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// Example no 4.9
// To find a)the minimum mean square error b)the standard deviation about mean value c)received power at d=2 km d)the likelihood that the received signal level at 2 km e) the percentage of area within 2 km
// Page no. 143
clc;
clear all;
// Given data
d0=100; // First receiver distance in meter
d1=200; // Second receiver distance in meter
d2=1000; // Third receiver distance in meter
d3=3000; // Fourth receiver distance in meter
p0=0; // Receved power of first receiver in dBm
p1=-20; // Receved power of second receiver in dBm
p2=-35; // Receved power of third receiver in dBm
p3=-70; // Receved power of forth receiver in dBm
// a)To find the minimum mean square error
n=2887.8/654.306; // Loss exponent after differentiating and equating the squared error function with zero
// Displaying the result in command window
printf('\n Loss exponent = %0.0f',n);
// b)To find the standard deviation about mean value
P0=-10*n*log10(d0/100); // The estimate of p0 with path loss model
P1=-10*n*log10(d1/100); // The estimate of p1 with path loss model
P2=-10*n*log10(d2/100); // The estimate of p2 with path loss model
P3=-10*n*log10(d3/100); // The estimate of p3 with path loss model
J=(p0-P0)^2+(p1-P1)^2+(p2-P2)^2+(p3-P3)^2; // Sum of squared error
SD=sqrt(J/4); // The standard deviation about mean value
// Displaying the result in command window
printf('\n The standard deviation about mean value = %0.2f dB',SD);
// The decimal point is not given in the answer given in book.
// c)To find received power at d=2 km
d=2000; // The distance of receiver
P=-10*n*log10(d/100); // The estimate of p2 with path loss model
// Displaying the result in command window
printf('\n The received power (at d=2 km) = %0.2f dBm',P);
// Answer is varying due to round off error
// d)To find the likelihood that the received signal level at 2 km
gam=-60; // The received power at 2km will be greater than this power
z=(gam-P)/SD;
Pr=(1/2)*(1-erf(z/sqrt(2))); // The probability that received signal will be greater than -60dBm
// Displaying the result in command window
printf('\n The probability that received signal will be greater than -60dBm = %0.1f percent',Pr*100);
// Answer is varying due to round off error
// e)To find the percentage of area within 2 km
A=92; // From figure 4.18, area receives coverage above -60dBm
// Displaying the result in command window
printf('\n The percentage of area within 2 km = %0.0f percent',A);
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