4-Ary Phase Modulation Methodolgy: Simulating the modulating and demodulating of 4-ary phase modulation can be accom- plished with the following steps. Step 1. Generate a random binary data packet of length 10, for example x=1011010011. Step 2. Map the binary data to 4-ary phase modulated signals as follows 00 $1, $1 = (VE.,0) 01 82, 82 = (0, VEO) 10 83, 8y = (-E, 0) 11 + $4, S3 = (0,-E), For x = 1010000100 we obtain s = $394928184. Since each sm, m = 1,2,3, 4, is a 2 dimensional vector the size of s will be 5 where each entry in s is a two dimensional vector indicating in Matlab s will be a matrix with size 5 x 2. Step 3. Generate a noise matrix, n, of size 5 x 2 where cach entry is gaussian with zero mean and variance No/2. Step 4. In order to simulate AWGN channel, add the noise matrix, n, to your signals matrix, s, to obtain the received signal matrix r i.e. set r=s+n. Step 5. The optimal decoder calculates the correlation metrics, C(7,5m) = 275 - ||5m|, and decided on 8m by choosing the largest Cirism). Notice that in our implemen- tation the received signal matrix, r, contains 5 consecutive signals. So we have to calculate 5 correlation metrics and decode 5 consecutive signals. Step 6. Assume that after decoding you have estimated the transmitted signal as = 5384848184. By using the mapping in step 2. we obtain the decoded binary data as x = 1011110011. By comparing x and we see that 1 x= 1011010011 x = 1011110011 there is 1 bit crror over a packet of 10 bits. To incrcase the accuracy of the simulation we have to repeat the above procedure many times and cumulate the number of errors obtained in each packet . Let as assume that we have decoded 1000 packets each with length 10 and we have obtained a total of 5 bit errors. This indicates that the bit error probability is 5/(1000 x 10)=0. 0005. Project Definition: 1. By using Matlab, verify the bit crror probability of 4-ary phase modulation by simulation. Create a Matlab plot where y axis shows the bit error probability and x axis shows the E/ No in dB units, where Ey/ No changes between 1 and 10dB with ld increments. 2. Plot the theoretical value for the probability of error of 4-ary together with its simulated value. Does theory and simulation match? Make comments on your results. 2 4-Ary Phase Modulation Methodolgy: Simulating the modulating and demodulating of 4-ary phase modulation can be accom- plished with the following steps. Step 1. Generate a random binary data packet of length 10, for example x=1011010011. Step 2. Map the binary data to 4-ary phase modulated signals as follows 00 $1, $1 = (VE.,0) 01 82, 82 = (0, VEO) 10 83, 8y = (-E, 0) 11 + $4, S3 = (0,-E), For x = 1010000100 we obtain s = $394928184. Since each sm, m = 1,2,3, 4, is a 2 dimensional vector the size of s will be 5 where each entry in s is a two dimensional vector indicating in Matlab s will be a matrix with size 5 x 2. Step 3. Generate a noise matrix, n, of size 5 x 2 where cach entry is gaussian with zero mean and variance No/2. Step 4. In order to simulate AWGN channel, add the noise matrix, n, to your signals matrix, s, to obtain the received signal matrix r i.e. set r=s+n. Step 5. The optimal decoder calculates the correlation metrics, C(7,5m) = 275 - ||5m|, and decided on 8m by choosing the largest Cirism). Notice that in our implemen- tation the received signal matrix, r, contains 5 consecutive signals. So we have to calculate 5 correlation metrics and decode 5 consecutive signals. Step 6. Assume that after decoding you have estimated the transmitted signal as = 5384848184. By using the mapping in step 2. we obtain the decoded binary data as x = 1011110011. By comparing x and we see that 1 x= 1011010011 x = 1011110011 there is 1 bit crror over a packet of 10 bits. To incrcase the accuracy of the simulation we have to repeat the above procedure many times and cumulate the number of errors obtained in each packet . Let as assume that we have decoded 1000 packets each with length 10 and we have obtained a total of 5 bit errors. This indicates that the bit error probability is 5/(1000 x 10)=0. 0005. Project Definition: 1. By using Matlab, verify the bit crror probability of 4-ary phase modulation by simulation. Create a Matlab plot where y axis shows the bit error probability and x axis shows the E/ No in dB units, where Ey/ No changes between 1 and 10dB with ld increments. 2. Plot the theoretical value for the probability of error of 4-ary together with its simulated value. Does theory and simulation match? Make comments on your results. 2