1 V NAME. Clock Pulse. Unipolar NRZ NRZ AMI NRZ HDB3

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1 NAME ES 442 Homework #9 (Spring 208 Due May 7, 208 ) Print out homework and do work on the printed pages.. Problem High Density Bipolar 3 (HDB3) (20 points) HDB3 is a line code developed to avoid long strings of zeros in a data stream. It uses AMI (alternate mark inversion) coding. There are four rules for HDB3 coding: () More than three consecutive zeros are not allowed to be present in the data waveform. For the fourth zero the code inserts a violation bit denoted by V. (2) Violation bits have to be of the same polarity as the previous mark. (3) Two consecutive violation bits must be of opposite polarity. (4) If the number of marks between two consecutive violation bits is even, the format must be B00V, where bit B is a stuffing bit and of opposite polarity to the previous mark. If the number of marks is an odd number, the format should be 000V. As an example of HDB3, consider the 2-bit data string of as shown below for unipolar, then for AMI and finally, expressed in HDB3 code. Clock Pulse Unipolar x x x x x x x x x x x x AMI HDB3 V V

2 Now for the exercise of this problem. Suppose we have a 2-bit data stream as shown in the figure below. Draw the correct HDB3 coding for this string of bits. Clock Pulse Unipolar x x x x x x x x x x x x AMI HDB3 Problem 2 Doppler Shift in Electromagnetic Signal (20 points) Given a cellular network where the mobile transceiver station antenna is communicating with a mobile cell phone being used by a subscriber in a moving vehicle. 2

When a cell phone is in motion with respect to the stationary base station antenna, Doppler shift changes the frequency of the signal being received (both the mobile cell phone and the base station

3 When a cell phone is in motion with respect to the stationary base station antenna, Doppler shift changes the frequency of the signal being received (both the mobile cell phone and the base station antenna are affected by Doppler shifting). The cellular communication band is 900 MHz (f C ) and v represents the automobile s velocity. (a) Assume that the angle is small so that cos ( ) can be safely assumed to be unity. Write an equation for the frequency shift due to Doppler shift fd as a function of velocity v. (b) If the automobile is moving directly toward the bay station antenna, what is the Doppler frequency shift (or Doppler spread) in Hz? Is the frequency increased or decreased by traveling toward the antenna? (c) If the frequency is changed to 2.4 GHz, now what is the Doppler frequency shift (or Doppler spread) in Hz? 3

4 Problem 3 US Digital Cellular Standard Data Rate (5 points) Bandwidth efficiency is computed from the data rate R divided by the channel bandwidth B. Remember from an earlier homework assignment that Shannon s channel capacity equation is given by S C = B log2 + in bits/second N where C is the capacity, B is bandwidth and (S/N) is the signal-to-noise ratio as usual. Capacity C may be thought of as the maximum data rate estimate for a communication channel (or maximum bandwidth efficiency max for the channel. The US Digital Cellular Standard (established in 99) calls for a data rate of 48.6 kbps with a channel bandwidth of 30 khz and signal-to-noise ratio of 20 db. By the way, US Digital Cellular operates from 824 MHz to 894 MHz (including both uplink and downlink). (a) Calculate Shannon s capacity C for the US Digital Cellular Standard with the above parameters. (b) How does your answer from part (a) above compare to 48.6 kbps? Problem 4 Latency in Wireless Communications (30 points) The speed of electromagnetic waves (often called speed of light with symbol c) is very fast. In fact, c = meters/second = 86,282 miles/second = feet/second in vacuum. However, while this velocity is extremely fast, radio waves still can have appreciable delay times in long distance communications such as in satellite links. This delay time is called latency. 4

5 (a) The speed of light is its maximum in vacuum, but propagation through matter slows it down. For example, in a coaxial cable the insulation between inner and outer conductors has a typical index of refraction of n =.5. Calculate the speed of a signal in a coaxial cable if we assume the speed in vacuum is 983,570,000 feet per second. (Note: the index of refraction n is the speed in vacuum c divided by the velocity v in the material being considered.) (b) Repeat part (a) but now using air as the medium instead of say Teflon for the material. Air has an index of refraction value of n = Find the velocity of electromagnetic waves in air. By what percentage does air slow down a radio wave relative to that of vacuum? (c) Does your answer justify ignoring the slowing of radio waves in air? (d) A geosynchronous satellite orbits the Earth around the equator at a velocity that keeps the satellite directly over on spot of the Earth. This altitude for geosynchronous orbit is 22,236 miles (= 7,406,080 feet). If you have a transceiver directly below the satellite, how long does it take a signal to travel from your station to the satellite? 5

6 (e) How long does it take an electromagnetic signal in air to travel one foot? Next, express your answer in feet per nanosecond. (f) What role does the index of refraction of air in satellite communication? Problem 5 Line Code Characteristics (5 points) In practice, most binary data is transmitted as (non-return to zero). As an example, refer to slide 9 of Lecture. (a) Why is predominately used? (b) The spectrum of data has nulls at integer multiples of the bit rate. A null means that no energy is transmitted at that frequency. Explain why that is true.. 6

Chapter 4 Digital Transmission 4.1

Chapter 4 Digital Transmission 4.1 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 4-1 DIGITAL-TO-DIGITAL CONVERSION In this section, we see how we can represent