ECE 5221 Personal Communication Systems

1. ECE 5221 Personal Communication Systems Prepared by: Dr. Ivica Kostanic Lecture 3: Planning for Coverage in Cellular Systems (Chapter 2.3 ) Spring 2011

2. Outline • Mobile propagation environment • Free space path loss model (review) • Two ray propagation model (review) • Log distance path loss model (review) • Examples Important note: Slides present summary of the results. Detailed derivations are given in notes.

3. Free space path loss model • Assumes free space between TX and RX • Realistic in microwave links to cellular towers • Not realistic in terrestrial propagation Definition of quantities: PT = power delivered to antenna terminals GT = gain of transmit antenna ERP = effective radiated power FSPL = free space path loss GR = gain of the receive antenna PR = received power delivered to receiver If the quantities are expressed in log-units: Free space propagation scenario

4. Free Space Path Loss (FSPL) Equation for FSPL (linear) d = distance between TX and RX l = wavelength of the RF wave Equation for FSPL (logarithmic) – Frii’s equations Notes: FSPL grow 20dB/dec as a function of distance FSPL grows 20dB/dec as a function of frequency FSPL curves are straight lines in log-log coordinate system Detailed derivation of Frii’s equations given in notes FSPL curves 1-3GHz range

5. FSPL example: Consider microwave communication link. Assume: power delivered to the antenna is 2W, transmit antenna gain is 20dB, the receive antenna gain is 5dB and minimum required signal level is -80dB. Estimate the maximum TX-RX separation for three frequencies: 1900MHz, 2.5GHz and 6GHz. Answers: For 1900MHz, distance 61.8 miles For 2.5GHz, distance 48.95 miles For 6.6GHz, distance 1.58 miles Notes: • Answers do not have any margin • RSL is received power expressed in dBm • Note decrease of distance with increase of frequency

6. Propagation in terrestrial environment • Three components of path loss • Separation between TX and RX • Log normal shadowing • Small scale fading • Separation between TX and RX • Exponential decay of signal level • Decay is expressed in X dB/dec • X is between 20 and 60 • Log normal shadowing • Additional path loss due to mobile being in a shadow of terrestrial objects • Modeled as a random variable normally distributed in log domain • Small scale fading • Large variations of signal level over distances comparable to wavelength Notes: - First two components of the path loss predicted through macroscopic propagation models - Third component is virtually unpredictable

7. Losses due to TX-RX separation • Simplified example: two-ray path loss model • Model derived for: • Flat Earth • Perfectly reflecting Earth • Assuming two ray addition at the RX point • Model predicts: • 40 dB/dec loss as a function of distance • 20 dB/dec dependence of losses on TX and RX heights • In practical situations: • Separation loss 20-60dB/dec (typical is still around 40dB/dec) • Dependence on antenna height still holds but is somewhat smaller (10-15 dB/dec) Notes: Detailed derivations are presented in notes

8. Example Brevard County, FL has an area of 1,557 sq mi. Assume that the county is to be covered with a cellular system. The parameters of the cell sites are: Height of the tower: 50m, height of the mobile: 1.5m, maximum path loss 120dB. Use two-ray path loss model to determine: • Size of a cell • The number of circular cells required (neglect the overlap between the calls) • Cell count assuming that there is about 20% overlap between cells Answers: • Radius of a cell is about 5.4 miles • The number of required cells is about 17 • Taking the overlap into account, the number of required cells is 22

9. Log normal fading Typical RSL measurements • Log normal shadowing introduces random variations of path loss • Random variations are modeled as a normal variable in log domain • Due to these variations the shape of cell is not regular • Practical problem: • Cover the area with irregularly shaped cells • Prevent excessive overlap between cells • Practical approach: Assume log distance path loss model • The form of the log distance model RSL distance plot Notes: The model is straight line approximation Variability captured by random variable

10. Log distance path loss model - details Equation of the model d0– reference distance PL – path loss in dB PL0– path in dB loss to reference distance d – distance m – slope Xs – log normal fading in dB Slope recorded in different us cities (after W.C.Y. Lee)

11. Properties of fading Probability density function Standard deviation fading as a function of environment Note: for nominal calculations standard deviation of 8dB is commonly assumed

12. Log distance path los model: example Consider a cell site with ERP = 50dBm. Assume that the path loss follows log-distance path loss model. The following data are known: reference distance is 1 mile, reference path loss is 109dB, slope 38.4dB/dec. Calculate: • Median RSL at the distance of 3 miles • Probability that the signal is above level given in 1. The RSL predicted by log-distance path loss model is -80dBm. Assume log normal shadowing with standard deviation of 7dB. Calculate probabilities: • RSL > -80dBm • RSL < -80dBm • RSL > -85dBm • RSL < -75dBm Homework 1 - assigned

13. Appendix – Normal distribution table