Part 3 - BER measurement

Objectives

You will implement a communications system using baseband pulses and record data to later generate a BER curve with. In the previous section the amplitude \(a\) was kept constant and \(\sigma\) was varied. By keeping the amplitude constant and varying \(\sigma\), the nice histogram plots were generated. However, in a real communications system one would normally vary the amplitude (or power) and keep the noise power \(\sigma^2\) constant, e.g. to represent the constant thermal noise.

In the experiment outlined below it is okay to keep \(a\) constant and vary \(\sigma\) since the measured bit error rate depends only on the ratio of \(a\) to \(\sigma\).

Part 3 deliverables

For this section, the deliverables are:

two datasets for later use in this lab.

Build bipolar flowgraph

Edit the GRC flowgraph from the last part of the lab. Remove the histogram and constellation sink blocks as well as the QT GUI Range block. Add a variable block. Set the ID of the variable to sigma.

Remember that the Amplitude parameter of the Noise Source block sets the noise standard deviation, \(\sigma\), and that the noise power of pure White Gaussian noise is the variance of the distribution (\(\sigma^2\)) (text section 3.1.3.4). Also recall from the theory section that \(P_B=Q\left( \frac{a_1 - a_2}{2\sigma_0} \right)\). Set the amplitude parameter to the new variable, sigma.

The bipolar bits \(a_1\) and \(a_2\) are fixed at -1 and 1 by the Char to Float and Add Const blocks. You will vary \(\sigma\) and measure \(P_B\) (which is the output of the BER block).

Collect bipolar BER values

Run the flowgraph.
Record a BER value for each sigma in [ 0.3, 0.5, 1, 1.5, 2, 3, 4, 5, 8, 12] (notice that the step size between the values changes).
- The reason for choosing these particular values of \(\sigma\) is because we want to collect BER values over a logarithmically spaced set of values of \(\frac{a_1 - a_2}{2\sigma_0}\).

Note

Note you will have to kill the flowgraph each time you need to set a new sigma value. Changing it during runtime with a QT GUI Range or similar will result in large delays for the BER to stabilize.

Build unipolar flowgraph

Edit the flowgraph once more by removing the Add Const block and setting the Scale of the Char to Float block to 1.

This is now a unipolar system. You may wish to add a constellation sink briefly to check that this is true.

The unipolar bits \(a_1\) and \(a_2\) are now 0 and 1.

Collect unipolar BER values

Run the flowgraph.
Record a BER value for each sigma in [ 0.3, 0.5, 1, 1.5, 2, 3, 4, 5, 8, 12] (notice that the step size between the values changes).

Review the section deliverables before moving on.