Übungen zu Drahtlose Kommunikation

Transcription

1 Übungen zu Drahtlose Kommunikation Wintersemester 2016/2017 Prof. Hannes Frey / Dr. Jovan Radak Assignment 1 voluntary submission until Wednesday as PDF via mail to vnuml@uni-koblenz.de

2 Drahtlose Kommunikation WS 2016/17 Assignment 1 2/7 Exercise 1 Goal of this exercise is to examine, why direct transmission of a square wave signal over a wireless channel is a bad idea. We represent the square wave signal as a Fourier series ff(tt) = 4 sin((2k 1)tt) ππ 2k 1 kk=1 Draw the first three terms of the sum (for k=1, 2 and 3). Which frequencies occur in this square wave signal? c) Why is it impossible to construct a perfect square wave signal in practice? d) During transmission of a wireless signal over a channel, different frequencies are attenuated differently. How does this affect: the shape of the signal? the amplitude of the signal? the bandwidth of the signal? the phase of the signal?

3 Drahtlose Kommunikation WS 2016/17 Assignment 1 3/7 Exercise 2 Given is a sender with an ideal directional antenna. It emits equal power in all designated directions. In all other directions no power is emitted. The antenna gain of the directional antenna is 20dB. In what percentage of all directions does this antenna emit power? Given the following scenario: a sender transmits a signal with 10dBm the senders' antenna has an antenna gain of 20dB the attenuation between sender and receiver is 60dB the receivers' antenna is an isotropic radiator What will be the received power? c) Will the received signal be stronger, if the receivers' antenna has antenna gain? d) Why is transmit power expressed in dbm, while antenna gain and attenuation is expressed in db?

4 Drahtlose Kommunikation WS 2016/17 Assignment 1 4/7 Exercise 3 Calculate the wavelength of an electromagnetic wave with a frequency of 868 MHz Given is an electromagnetic wave with a wavelength of 6 cm. Calculate the frequency. c) A sender has a λ/4 antenna with a length of x. For which frequency was it designed? (c is speed of light 3*10 8 m/s) Exercise 4 There is a relationship between the wavelength λ and a circular effective area A with efficiency factor ea which is as follows. (c is speed of light 3*10 8 m/s) Determine the antenna gain G (in db) of a dish antenna with a diameter of 0,6 m and an efficiency factor of 60% that operates in the satellite frequency band at 4 GHz. How would the antenna gain change if the diameter of the dish antenna is increased to 0,9m?

5 Drahtlose Kommunikation WS 2016/17 Assignment 1 5/7 Exercise 5 During a wireless transmission in the free space it is assumed that the signal attenuates at the square of the distance, while in a wired transmission the attenuation increases linearly by a fixed db value. The following table should show the relationship between attenuation of wireless and wired transmission. The attenuation of wired transmission shall increase by 3 db per kilometer while the wireless attenuation shall increase according to Friis free-space path loss. Fill in the table. distance (km) wireless (db) wired (db)

6 Drahtlose Kommunikation WS 2016/17 Assignment 1 6/7 Exercise 6 Given is the following scenario: (x and y are given in meter) A base station (BS) is located at position (7,0). A mobile terminal (MT) is located at position (3,0). A wall is located at y=3. The radio link between BS and MT consists of two paths, the line of sight (LOS) and the reflection at the wall. The MT transmits to BS. The data is modulated on a carrier wave with a wavelength of 40 cm. (1) How is the wave altered by the reflection at the wall? (2) Calculate the phase offset (angle) between the two incoming waves at the BS. Show your calculations. (3) Is the interference of the two incoming waves at the BS constructive or destructive? Give a short explanation. (4) Calculate the attenuation for each path. Assume free-space path loss and an attenuation of 10 db for reflection at the wall. (5) Assume that the MT moves from its current position (3,0) to the position (1,0). ( Determine how many destructive and constructive maxima of interference occur at the base stations' antenna during the movement. ( How does that number change if the frequency is doubled?

7 Drahtlose Kommunikation WS 2016/17 Assignment 1 7/7 Exercise 7 A mobile terminal uses a λ/4 monopole antenna with an antenna gain of 3 db. The carrier frequency is 900 Mhz. (For simplification assume speed of light to be: 3 * 10 8 m/s) What is the antenna length of the mobile terminal? What is the effective area of the antenna at an idealized efficiency factor of 100%?(see exercise 4, assignment 1) c) What is the received power at the mobile terminal according to Friis free-space path loss, if the cellular base station is located at 2 km distance and transmits with 10 Watt power and has an antenna gain of 3 db. (Assume L=1) Exercise 8 ( What can be modelled by the log-normal shadowing model? Choose one of the given answers and give a short explanation. (1) The progression of signal attenuation in time of a node pair during a transmission. (2) The signal attenuation between different node pairs at different places. ( What is expressed by the log-normal distributed random variable in the log-normal shadowing model?