ELCT562_PA1

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Apr 3, 2024

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ELCT 562 PA#1 Assume that we want to understand a Wi-Fi system's performance. Let 𝑃 tx = 0.1 W, 𝑓 = 2.450 GHz, G 𝑡 = 9 dBi, G 𝑟 = 2 dBi. No cable losses. 1. What is the TX power in dBW and dBm? dBW: 10log ( 0.1 ) =− 10 dBW dBM: 10log ( 0.1 ) + 30 dB = 20 dBm 2. What is the coverage range with the free-space path loss model and simplified path loss model if the desired received signal power is -70 dBm (assume that 𝑑 0 = 1, 𝛾 = 3.5, and 𝐾 based on FSPL) FSPL: L PL ≤ 10log ( 0.1 ) − ( − 70 ) = 90 dB m L FSPL = 20log ( r ) + 20log ( f ) − 147.55 − G t − G r = 90 20log ( r ) = 60.7667 r = 1092.3 m Simplified: P L = K + 10 γ log ( d d 0 ) K = L FSPL ( d 0 ) 90 = 29.233 + 35log ( d ) d = 54.5 m

3. Consider the simplified path loss model above. Assume that the shadowing variance is 6 dB. a. Plot the outage probability versus distance in MATLAB. Matlab Code: clc clear all c = 3e8; Gt = 9; Gr = 2; f = 2.45E9; d = linspace(0,100,1000); d0 = 1; gamma = 3.5; Pmin = -70; Pt = 20; fMhz = f/1e6; rkm = d;

for variance = [6]; Pfspl = 20*log10(d0)+20*log10(f)-147.55-Gt-Gr; Psimplified = Pfspl + 10*gamma*log10(d) - 10*gamma*log10(d0); Poutage = 1-qfunc((Pmin-(Pt-Psimplified))/sqrt(variance)); plot(rkm,Poutage, 'displayname' , [ '\gamma = ' num2str(gamma), ', \sigma^2 = ' num2str(variance) ' dB' ]) xlabel( 'Distance [m]' ) ylabel( 'Outage Probability' ) grid on hold on end b. Plot the coverage rate versus distance in MATLAB. Matlab Code: clc clear all c = 3e8; Gt = 9; Gr = 2; f = 2.45E9; d = linspace(0,100,1000); d0 = 1; gamma = 3.5; Pmin = -70; Pt = 20; fMhz = f/1e6;

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rkm = d; for variance = [6]; Pfspl = 20*log10(d0)+20*log10(f)-147.55-Gt-Gr; Psimplified = Pfspl + 10*gamma*log10(d) - 10*gamma*log10(d0); a = (Pmin-(Pt-Psimplified))/sqrt(variance); b = 10*gamma*log10(exp(1))/sqrt(variance); Cr = qfunc(a) + exp((2-2*a*b)/b^2).*qfunc((2-a*b)/b); plot(rkm,Cr, 'displayname' , [ '\gamma = ' num2str(gamma), ', \sigma^2 = ' num2str(variance) ' dB' ]) xlabel( 'Distance [m]' ) ylabel( 'Coverage rate' ) grid on hold on ylim([0, 1]) end c. What is the distance if the maximum outage probability is 0.1? The maximum distance is 44.44 meters if the maximum outage probability is 0.1

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