BLEKINGE INSTITUTE OF TECHNOLOGY School of Engineering Exam in:

Course code: ETD020 Date: 2007-05-29 Time: 9:00-14:00

Maximum total points: 100 A minimum of 50 points is needed for passing the exam. All questions carry equal points. Examiner: Hans-Jürgen Zepernick AIDS ALLOWED: To be supplied by Candidate:

Calculator, Lecture notes, Textbook: T. S. Rappaport “Wireless Communications”

To be supplied by University:

Nil

NOTE: Principal working steps must be shown in all solutions ___________________________________________________________________________ 1. Consider a base station antenna of effective height ht = 60m . A mobile station is located at a distance d = 5km away from the base station and its antenna is located hr = 4m above ground. A mountain of height hobs = 400m at d1 = 3km distance to the base station is blocking the line-of-sight propagation path to the mobile station. The mountain may be modeled as knife-edge, and the carrier frequency is assumed to be 900 MHz . 1.1. Sketch the knife-edge geometry for this set up. 1.2. Determine the diffraction loss caused by the mountain. 1.3. Determine the height of an obstacle required to induce a diffraction loss of 25dB. 2. Consider the power delay profile for hilly terrain given in Table 1. Table 1 Tap number 1

Relative time ( μs ) 0.0

Average relative power (dB) 0.0

2

0.1

-1.5

3

0.3

-4.5

4

0.5

-7.5

5

15.0

-8.0

6

17.2

-17.7

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In addition, some system characteristics are provided in Table 2 for the two second generation cellular systems GSM and IS-54 as well as for the second generation private mobile radio system TETRA. Table 2 GSM

IS-54

TETRA

890-915

824-849

380-400

935-960

869-894

Carrier spacing (kHz)

200

30

25

Carrier bit rate (kbps)

270.8

48.6

36

Frequency band (MHz)

2.1. Calculate the rms delay spread of the channel with the power delay profile given in Table 1. 2.2. Estimate the 50% coherence bandwidth of the channel. 2.3. Would this channel be suitable for GSM, TETRA, or IS-54 service without the use of an equalizer? Give reasons for your answers. 2.4. In case an equalizer is required, what would be the maximum number of bits that could be transmitted without updating the equalizer if the mobile is travelling with a speed of 50km / h . You may assume that the carrier frequency is chosen in the middle of the uplink frequency band. Hint: Use the geometric mean equation to compute coherence time.

3. Consider a

π

QPSK modulator and assume that the initial phase θ 0 = 0 0 . The data bit

4 stream 10010011 is to be sent with the leftmost bit being first applied to the transmitter. The carrier phase shifts corresponding to the various input bit pairs are given in Table 3. Table 3 Information bit mIk, mQk 11 01 00 10

Phase shift φk π/4 3π/4 -3π/4 -π/4

3.1. Determine the phase θ k of the kth symbol, the value I k of the kth in-phase pulse, and the value Qk of the kth quadrature pulse for k=1, 2, 3, and 4. 3.2. Sketch the constellation diagram of the

π 4

QPSK signal determined in 3.1.

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3.3. Assume that the transmitter and receiver are perfectly phase locked, and Ď&#x2020;0 = 0 . Using the

Ď&#x20AC;

QPSK signal of 3.1, demonstrate how the received signal can be 4 detected correctly using a baseband differential detector.

4. Consider the convolutional encoder shown in Figure 1, where operations are performed in GF(2):

u1 Input

Output u2

Figure 1: Convolutional encoder 4.1. Draw the state diagram of the encoder. 4.2. Draw the trellis diagram of the encoder for time t1 to t 6 . 4.3. Assume the message sequence m and the received sequence Z are given as follows: Time:

t1

t2

t3

t4

t5

m=

1

1

0

1

1

Z=

11

00

01

10

00

4.3.1. Use hard-decision Viterbi decoding in combination with Hamming distance as metric to decode the received sequence Z succeeding from time t1 to t 6 . 4.3.2. Specify the output sequence that the decoder has released until time t 6 . ___________________________________________________________________________ END OF PAPER

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