Reference no: EM13707478

Matlab Project: The below set of problems will have you simulate the transmission of digital information over a noisy channel using antipodal signaling. The digital message bits will be encoded onto antipodal waveforms. They will then be corrupted by AWGN and then decoded using a correlation detector. Performance will be measured based on comparisons between the theoretical and simulated probability of bit error. The signals from the various output stages of the system will also be plotted in order to develop an understanding of the workings of the various stages of the correlation detector function.

The correlation detector for antipodal signals is shown in the following figure.

Given the following antipodal pulses:

a. Write a program to plot a graph of the theoretical probability of error versus 10log10(Eb/N0) ranging from 0 to 12 dB in increments of 1 for the signals. This will be used to evaluate your simulations.

b. Write a simulation program to estimate and plot the probability of error for a binary communication system that uses the correlation detector. The specifics are as follows:

(i) Generate a random m = 0, 1 message stream where the bits (0, 1) are equiprobable.

(ii) Encode the message stream into the above waveforms with "0"→ x1 (t) and "1"→ x2 (t)

(iii) Let x1 (t) and x2 (t) consist of 24 samples each.

(iv) Add various amount of random noise to your message stream to create signals with Eb/N0 from 0 to 12 dB in increments of 1. You can adjust the signal's Eb/N0 by changing the noise generator's variance.

(v) Construct a correlation receiver to detect the noisy signals. As noted elsewhere, the correlation receiver should consist of multipliers, integrators (or summers) and a comparator.

The output of the comparator will be the message m ˆ .

(vi) Compare the values of m andm ˆ . Have an error counter in your correlation detector count the number of errors in order that you can calculate the error probability.

(vii) For each value of Eb/N0, calculate an error probability based on the 10,000 generated and received data bits, and then overlay with an "x" on the plot generated in above step (a).

(viii) Repeat the above so that you have the error probability for each value of 10log₁₀(Eb/N0) from 0 to 12 dB in increments of 1 dB.

(ix) Note the degree of closeness the simulated points are to the theoretical plot. You might also note that as Eb/N0 increases it takes more samples to reach the theoretical value of the error probability. Why?

c. Plot the signals from the various detector stages. The outputs should conform to what is expected. Make any observations and state any conclusions.