Lab 2 - Pulse shaping and matched filters

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In this lab, you will use GNURadio to construct a baseband digital communication system including data source, pulse shaping, AWGN channel, receiver and bit error rate counter. Previously (in Lab 1) you built a 1-sample-per symbol system with no pulse shaping. In this lab you will build an N-sample-per-symbol system with pulse shaping.

If you are unfamiliar with GNU Radio, it is strongly recommended that you complete the introductory GRC tutorials hosted on this site before trying these labs.

You will learn about:

• pulse shaping
• timing recovery in baseband receivers
• BER (bit error rate) measurements
• The \(\frac{E_b}{N_0}\) metric

Prelab

1. Read the theory page of this lab.
2. Read the notes at the start of Dr. Driessen’s chapter 3 worksheets (Worksheet #5).
3. Consider a matched filter. Derive an expression for \(\frac{E_b}{N_0}\) in linear terms as a function of \(a_i, \sigma_0, W, R\) (also all in linear terms). Sklar equations 3.30 and 3.45 are a good starting point.
4. Take the derived expression above and rearrange it to solve for \(\sigma_0\). This time the expression should be a function of \(a_i, W, R\) (in linear terms) and \(\frac{E_b}{N_0}\) (in dB).
5. Consider the the above derived expression for \(\sigma_0\) in the context of a sampled system. \(a_i\) is the signal amplitude (and so \(a_i^2\) is the signal power), \(R\) is the symbol frequency (\(f_{SYM}\)) and \(W\) is the channel bandwidth. Rewrite the expression for \(\sigma\) as a function of \(a_i^2\), \(\frac{E_b}{N_0} \text{ (dB)}\), \(f_{SYM}\), and \(f_s\).

Prelab

Show this expression for \(\sigma_0\) to your TA before beginning the lab.

Deliverables

In this lab there are the following deliverables:

• a single page of answers to the deliverable questions laid out in the lab. In this lab there are 6 of them. They are all highlighted and labelled with their respective question numbers. Each question will require some thought and should be answered concisely with 1 to 2 sentences of text and perhaps an accompanying figure.
• a short code you write to generate some BER versus Eb/N0 curves
• your final BER versus Eb/N0 figure