With Path Loss Exponent
At Geogia Tech
Stephen Gesualdo, Student, Georgia Institute of Technology
Propagation models used today by many cellular companies need updating. These old models were designed for users in vehicles traveling on roads, where there is low path loss. However, since the implementation of these models indoor use of cell phones has increased heavily. Building penetration loss and shadowing effects add considerable loss of power for indoor users. Updated propagation models accounting for these losses are necessary in order to reduce outages for the indoor consumer.
This section describes the theory behind the proposed propagation model. A discussion of the link budget equation, path loss exponent, and antenna gain introduces an explanation of the construction of the model.
Path Loss and Path Loss Exponent
Path loss is defined as the ratio between transmitted power and received power after antenna gains and system losses have been controlled for. The link budget equation, given in Eq. 1, shows this relationship in log form (dBm):
where PT and PR are in dBm, GT and GR are in dB, and PL is with respect to 1 meter in freespace . This path loss includes distance dissipation and also losses due to shadowing and penetration. A general path loss exponent can be used in order to approximate path loss a region. Using the path loss exponent, n, path loss would take on the form in Eq. 2:
The path loss exponent is specific to the propagation environment. The value of n is 2 for free space and larger when obstructions are present . For practical use, n can be found for an area if path loss measurements are taken at known distances using the following equation:
Measurements taken around the Georgia Tech campus produce a path loss exponent of 3.4, which is consistent with values measured in suburbs . The link budget equation with path loss exponent of 3.4 was used in the proposed model, along with antenna directivity, discussed in the next section.
Antenna gain is determined by the shape of the antenna. Antenna gain patterns are a function of azimuth and elevation and have an associated half-power bandwidth. Generally, the gain of an antenna is higher when the directivity is more concentrated, i.e., the antenna has a lower half-power bandwidth. Antennas have an associated efficiency. Gain can be described by:
Where G is gain, φ is azimuth, θ is elevation, and Ae is the effective aperture. Effective aperture is related to the size and shape of the antenna and is also a function of azimuth and elevation .
For the proposed model, the shape of the antenna is unknown. A general pattern for the gain of the antenna can be deduced from data of power received around the antenna. The directivity of the antenna used in the model has a cos3/4(φ) dependency, with an associated half-power bandwidth of 133o.
To more effectively model wave propagation for indoor and outdoor users, the proposed model uses the link budget equation in equation 1 with a path loss exponent. A path loss exponent of 3.4 was obtained using recorded data from around the Georgia Tech campus, including indoor measurements, from 3 different antenna sites. The data was plugged into Equation 3 to obtain the value. The model employs a gain pattern with a cos3/4(φ) dependency and a constant multiplier of 25, which corresponds to peak gain. These values were obtained from measurements around the Georgia Tech campus. The receiver gain was not given. Using the measured data and the wavelength corresponding to the given frequency of 850 MHz as 35.3 cm, a constant value of 7 dB is added to the model. A few other key concepts having to do with location of the antennas are taken into account in the model.
The transmitting antennas are located on the tops of buildings. The propagating waves can travel over buildings and trees with relatively low loss. Directly behind buildings loss may be high due to shadowing effects, but far behind the building loss may actually not be severe due to propagation over the building. Thus path loss may not drop off with the path loss exponent at far distances. In addition, electromagnetic noise levels have been measured as high as -80 dBm at industrial and inner city commercial sites . For these reasons, the proposed model does not exceed -83 dBm.
The location of the antennas also effects power received at small distances from the transmitter. Measuring received power next to or inside of the building that carries the transmitter antenna entails large penetration loss, and is also constrained by the directivity of the transmitter with respect to elevation. For this reason, a level maximum level of -50 dBm is imposed on the model.
The transmitter gain is primarily focused “forward.” Antenna gain behind the antenna is dramatically reduced; the power has been reflected to the front of the antenna. The proposed model has a maximum power of -70 dBm behind the antenna.
The model was coded using Matlab 7.0. The code for the model can be found in Appendix A.
The proposed model was tested for 4 different antennas at 3 different locations in the Georgia Tech campus. The model was run using Matlab 7.0 and tested against measured data for each of the 4 antennas. The average error of the model was computed during the test in the form of standard deviation and mean error. The model obtained a standard deviation of 10.4 dB and a mean error of 2.6 dB. Figures 1 and 2 show the measured and modeled data for antenna A.
Fig. 1. Measured power received from antenna A. Fig. 2. Modeled power received from antenna A.
Error at site A is 9.99 dB standard deviation and 2.33 dB mean. The model displays very symmetric loss and does not account for building and road locations. However, the directivity of the model, as opposed to a perfectly uniform path loss exponent, lowers the standard deviation significantly. Results for antennas B, C, and D can be found in Appendix B.
The proposed model computes received power strength with moderate accuracy. The model provides a very practical way for companies to predict signal strength in and around buildings and around trees and roads. However, the model does not use specific building locations. Immediate shadowing and penetration loss effects are unaccounted for, thus users may still experience outages around buildings if this model is relied upon too heavily. The model does work exceptionally well within the half-power bandwidth in any environment. The use of this model will decrease uncertainty compared to many current models, and should save companies millions of dollars nationwide. There is still a large amount of revenue to be captured along with a model that predicts penetration loss and shadowing effects accurately.