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# Homework 10

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• Chapter 2 in the Anderson text

## Problems

1. Suppose and be an orthonormal basis for signal space given by

1. Verify that and are orthonormal.
2. Sketch matched filters for and .
3. The following look-up table is used in the modulator.
 signal bits symbol 000 001 010 011 100 101 110 111
Sketch the eight possible transmitted waveforms. Assume that the symbol period is second.
4. Sketch the waveform that is transmitted if the six bits are fed into the modulator.
5. Sketch the constellation.
6. Sketch the ML decision regions.
7. What is min?
8. Compute the average symbol and bit energy.
9. Suppose that the following set of measurements were observed at the output of a bank of filters matched to and .
 Symbol Period
What what symbol sequence and bit sequence would come out of the ML receiver for this set of measurements?
10. Compute the probability that the ML receiver decides that was transmitted when in fact was actually transmitted.
11. Use the union bound to compute an upper bound for the probability of error for this constellation using an ML receiver.

2. Sketch the impulse response of a filter matched to the square-root raised cosine pulse. Follow the procedure on page 60 and 61 of the Anderson text.
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, June 29). Homework 10. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Communication_Systems_I_1/hw10.html. This work is licensed under a Creative Commons License