Chapter 3 - 16 Problems and Solutions (Chapter 3) 1. A...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 16 Problems and Solutions (Chapter 3) 1. A wireless receiver with an efi'ective diameter of 250 cm is receiving signals at 20 GHz from a transmitter that transmits at a. power of 30 mW and a gain of 30 dB. (5) What is the gain of the receiver antenna? (1)) What is the received power if the receiver is 5 km away from the transmitter? [Solution] Given .1, = Efl'ective diameter = 250 cm. in = Carrier frequency = 20 'GHz. 1": = ’Iransmitter power = 30 mW G: = Transmitter gain = 30 dB = 1000. d = Distance of receiver = 5 km. A. m Efl’ective area = (2%) = 4.91 m2 A = Wavelength = = 0.015 m (e) G, = Receiver entenne gain = lees = 2.74»: 105 = 54.38 dB. (b) P, = Received power at distance of 5 km = 43%;; = 4.094: W7 Watts. . Consider an antenna transmitting a. power of 5 W at 900 MHz. Calculate the received power at a. distance of 2 km if propagation is taking place in free space. [Solution] Transmitted power = H = 5 W Cmierfiequency=900MHzr=>A=f =0.33m d = 2 km Assuming unit gain in free space model, i.e., G; = G,- = 1 Received power can be calculated by the formula P _ GtGr‘Pt r— 4nd)§ A = 8.8 x 10-10 W 17 3. In a cellular system, diffraction. reflection, and direct path take different amount of time for the signal to reach a MS. How do you difi’erentiate and use these signals? Explain clearly.Compute the level arming rate with respect to the rms level for a vertical monopole antenna. assuming the Rayleigh faded isotropic scattering case. The receiver speed is 20 km/hr and the transmission occurs at 800 MHz. [Solution] Dilfraction results in small-scale fading and reflection results in large scale fading. So on receiving the different signals, we can study the spatial and temporal variations of the signal strengths with respect to distance traveled to understand about the difi'racted and reflected signals. If the variations change fast with respect to time and distance, then We conclude it to be difiraction and reflection otherwise. . . The transmission power is 40 W, under a free space propagation model, (a) “That is the transmission power in unit of dBm? (b) The receiver- is in a distance of 1000 In, what is the received power, assuming that the carrier frequency fc = 900 MHz and G; 2 GP = 1 dB? ' (c) Express the free pace path loss in dB. [Solution] (8.) 10 x log (40 x 1000) = 46 dBm. (b) _aee ‘ es)“ __ 40 x 1 x 1 x — (4 x 1r x 1000)2 = 2.82 x 10-_a w. P.- (c) Pr (dB) = 10 x log (2.82 x 10-3) = —75 dB. . A receiver is tuned to 1 GHz transmission and receives signals with Doppler frequencies ranging from 10 Hz to 50 Hz when moving at a. speed of 80 km/hr. What is the fading rate? [Solution] Moving speed 0 = 80 km/hr. = 22.22 In/sec ‘ v = 1 GHz Thus, A = c/u, , where c is free space propagation speed and equals to 3 x 103 rn/sec. 18 A = 0.1 m Therefore, the fading rate N(rm) = % __ 2 x 22.22 _ 0.1 = 444.4 Hz. Here we are not considering the Doppler shift because the 9 is not given. . What does a. small delay spread indicate about the characteristics of a. fading channel? If the delay spread is 1 microsecond, will two different frehuencies that are 5 MHz apart, experience correlated fading? [Solution] A all delay spread indicates that smearing or spreading out eEect is less. The delay spread determines to what content the channel fading at two difi'erent frequencies f; and f2 are correlated. Small delay spread indicates larger coherence bandwidth and hence correlated fading. 1 microsecond delay spread indicates Bc .—. Coherence bandwidth = W = 159.15 kHz. Since 1 f1 - f2| > Be, correlated fading will not be experienced. . Consider an antenna transmitting at 900 MHz. The receiver is traveling at a speed of 40 Ian/h. Calculate its Doppler shift. {Solution} 33.67 Hz 8. Repeat Problem 3.6. Calculate the average fading duration if p = 0.1. [Solution] where f," is the Doppler frequency. 19 9. Describe the consequence of the Doppler effect on the receiver in an isotropic scattering environment. Based on your description, speculate on the meaning of the term “Doppler Spread”. (a) Is the term “Doppler Spread” more appropriate in describing the channel than “Doppler Shift” in a scattering environment? Why? (13) ObServe the inverse relationship that exists between “Coherence Band- width” and “Delay Spread” in a wireless channel. Attempt to simi- larly define a term “Coherence Time” that has an inverse relationship with the “Doppler Spread”. What information does this term give about the channel? I [Solution] The multiple reflections of signals cause a dynamic change in propagation time. Each reflection received is liable to be suffering a different Doppler shift. This means that a carrier transmitted on a single frequency will receive multiple reflections and each reflection will arrive at the receiver shifted in frequency by a different amount. The difl'erence between the highest shift and the lowest shift gives the Doppler spread. (a) Since the term Doppler spread determines the difference between highest and lowest Doppler shifts, it doesn’t inform about the max- imum Doppler shift experienced. So Doppler spread is more appro- priate in describing the channel than “Doppler shift” in a scattering environment. (1')) Delay spread and coherence bandwidth are parameters which de- seribe the time dispersive nature of the channel in a local area. How- ever, information about the time varying nature of the channel caused by either relative motion between the mobile and base station, or by movement of objects in the channel is not given. Coherence time is the time domain dual of Doppler spread and is used to characterize the time varying nature of the frequency dispersiveness of the channel in the time domain. Coherence time is the time duration aver which two received signals have a strong potential for amplitude correlation. If the reciprocal bandwidth of the baseband signal is greater than the coherence time of the channel, then the channel will change during the transmission of the baseband message, thus causing distortion at the receiver. 10. How can you compensate for the impact of Doppler effect in a cellular system? Explain. [Solution] We can compensate the impact of Doppler efi'ect at receiver by adaptive detection to track the channel variations. 20 11. 12. 13. 14. How is radio propagation on land different from that in free space? [Solution] Propagation in free space does not have any obstacles and hence it char- acterizes the most ideal situation for propagation. Whereas, radio prop- agation on land may take place close to obstacles which cause reflection, difl'raction, scattering. ' What is the difi'erences between fast fading and slow fading? [Solution] Slow fading is caused by movement over distances large enough to produce gross variations in overall path length between base station and mobile station. In other words, the long term variation in the mean level is known as slow fading. Rapid fluctuations caused by local multipath are known as fast fad- ing. It is short-term fading. Path loss, fading, and delay spread are the three important radio propaga- tion issues. Explain why those issues are important in a. cellular system? [Solution] The wave propagation in multipath channel depends on the actual envi- ronment including factors like antenna height, profile of the buildings, road and the terrain. Therefore we need to describe the behavior of mobile ra- dio channels using a good and relevant statistical mechanism. Thus this is provided by studying the path loss and fading phenomenon to understand about the characteristics of the land and terrain profile. The delay spread is also necessary to understand about the propagation channel. whether the signal is propagating through the frequency selective or the flat fading channels. A BS has a 900 MHz transmitter and a. vehicle is moving at the speed of 50 mph. Compute the received carrier frequency if the vehicle is moving (a) Directly toward the BS. (b) Directly away from the BS. (c) In a. direction which is 60 degree to the direction of arrival of the transmitted signal. [Solution] Given fc = Carrier frequency = 900 MHZ A: Wavelength=fi =0.3333m v = Velocity = 50 mph = 22.22 m/s. Let Doppler shift frequency be denoted by f4. 15. 16. 17. 21 (a) 9 = 180, (direction is towards BS.) fd = i 0039 = —67.06 Received carrier frequency: 7 f.» = f: — fd = 900 * 10° + 67.06 = 900.000067 1- 10s me. (b) 9 = 0, (direction amy from BS.) f4 = f 0059 = 67.06 Received carrier frequency: fr = for - fa = 900 1: 10° — 6?.06 = 89939993: 106 MHz. (c) 9 a 60, (direction is towards BS.) f4 = f case = —33.53 Received carrier frequency: fr = f: - fs = 900 * 103 +3353 = 900.000033 4: 1010 MHz. What is the diversity reception? How can it be used to combat multipath? [Solution] Diversity reception: Two frequencies, that are larger than the coherence bandwidth, fade independently. This concept is used in diversity recep- tion. Therefore, it is a radio reception in which a resultant signal is ob- tained by combining or selecting signals, from two or more independent sources. They are modulated with identical information-bearing signals. (i.e., multiple copies of same message are sent using different frequencies.) Combating with multipath: The signals are chosen such that the frequen- cies are larger than coherence bandwidth, therefore their fading charac- teristics are independent at any given instant. This dfects of correlated fading. ' 7 What is the role or usefulness of reflected and diffracted radio signals in a cellular system? Explain with suitable examples. [Solution] Role of reflected and diflracted waves help in signal propagation even in worst cases when there are no LOS component between T3: and Rx. Ex. Tx and Rx separated by the hilly terrains, communication in urban areas with high rise buildings. What is the intersymbol interference (181)? Does it affect the transmission rate of a digital channel? Explain clearly. [Solution] Inter-symbol interference (181) is caused by time delayed multipath signals, where in the second multipath signal is delayed such that it is received during the next symbol. Therefore, the received signals tend to get elon- gated and smeared into each other. Thus, 181 is caused by time delayed multipath swells. 22 18. 19. The time for which second multipath signal is delayed is delay spread Ta. In time-dispersive medium, transmission rate R for digital transmission is limited by this delay spread Td. Therefore, for a low-error~rate perfor- mance, 1 R<-2—I-;; 151 also affects burst error rate of channel. A MS is not in the direct line of sight of a BS transmitting station. How is the signal received? Explain. [Solution] With the help of mifltipath fading signals can reach the places inside build. ings and places which are hidden by tall buildings and trees. With multi- path fading signals are reflected, diifracted and scattered which results in multiple low power signals traveling in different directions. Consider two random variables X and Y that are independent and Gaussian with identical variances. One is of zero mean and the other is of mean p. Prove that the density function of Z = VX + Y is Rician distributed. {Solution} Suppose T = X 2 + 1"”. Since X and Y are statistically independent Gaussian random variables with mean 0 and n, and common variance 0'2, T has a noncentral chi-square distribution with oncentrality parameter 52 =0+,u2 =p2. The deofTis given by 1 _ 3 t M'(t)=2—OEE t>0 Nowwe defineenew random variableR=Ji ThepdfofRisgiven by t -0” ’ tp Ps(t)=;§e 73—10(35), 1320. This is the pdf of a Ricean—distributed random variable. What causes the intersymbol interference and how can you reduce the intersymhol interference in the wireless communication system? [Solution] Intersymbol interference is caused by time-delayed multipath signals. The most common methods to reduce intersymbol interference are: guard time, pulse shaping, signal encoding and equalization. ...
View Full Document

This note was uploaded on 12/10/2010 for the course DCIS 32 taught by Professor Go during the Spring '10 term at College of E&ME, NUST.

Page1 / 7

Chapter 3 - 16 Problems and Solutions (Chapter 3) 1. A...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online