, the base station is located above the surrounding buildings while the subscriber is located at street level and is surrounded by buildings so that the base station is not within the line-of-sight (LOS). The signal received as the subscriber moves along a street is indicated in Figure 1, and is seen to involve fades that can be as large as 20 dB and are separated by about one half wavelength.
For signals that are not-line-of-sight (NLOS), the variation over a segment of 20 or so wavelengths is treated as a random variable. Its distribution function is typically found to be that of a Rayleigh distribution. This Rayleigh fading, or fast fading, is due to the interference of signals arriving at the mobile from all directions as a result of reflections and scattering by buildings, vehicles and other obstacles in the vicinity of the subscriber [1,2]. The fast fading is similar to the standing wave pattern set up by waves propagating in opposite directions. However, it is due to waves arriving with roughly equal amplitudes from all directions in the horizontal plane. As a result, similar patterns are found when moving horizontally in any direction, and each pattern loses correlation with itself after about one half wavelength [2]. Similar patterns are found for all polarizations of the subscriber antenna, but the patterns for orthogonal polarizations are uncorrelated [3,4]. Fading is also observed for a stationary subscriber if the frequency is swept slowly, since the differential phases of the various multipath components change rapidly with requency[5]. Fading will even be observed by a stationary subscriber operating at a constant frequency due to motion of scatters, such as people, vehicles and trees, in the vicinity of the subscriber [6, Sec. VI].
The Probability Density Function (PDF) of the Raleigh-distributed random variable is given by equation 4.49 in your text:
[pic]
This tells you the probability that the rms VOLTAGE will be equal to v.
The standard deviation, (, is:
[pic]
Where is the average rms voltage over the sector being measured.
The Cumulative Distribution Function (CDF) of the Raleigh-distributed random variable is given by equation 4.50 of your text:
[pic]
The CDF tells you the % probability that the voltage will be above V. (Question 2)
On line-of-sight (LOS) paths the direct ray is substantially stronger than the rays reflected from buildings, or scattered from cars and other objects. As a result, the fast fading statistics are Ricean, rather than Rayleigh [6 Appendix II, 25]. The probability density function for the Ricean distributed random variable is shown in Figure 4.18 of your text and is given by equation 4.55.
When the signal is averaged over a distance of 20 or so wavelengths, the result is referred to as the sector average, several of which are shown as dots in Figure 2. The sector average will be used to compute the large-scale path loss. Variation of the sector average as the subscriber moves along the street is known as slow fading or shadow fading since the scale over which it takes place is on the order of building widths. Averages for a group of sectors at the same distance from the base station may again be treated as a random variable, and their variation about the overall average is typically found to have a log normal distribution. More commonly, the slow fading statistics are obtained by plotting the sector averages in dB versus distance R from the base station on a logarithmic scale, as in Figure 2. A regression or least-squares fit, which is a straight line of the type shown in Figure 2, is then made to the data. The regression fit corresponds to the range dependence A/Rn, where A is an amplitude constant and n is the slope index. For two antennas located in free space, the value of n is 2. The deviations of the sector averages in dB from the fit line are then treated as a random variable, which is typically found to have a Gaussian or normal distribution, corresponding to a log normal distribution of the received signal in Watts normalized to A/Rn. For measurements made over a wide area of a city, the slow fading distributions can have a standard deviation of as much as 8 dB.
The log normal character of the slow fading distribution has been observed in many environments, both outdoor and indoor, and appears to be due to the fact that several random processes act on the signal in sequence. Since multiplication by a sequence of random variable is equivalent to their addition when expressed in dB, and since the sum of several random variables tends to a Gaussian or normal distribution [8], the signal in dB tends towards a normal distribution.
B. In-Building Propagation
When base station and subscriber are located inside a building, many paths exist by which the signal can propagate between them. Since both are located in the clutter, fast fading will be observed when either is moved. If a LOS path exists between them, such as down a hallway, the fast fading statistics are Rician, otherwise they are Rayleigh [8,9]. Following the tradition established for the macrocells of CMR, a sector average signal is usually defined by averaging the signal measured as one end of the radio link is moved over a path whose length is about 20λ. To fit within a room, this is frequently accomplished by moving the link end in a circle of radius 1 m from 900 MHz signals, or on a raster path, or cross, as will be used for these measurements. The fast fading pattern measured on a circular path is shown in Figure 3.
When reporting in-building measurements over a single floor, investigators typically plot the signal in dB versus the direct line distance R between base station and subscriber on a logarithmic scale. For propagation down hallways, the measurements indicate a 1/Rn signal dependence with n less than the value 2 for free space [10]. For propagation through rooms and walls, the slope index n is larger than 2, and increases rapidly with R[10,11]. For propagation between floors, a different dependence is obtained [12].
III. Data Processing and Report
Prepare a report that will first examine the fast fading characteristics at a line-of-sight (LOS) sector and at a non-LOS sector, and their dependence on polarization. The sector averages will then be compared for all sectors as a function of distance from the transmitter.
Data is given in an excel spreadsheet for this lab. You may use any method to program this assignment. To use the data in something other than Excel, just open the file and cut-and-paste the data into another file type of your choosing. V=vertical polarization, H=horizontal polarization. The transmitting antenna is in the vertical polarization. Frequency = 915 MHz.
A. Fast Fading
Plot values of voltage for both polarizations on the same graph for each sector.
For your write up discuss the differences between the plots for LOS versus non-LOS propagation.
1. The difference in average signal for the two polarizations
2. The range in dB of the signal variation for each polarization
3. The location of the minima and maxima for the two polarizations.
4. The average separation between minima in wavelengths.
B. Fast Fading Statistics
1. Analytical Models for Raleigh and Rician distributions
Verify the PDF (Figure 4.16 of Rappaport) and CDF (Figure 4.17 of Rappaport) for the Raleigh Distribution using equations 4.49 and 4.50. When do you expect the data to follow a Raleigh distribution?
Verify the PDF (Figure 4.18 of Rappaport) for the Rician Distribution using equations 4.55 using various values of K. Verify the CDF (Figure 4.17 of Rappaport) by integrating or adding up the values of the PDF. When do you expect the data to follow a Rician distribution? Note: You can find Io(x) using the Bessel function operator in Matlab.
2. Measured data
Use the data given in the spread sheet. There are 100 values of signal for each sector, and these can be treated as a random variable. Data are measured 1 inch apart in sectors that are defined (distance) on the attached floorplan of the building. You will not need to know the exact distance for fast fading statistics. Construct the cumulative distribution function (CDF) and probability distribution function (PDF) of your data by following the directions below.
It is first necessary to convert the dBm values measured into normalized voltage (vn = 10dBm/20 for n = 1, 2, ..., 100). Then compute the average of the set vn and normalize the signals to the average to produce vn/. Convert the normalized values back into dB, that is define Vn = 20log)Vn/). Count the number Np of measurement points for which Vn lies in the range Vn < p + 0.5 for p = -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8 dB. This gives you the PDF. To find the CDF, you will integrate (add up) the number of measurement points (Np) that have Vn ( p+0.5. This means that in making this count for any value of p, you will include all the points counted for p-1, in addition to those for which Vn is between p -0.5 and p + 0.5. This result of this count is the CDF, in percent, of the set of 100 measurements.
Prepare a cumulative distribution function using the foregoing procedure for both polarizations for all sectors. Compare them to the Raleigh and Rician distributions computed using the analytical equations by plotting them on the same graph.
In your report, discuss which of the CDF’s most closely follow a Rician distribution, and which most closely describe a Rayleigh distribution.
C. Distance Dependence (Large Scale Fading)
In order to determine how the sector average path loss depends on distance from the transmitter, it is first necessary to convert the measured signal into path loss PL in dB, which is defined in terms of the ratio of received power to transmitted power as
PL = - 10 log(Preceived/Ptransmitted).
Since PL depends on the antenna gains and cable losses, by subtracting the path loss a 1 m separation PL(1), we are left with effects due only to the building. Thus we can determine the path loss relative to 1 m separation, PL - PL(1), using the calibration measurements.
For each group of 5 calibration measurements, convert the dBm values to watts. Average the 5 values and re-convert to dBm. For the two sets of sector measurements made with the same antenna and spectrum analyzer, subtract the average in dBm just found from each member of the set of 100 measured values, and subtract 14 dB corresponding to the increase in the transmitted power in going from the calibrations to the sector measurements. The result is then the negative of PL - PL(1) in dB. Now computer the average of the 100 values of PL - PL(1). Note that since you will only use the average, you may average the 100 sector measurement values first, and then subtract the calibration average and 14 dB.
Using the floor plan, find the distance R between the transmitter and each sector. On a piece of semi-log graph paper (or using Matlab or similar), plot in dB on the uniform axis versus R on the logarithmic axis for each polarization and each sector. Draw a straight line between the vertical polarization averages for the LOS paths. Fit a straight line to all other (non-LOS) vertical polarization sector averages. Fit a third straight line to all horizontal polarization sector averages. Computer the slopes of the three straight lines in dB per decade of R. Note that for antennas in free space the slope is 20 dB/decade corresponding to a spatial dependence of 1/R2 for the received power.
In your write up discuss the difference in the slopes of the three lines in relation to free space propagation. Also discuss the relative signal amplitude on LOS and non-LOS paths, and for vertical and horizontal polarization.
IV. References
[1] G.L. Turin et at., “A Statistical Model of Urban Multipath Propagation,” IEEE Trans.on Veh.Tech., VT-21, pp. 1-9, 1972.
[2] W.C.Y. Lee, Mobile Communications Engineering, McGraw-Hill Book Co..., New York, Chapters 1, 6, 1982.
[3] W.C.Y. Lee and Y.S. Yeh, “Polarization Diversity System for Mobile Radio,” IEEE Trans. On Comm., COM-20, pp. 912-913, 1972,
[4] R.G. Vaughn, “Polarization Diversity in Mobile Communications,” IEEE Trans. On Veh. Tech., VT-39, pp. 177-186, 1990.
[5] D.L. Shilling, “Broadband-CDMA: A PCS Wireless Technology to Achieve Wireline Quality and Maximize Spectral Efficiency,” in Wireless Personal Communications, M.J. Feuerstein and T.S. Rappaport, Eds., Kluwer Academic Publishers, Boston, pp. 77-91, 1993.
[6] N.H. Shepherd et al “Coverage Prediction for Mobile Radio Systems Operating in the 800/900 MHz frequency Range,” Special Issue IEEE Trans. Veh. Tech., VT-37, pp. 3-72, 1988.
[7] C. Chrysanthou and H.L. Bertoni, “Variability of Sector Averaged Signals for UHF Propagation in Cities,” IEEE Trans. On Veh. Tech., VT-39, pp. 352-358.
[8] R.J.C. Bultitude, S. Mahmoud and W. Sullivan, “A Comparison of Indoor Radio Propagation Characteristics at 910 MHz and 1.75 Ghz,” IEEE Jnl. On Selected Areas in Comm., 7, pp 40-48, 1989.
[9] T.S. Rappaport and C.D. McGillen, “UHF Fading in Factories,” IEEE Jnl. On Selected Areas in Comm., 7, pp 4048, 1989.
[10] J.F. Lafortune, M. Lecours, “Measurement and Modeling of Propagation Losses in a Building at 900 MHz,” IEEE Trans. On Veh. Tech., vol. VT-39, May 1990, pp. 101-108.
[11] W. Honcharenko, H.L. Bertoni, J. Dailing, J. Qian, H.D. Yee, “Mechanism Governing Propagation on Single Floors in Modern Office Building”, IEEE Trans. On Veh. Tech., 41, pp. 496-504, 1992.
[12] W. Honcharenko, H.L. Bertoni, J. Dailing, “Mechanism Governing Propagation Between Different Flors in Buildings”, IEEE Trans. On Veh. Tech., VT-42, pp. 787-790, 1993.
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