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ELT-41307 COMMUNICATION THEORY 12.12.2016

No materials, no calculator. Prepared by and return to: Mikko Valkama.

NB 1: If you wish to take the Full Exam, answer to all the guestions 1-6. If you wish to take only the 2"4
Midterm Exam, answer only to the guestions 4-6.

NB 2: Pay special attention to clear handwriting. If I cannot read your text with reasonable effort, your
paper cannot be unfortunately graded. So, please, try to write in a clear manner. Thank you.

I: Explain shortly the following concepts: a) amplitude spectrum, b) cross-correlation,
€) wide-sense stationary random signal, d) spectral density, e) white noise. No need to dwell on
details, rough explanation which shows your understanding is enough. (5p)

2. — Assume z(t) isa real-valued wide-sense stationary random signal. Suppose another random signal
y(t) is created as y(t) = x(t) + ax(t — T,) where a, and Tj are known constants. First,
calculate the autocorrelation function of y(f) and express it in terms of the autocorrelation function
of (ft). Suppose then that x(t) is white noise. In that case, what are the autocorrelation function and
spectral density of y(t) ? (5p)

3: Explain the general concept of I/O modulation. Illustrate the principle by drawing a block-diagram of
an I/O modulator, and some example spectral contents of the relevant signals in different stages. How
does I/O modulation utilize the structure of a general bandpass signal, sketched below, and how can
the receiver recover the I and O components ? (5p)

Tap(t) = Alt) cos(wyt + plt)) = 7(t) cos(wyt) — zy(t) sin(wot)

4. Explain shortly the basic principle of Nyguist pulse-shaping filtering and pulse amplitude modulation
(PAM), in the context of baseband digital communication. What does the concept of intersymbol
interference mean ? (5p)

5: Suppose you are to design an I/O modulated single-carrier M-OAM digital communication system
where the target physical layer bit rate is 32 Mbit/s, and that you have 10 MHz bandwidth available
around a center-freguency of 1800 MHz. Design the system in terms of the needed OAM symbol
alphabet size, symbol rate and feasible nonzero excess bandwidth (rolloff) factor for a raised-cosine
pulse. (5p)

6. Explain shortly the concepts of entropy, mutual information and channel capacity. What is the
meaning of channel capacity for a communications engineer ? In an additive Gaussian noise channel,
what is dictating or determining the channel capacity ? (5p)

Maximum points, Full Exam: 5+5+5+5+5+5 = 30p.

Maximum points, 2*4 Midterm Exam: 5+5+5 = 15p.