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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

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**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.

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**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

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**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

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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

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**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

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**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

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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

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**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

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**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)

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**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

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**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

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**Appendix – Normal distribution table**

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