BLEKINGE INSTITUTE OF TECHNOLOGY

School of Engineering

Exam in: Radio Communications ETD020 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 mht 60= . A mobile station is located

at a distance away from the base station and its antenna is located kmd 5= mhr 4=

above ground. A mountain of height mhobs 400= at kmd 31 = 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 . MHz900

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 Relative time ( sμ )

Average relative power (dB)

1 0.0 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 Frequency band (MHz)

Uplink

Downlink

890-915

935-960

824-849

869-894

380-400

Carrier spacing (kHz) 200 30 25

Carrier bit rate (kbps) 270.8 48.6 36

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 . 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.

hkm /50

3. Consider a 4π

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

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.

00 0=θ

Table 3

Information bit mIk, mQk Phase shift φk

11 π/4 01 3π/4 00 -3π/4 10 -π/4

3.1. Determine the phase kθ of the kth symbol, the value of the kth in-phase pulse, and

the value Q of the kth quadrature pulse for k=1, 2, 3, and 4. kI

k

3.2. Sketch the constellation diagram of the 4π

QPSK signal determined in 3.1.

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3.3. Assume that the transmitter and receiver are perfectly phase locked, and 00 =φ .

Using the 4π

QPSK signal of 3.1, demonstrate how the received signal can be

detected correctly using a baseband differential detector.

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

Input Output

u1

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 to . 1t 6t

4.3. Assume the message sequence m and the received sequence Z are given as follows:

Time: 1t 2t 3t 4t 5t

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 to . 1t 6t

4.3.2. Specify the output sequence that the decoder has released until time . 6t

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