Bit Error Rate (BER) for Binary Signals in AWGN Channel Assignment
Assignment Task for Bit Error Rate (BER) for Binary Signals in AWGN Channel
Signal tx and rx
BER Expression
Task 1: Theoretical BER
Consider antipodal signaling, where a2=−a1a2 = -a1a2=−a1.
Let a1=[0.25,0.5,0.75,1,1.25,1.5,1.75,2,2.5,3,3.5]a1 = [0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2, 2.5, 3, 3.5]a1=[0.25,0.5,0.75,1,1.25,1.5,1.75,2,2.5,3,3.5].
Noise variance σ2=1sigma^2 = 1σ2=1.
a) Using the MATLAB function erfc, calculate the theoretical BER for each value of a1a1a1.
b) Plot the theoretical BER as a function of SNR. Use the loglog function instead of plot.
Monte Carlo Simulation
Consider a1=−a2a1 = -a2a1=−a2. Generate signal aaa randomly from [a1,a2a1, a2a1,a2] using the rand or randi MATLAB function.
Generate noise using the randn function.
Generate zzz using signal aaa and noise. If z>(a1+a2)/2z > (a1 + a2)/2z>(a1+a2)/2, declare the received signal as bit 1; otherwise, declare it as bit 0.
Repeat the above process 10,000 times. Count the number of times bit 1 is transmitted. Count the number of times z=z =z= bit 1.
Simulated BER =1−(z = bit 1#times bit 1 transmitted)= 1 - left( frac{ ext{z = bit 1}}{# ext{times bit 1 transmitted}} ight)=1−(#times bit 1 transmittedz = bit 1).
Task 2: Simulated BER
Let a1=[0.25,0.5,0.75,1,1.25,1.5,1.75,2,2.5,3,3.5]a1 = [0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2, 2.5, 3, 3.5]a1=[0.25,0.5,0.75,1,1.25,1.5,1.75,2,2.5,3,3.5].
Noise variance σ2=1sigma^2 = 1σ2=1.
a) Calculate the BER from the Monte Carlo simulation for each value of a1a1a1.
b) Plot the simulated BER as a function of SNR. Use the loglog function instead of plot. Plot it on the same plot as the theoretical BER using the MATLAB function hold on.
c) Insert labels for the axes and a legend in the plot.
