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Exam Problems, Modulation - Mobile Communication Systems | ECE 732, Exams of Electrical and Electronics Engineering

George Mason University (GMU)Electrical and Electronics Engineering

Prof. Bernd-Peter Paris

Material Type: Exam; Professor: Paris; Class: Mobile Comm Systems; Subject: Electrical & Computer Enginrg; University: George Mason University; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 02/10/2009

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ECE 732: Mobile Communication Systems—Collected Exam Problems

1. Modulation The symbol sequence b={−1,1,1,−1,1,1,−1,−1}is to be

transmitted at a rate of one symbol per Tseconds. For each of the following

modulation formats sketch in the space provided below

•the magnitude,

•the phase, and

•the modulated signal assuming a carrier frequency of 1/T .

(a) Binary Phase Shift Keying (BPSK) with rectangular pulses.

Discover Exams of Electrical and Electronics Engineering George Mason University (GMU)

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Modulation The symbol sequence b = {− 1 , 1 , 1 , − 1 , 1 , 1 , − 1 , − 1 } is to be transmitted at a rate of one symbol per T seconds. For each of the following modulation formats sketch in the space provided below - the magnitude, - the phase, and - the modulated signal assuming a carrier frequency of 1 /T.

(a) Binary Phase Shift Keying (BPSK) with rectangular pulses.

t/T

Magnitude

Phase

modulated signal

t/T

Magnitude

Phase

modulated signal

(d) Partial-response (L = 2) Continuous Phase Modulation (CPM) with modulation index h = 1/ 2 and rectangular pulses.

t/T

Magnitude

Phase

modulated signal

T T

f0 f1 fL

(b) How many memory elements L are there in the tapped delay-line? (c) What are values for the coefficients in the tapped delay-line model? (d) Find the distribution (type, mean, variance, etc.) of the additive noise Nn samples in the tapped delay line model.

Maximum Likelihood Sequence Estimation A binary sequence of five symbols In, n = 1,... , 5 (elements are drawn fromIn ∈ {− 1 , 1 }) is trans- mitted over a channel which is characterized by tapped delay-line with coef- ficients f = { 35 , 45 }. The observation is further corrupted by additive white Gaussian noise. The following sequence Rn is observed at the output of the tapped delay line Rn = { 1 ,

(a) Given the observed sequence Rn, determine the most likely input se- quence In. Clearly, show how you arrived at your solution. (b) Draw and clearly label a trellis diagram and indicate the path through the trellis which corresponds to the most likely sequence. (c) For the remainder of the problem the coefficients f of the tapped delay- line are unknown. However it is known that the first five input symbols

0.6 0.

are In = { 1 , − 1 , 1 , − 1 , − 1 }. In total, the input sequence is eight symbols long and the observed output sequence is

Rn = { 1 , 0. 1 , 0. 3 , 0 , − 1. 4 , 0 , 1. 8 , − 0. 4 , − 0. 4 }

Find the best estimate for the channel coefficients based on the knowl- edge of the first five symbols in the sequence. (d) Use your estimate for the channel coefficients to determine the most likely sequence of the remaining three symbols.

Continuous Phase Modulation Equally likely random symbols In ∈ {− 1 , 1 } are to be transmitted at a rate of one symbol per T seconds over an additive white Gaussian noise channel. The symbols are modulated using partial response (L = 2) continuous phase modulation with modulation index h = 12 and rectangular pulses.

(a) Sketch the phase of the transmitted signal resulting from the sequence

I = { 1 , − 1 , 1 , 1 − 1 , − 1 , − 1 , 1 }.

(d) A packet of N bits is to be transmitted over the channel using BPSK modulation. The bit period is Tb seconds. For each of the following cases explain qualitatively the influence of the channel on the transmit- ted signal: i. Tb ¿ Tc and N Tb ø (^) f^1 d ii. Tb ¿ Tc and N Tb ≈ (^) f^1 d iii. Tb ≈ Tc and N Tb ø (^) f^1 d (e) For each of the three cases, explain which provisions must be made in the receiver to ensure reliable communication.

Control Channels in Mobile Communication Systems To ensure proper functioning of mobile communication systems the follow- ing transactions must be supported by the employed protocol: - (mobile originating/terminating) Call establishment and release - Handover - Periodic reporting of signal quality and strength measurements - Location updating

(a) Explain under what conditions each of these transactions has to be per- formed. Estimate how many control messages are necessary in both the up-link and down-link direction to complete each transaction. Justify your answers. (b) For the remainder of the problem, the following assumptions regarding the traffic to be supported by the mobile network are made:

There is an equal number of users from two classes: the first moves at a speed of 50 km/h and the second is moving at a speed of 3 km/h.
Each cell has 10 traffic channels which are in continuous use^1.
The average call duration is 2 minutes.
A location area comprises 10 cells.
Measurements are reported every 10 seconds for every active call.
The cell radius is 1 km for all cells. (^1) This is a pessimistic assumption but it avoids the use of queuing theoretic methods in this prob-

lem.

Estimate the total number of control messages which have to be ex- changed in support of the transactions above in one hour in a location area (10 cells). (c) Assuming each message contains 100 bits, how much channel capacity is required to carry the control traffic for the location area. (d) How do your answers change if the cell radius were reduced to 100 m? Would a measurement reporting interval of 10 seconds still be suffi- cient? Explain.

Maximum Likelihood Sequence Estimation A binary sequence of five symbols I (elements are drawn fromIn ∈ {− 1 , 1 }) is transmitted over a channel which is characterized by tapped delay-line with coefficients a = 5 and b = − 4. The observation is further corrupted by additive white Gaus- sian noise. The following sequence r is observed at the output of the tapped delay line r = { 7 , − 1 , − 4 , − 5 , 7 , − 2 }

n r

x a x b

(a) Given the observed sequence r, determine the most likely input se- quence I. Clearly, show how you arrived at your solution. (b) Draw and clearly label a trellis diagram and indicate the path through the trellis which corresponds to the most likely sequence. (c) What is the Euclidean distance associated with the two sequences I 1 = { 1 , 1 , − 1 , − 1 , 1 } and I 2 = { 1 , 1 , 1 , − 1 , 1 }, respectively? Explain.

Modulation The symbol sequence b = {− 1 , 1 , 1 , − 1 , 1 , 1 , − 1 , − 1 } is to be transmitted at a rate of one symbol per T seconds. For each of the following modulation formats sketch in the space provided below
- the magnitude,
- the phase, and
- the modulated signal assuming a carrier frequency of 1 /T.

(a) Binary Phase Shift Keying (BPSK) with raised cosine pulses.

t/T

Magnitude

Phase

modulated signal

t/T

Magnitude

Phase

modulated signal

Exam Problems, Modulation - Mobile Communication Systems | ECE 732, Exams of Electrical and Electronics Engineering

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