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Mobile Radio Communications – DSSS simulation

In this computer lab, we are going to do a simple simulation of a Direct Sequence Spread Spectrum transmission and reception system. We imagine we have two users who will share the same spectrum, and a receiver that wants to receive and decode signals from both users. Each user is going to send a text message encoded in ascii binary. The block diagram of what is being simulated is effectively the same as Fig 6.49 in Rappaport (also in lecture notes), except that:

1- We skip the up/down conversion to/from the carrier and just work at baseband, and

2- We assume we have a synchronised receiver

It may be useful to assume the messages are sent at a certain rate, so we will (arbitrarily) define the base binary bit rate of the messages to be 1 kbps. You can do the lab in any programming language of your choice. In principle this could be done in a spreadsheet, but that is not recommended. Include the code in your report. Results in workbook format (e.g. jupyter notebook) are ok, but you need to include the usual sections and text associated with a lab report or assignment. As always, plots should have labels, axes etc and you should sanity check your results.

Part 1 – Generate binary message signals User 1’s message is “Hello world!”. User 2’s message is “I like DSSS!”

Task 1.1: Using 8-bit ascii characters, translate these messages (without quotation marks) into a bit stream, which should be 12*8=96 bits long. Matlab has built-in commands for this. Python/other users can search for a solution (e.g. here). Turn the bits into -1 or +1 rather than 0 or 1 so that they can be multiplied later.

Task 1.2: Print or plot the first 16 bits to verify your conversion.

Convert your bits back to ascii to ensure you get the original message back (noting you may need to go back to 0 and 1).

Part 2 – Generate PN codes for two users

We will use a processing gain of 100. Question 2.1: Given the length of the binary messages above, how many chips in total will be sent for each message? Task 2.2: Generate two unique random binary sequences for the length calculated. Again, convert the binary to be -1 and +1 rather than 0 and 1. Task 2.3: Plot the first few hundred or

Task 2.3: Plot the first few hundred or so chips

(adjust the number plotted depending on whether the plot can be clearly read) for both sequences in the same plot such that both can be seen, and comment.

Question 2.3: What is the correlation between the sequences? (Compute it) Part 3 – Generate DSSS signals

Task 3.1: Generate the DSSS encoded signals for each user.

Task 3.2: Plot a selection of the signal and comment on the result.

Note that this is a voltage-like signal that (in the real world) would be multiplied by a carrier to get a DSSS signal at the carrier frequency. We skip the carrier part here.

Part 4 – “Transmit” the signals with noise We assume the signals are transmitted simultaneously and received by a perfectly synchronised receiver, which generates baseband samples of its output voltage at the same rate as the chip rate. The channel and receiver also add noise, which is a continuous quantity, not binary. AWGN is represented by a normal distribution of samples with zero mean. (matlab: “normrnd”. Python: numpy.random.normal.) The relative power of the noise compared to the signal can be variable, but initially make it the same as the signal.

Question 4.1: What quantity associated with the signal and noise must be the same for this to be true? (Remember that your samples are voltage-like.)

Task 4.2: Generate the output voltages from the receiver and plot the first few hundred samples for zero noise and for noise power=signal power. (I.e. power SNR=1)

Part 5 – Decode the signals

Task 5.1: To decode the messages, we first multiply the received signal by the respective PN code to “de spread” the signal.

Task 5.2: Plot the resulting first few hundred samples for both messages and comment on the results.

Task 5.3: Finally, for each group of samples of size equal to the processing gain, calculate the average for that group and plot the values for each message. This will be 96 numbers.

Question 5.4: This final step is important – what component of an analogue circuit does this step emulate and what effect does it have?

Task 5.5: Decode the bit as 0 if the average is 0. This will result in 96 bits that can be converted back to ascii. What are the received messages?

Task 5.6: Experiment with adjusting the relative power of the noise compared to the signals.

Question 5.7: We learned in class that the bit error rate is quite small for voltage SNR > 3 (recall the Q function). Taking into account the processing gain, how much noise power.

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