# Given a modulation system with M = 4 and N = 2 with four equiprobable signals defined as, apart from

Given a modulation system with M = 4 and N = 2 with four
equiprobable signals defined as, apart from a constant factor

a. Sketch the signal space (constellation diagram)

b. Write down the orthonormal basis functions for this
signal space.

c. Write down the corresponding timedomain signals in terms
of the orthonormal basis functions.

d. Determine the average symbol energy.

e. How can you assign the di-bits to each symbol so as to
minmimize the probability of bit error?

f. Show the optimum decision regions and explain how you
obtained them.

g. Determine the pairwise error

Given a modulation system with M = 4 and N = 2 with four
equiprobable signals defined as, apart from a constant factor

a. Sketch the signal space (constellation diagram)

b. Write down the orthonormal basis functions for this
signal space.

c. Write down the corresponding timedomain signals in terms
of the orthonormal basis functions.

d. Determine the average symbol energy.

e. How can you assign the di-bits to each symbol so as to
minmimize the probability of bit error?

f. Show the optimum decision regions and explain how you
obtained them.

g. Determine the pairwise error probabilities and the upper
bound on the average signal error probability in an AWGN channel with zero mean
and a variance N0/2. Explain which Euclidean distances dominate the average
symbol error probability.

h. Find the signal most likely to have been sent if all the
signals are equally likely and the observation vector is x =
(0.25,_0.25).

## Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
\$26
The price is based on these factors:
Number of pages
Urgency
Basic features
• Free title page and bibliography
• Unlimited revisions
• Plagiarism-free guarantee
• Money-back guarantee
On-demand options
• Writer’s samples
• Part-by-part delivery
• Overnight delivery
• Copies of used sources
Paper format
• 275 words per page
• 12 pt Arial/Times New Roman
• Double line spacing
• Any citation style (APA, MLA, Chicago/Turabian, Harvard)

# Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

### Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

### Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

### Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.