COSC 3213: Computer Networks I: Chapter 3 Handout #4 Instructor: Dr. Marvin Mandelbaum Department of Computer Science York University Section A Topics: 1. Line Coding: Unipolar, Polar,and Inverted ; Bipolar; Manchester and Differential Manchester. 2. Digital Modulation Schemes: ASK, PSK, FSK, and QAM 3. Modems 4. Transmission Media Garcia: Sections 3.5 3.8
Line Coding (1) Line Coding: Converts a binary sequence into a digital signal Unipolar : Bit 1 is represented by +A Volts Bit 0 is represented by 0 Volts Unipolar 1 0 1 0 1 1 1 0 0 Average transmitted power per pulse = 1/2 (A 2 ) + 1/2 (0) = A 2 / 2 Average value of signal = A / 2 Volts 2
Line Coding (2) 2. Polar : Bit 1 is represented by +A/2 Volts Bit 0 is represented by A/2 Volts Unipolar Polar 1 0 1 0 1 1 1 0 0 Average transmitted power per pulse = 1/2 (A/2) 2 + 1/2 ( A/2) 2 = A 2 / 4 Half the power used as compared to Unipolar with same distance between levels Average value of signal = 0 Volts 3
Line Coding (3) 3. -inverted: First bit 1 is represented by +A/2 Volts No change for bit 0; Flip to the opposite voltage for next bit 1 Unipolar Polar -Inverted (Differential Encoding) 1 0 1 0 1 1 1 0 0 Average transmitted power per pulse = A 2 / 4 Average value of signal = 0 Volts 4
Line Coding (4) 4. Bipolar: Bit 0 is represented by 0 Volts First bit 1 by +A/2 Volts; Consecutive 1 s by +A/2 and A/2 Unipolar Polar 1 0 1 0 1 1 1 0 0 -Inverted Bipolar Encoding Average transmitted power per pulse = A 2 / 8 Average value of signal = 0 Volts Better scheme for strings of 1s in data. 5
Line Coding (5) 5. Manchester: Bit 1 Bit 0 A/2 -A/2 -A/2 A/2 Unipolar 1 0 1 0 1 1 1 0 0 Polar -Inverted Bipolar Encoding Manchester Average transmitted power per pulse = A 2 / 4; Average value of signal = 0 Volts 6
Line Coding (6) 6. Differential Manchester: Bit 1 Next 0: No change A/2 -A/2 Next 1: Flip to -A/2 A/2 Unipolar 1 0 1 0 1 1 1 0 0 Polar -Inverted Bipolar Encoding Manchester Differential Manchester Average transmitted power per pulse = A 2 / 4; Average value of signal = 0 Volts 7
Line Coding (7) Power spectra of different line coding schemes: 1.2 1 power density 0.8 0.6 0.4 0.2 : Unipolar Bipolar Manchester 0-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 is typically used for lowpass channels. Bipolar is used for telephone transmission system that do not pass frequencies < 200 Hz Manchester used for LAN (Manchester for Ethernet & Differential for Token ring) where bandwidth efficiency is relatively not important f T 8
Digital Modulation (1) Why Modulation: 1. Modulation shifts the frequency content of message signal to a range that is passed by the channel. Example: Spectrum of the signal is represented in green while the channel is represented in blue 0 f 1 f c f 2 f Output is zero 0 f 1 f c f 2 f Modulation shifts the signal spectrum. Signal is transmitted without distortion. 2. Selecting a different carrier frequency for different signals lead to multiple access. 3. Effect of channel noise can be reduced by selecting an appropriate carrier frequency. 9
Digital Modulation (2) Amplitude Shift Keying (ASK): Represent bit 1 with cos(2πf c Represent bit 0 with 0 Volts Information 1 0 1 1 0 1 ASK 0 T 2T 3T 4T 5T 6T t 10
Digital Modulation (3) Frequency Shift Keying (FSK): Represent bit 1 with cos(2πf 1 Represent bit 0 with cos(2πf 2 Information 1 0 1 1 0 1 ASK 0 T 2T 3T 4T 5T 6T t FSK 0 T 2T 3T 4T 5T 6T t 11
Digital Modulation (3) Phase Shift Keying (PSK): Represent bit 1 with cos(2πf c Represent bit 0 with cos(2πf c t + π) = cos(2pf c Information 1 0 1 1 0 1 ASK 0 T 2T 3T 4T 5T 6T t FSK 0 T 2T 3T 4T 5T 6T t PSK 0 T 2T 3T 4T 5T 6T t 12
PSK - Modulation 1. Represent binary information with a polar Information 1 0 1 1 0 1 Baseband Signal X i ( 2. Multiply X i ( with sine wave generator 0 T 2T 3T 4T 5T 6T t 1 / W A k x Y i ( = A k cos(2πf c cos(2πf c PSK 0 T 2T 3T 4T 5T 6T t 13
PSK - Demodulation PSK 0 T 2T 3T 4T 5T 6T t 1. Multiply PSK signal with sine wave generator Y i ( x 2Y i ( cos(2πf c Output can be expressed as 2Y i ( cos(2πf c = A k ( 1 + cos(2π2f c ) 2 cos(2πf c 1 / W 0 T 2T 3T 4T 5T 6T t Transmission rate = 1 bit / pulse duration = W bps for a channel with BW = W Hz 14
PSK Demodulation (2) PSK 0 T 2T 3T 4T 5T 6T t 2. Filter out the high frequency component Y i ( x 2Y i ( cos(2πf c Low-pass Filter with cutoff f c Hz 2 cos(2πf c 3. A k is retrieved Baseband Signal X i ( 0 T 2T 3T 4T 5T 6T t 15
QAM - Modulation 1. Split information stream into two sequences of odd and even numbered bits 01011100 Splitter 0010 (odd #) 1110 (even #) 2. Determine the bipolar sequences: B k for even #ed bits and A k for odd #ed bits 3. Multiply A k with cosine wave and B k with sine wave A k x Y i ( = A k cos(2πf c B k cos(2πf c x Y q ( = B k sin(2πf c + Y( sin(2πf c 16
QAM Signal Constellation 3. Signal Constellation: is a method of representing signal states in terms of inphase (cos(2πf c ) and quadrature (sin(2πf c ) components. How to draw signal constellation for Y( =A k cos(2πf c + B k sin(2πf c Take cos(2πf c as the horizontal axis and sin(2πf c as the vertical axis Derive all possible combinations of Y( =A k cos(2πf c + B k sin(2πf c by selecting different combinations of A k and B k. Represent each combination of Y( =A k cos(2πf c + B k sin(2πf c as a coordinate (A k,b k ) on the Cartesian axis sin(2πf c 1 1 1 1 cos(2πf c 4 levels / pulse 2 bits / pulse 2W bps Activity I: Draw constellation for QAM system where A k and B k have values ( 1, 2/3,1/3,1)? 17
QAM - Demodulation Multiply Y( with sine and cosine wave followed by lowpass filtering Y( x Low-pass Filter with cutoff W/2 Hz A k 2cos(2πf c x Low-pass Filter with cutoff W/2 Hz B k 2sin(2πf c Activity II: Show that the above system restores A k and B k? 18
Telephone Modems Telephone Channels: Passband range: 500 Hz to 2900 Hz (BW =?) SNR = 40 db Duration of pulse =? (1 / BW) Why? Channel Capacity =? Pulse Rate 2400 pulses/s 2400 pulses/s 2400 pulses/s 2400 3429 pulses/s Modulation Trellis 128 w/ 64 valid Trellis 32 w/ 16 valid QAM 4 (all valid) Trellis 960 V.32bis 6 x 2400 = 14,400 bps 4 x 2400 = 9,600 bps 2 x 2400 = 4,800 bps V.64bis 2400 33,600 bps Activity III: Derive the pulse rate and channel capacity of the telephone channel? 19
Digital Media 1. Twisted Pair 2. Coaxial Cable 3. Optical Fiber 4. Microwave The topic will not be covered explicitly in the class Review section 3.7 for details 20