# ECE 5221 Personal Communication Systems

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

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.

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

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

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 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

Propagation in terrestrial environment
Three components of path loss Separation between TX and RX Log normal shadowing Small scale fading Exponential decay of signal level Decay is expressed in X dB/dec X is between 20 and 60 Additional path loss due to mobile being in a shadow of terrestrial objects Modeled as a random variable normally distributed in log domain 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

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

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

Typical RSL measurements
Log normal fading 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 Typical RSL measurements RSL distance plot Notes: The model is straight line approximation Variability captured by random variable

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 Environment Slope (dB/dec) Free space 20 Terrestrial 20-50 Forested areas Up to 60 In building 16-20 Microcell 16-25 Slope recorded in different us cities (after W.C.Y. Lee)

Standard deviation (dB)
Properties of fading Probability density function Standard deviation fading as a function of environment Environment Standard deviation (dB) Rural 5-7 Suburban 6-8 Urban 8-10 Dense urban 10-12 Note: for nominal calculations standard deviation of 8dB is commonly assumed

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

Appendix – Normal distribution table