Tasks in Channel Coding, Gray Coding, and Doppler Spread

Task1: Creating a bit-error rate curve for a [127,120] Hamming code

These are ways of adding redundant information to a signal so that errors caused by a noisy channel may be identified and even corrected by the receiver.

This is a method of assigning bits to symbols which ensures that, for reasonably high SNR, each symbol error only results in one bit-error.

This is a spreading out of the signal on the frequency axis, caused by many different versions of the signals arriving at the receiver with different frequencies, having reflected off moving objects.

Download models basicBPSK.slx and HammingBPSK.slx and the Matlab programme BER_Script.m from the Blackboard site and make sure they’re all in the same Matlab directory. Run BER_Script.

This will put different values of the parameter EbN0 into each of the models and extract the resulting error rate. It should then plot the BER curve for the BPSK modulation scheme with and without a Hamming code.

• What is the overhead for this code? What percentage extra data has to sent?

• What coding gain does this coding scheme give?

• At what BER value does the model with the Hamming code start to be better than the model without?

• How does this compare to the theoretical value?

• What is the highest value of BER seen in this experiment?

• What changes would you need to make to the code or models if you wanted to look at BER values down to 10-9?

Download the model HammingBPSK2.slx and the Matlab programme BER_Script2.m from the Blackboard site and make sure they’re in the same Matlab directory. Run BER_Script2 and watch the displays on the constellation diagram as the value of Eb/N0 changes. As before, the script will produce a BER curve. Paste this into your lab-book.

However, this time, there is an extra block in the model, the SISO block, which adds some doppler spread to the signal, as might be seen next to a busy highway. To answer these questions, you may want to compare the output to the model without the SISO block. An easy way to do this is to right-click on the SISO block and select ‘Comment through’. This is a convenient way of temporarily removing a block from a model. You may also want to change the values in EbN0list if the run takes too long.

• What is the set of different symbols are used in this scheme?

• What bit error rate does this model achieve?

• What is the highest value of Eb/N0?

• From looking at the constellation diagram, what do you think is preventing the model from achieving a good BER?

• Can the model achieve a good BER if the channel coding is changed to [7,4] Hamming?

Download the model basicFSK.slx and the Matlab programme runFSK.m. Notice that the low-pass filter in the model is commented out. Run runFSK.m and watch the displays on the spectrum analyser as the value of Es/N0 and the number of bits per symbol (nbps) change. The script will produce a BER plot with four different curves on it. Paste this into your lab-book.

Now right-click on the low-pass filter and select ‘Uncomment’ to make the filter operational. Save the model and run it again from the programme.

Put the two BER plots in your lab book and answer the following questions.

• What four modulation schemes are tested in this model?

• Which of the four different modulation schemes is the best when the filter is not present and why?

• Which of the four different modulation schemes is the best when the filter is present and why?

• What is the SNR value in decibels needed to achieve a 1% BER with any filtered FSK modulation scheme? (indicate on your graph where you get this information from)

Download the models basicQAM.slx and GrayQAM.slx and the Matlab programme runQAM.m. Run runQAM.m and paste the plot it produces into your lab-book. Now answer the following questions.

• What modulation scheme is represented by each of the four lines?

• What coding gain is achieved by using Gray coding in each case?

• If the coding gain achieved is different in each case, explain why one is better than the other.

• What would the coding gain be for binary PSK modulation?

• By how much would the Gray scheme improve the symbol error rate in 2048QAM?