ECE 4710: Lecture #2 1 Frequency  Communication systems often use atmosphere for transmission  “Wireless”  Time-varying Electro-Magnetic (EM) Wave  Propagation characteristics of EM wave thru atmosphere are highly dependent on frequency/wavelength  f is frequency   is wavelength  c is speed of light = 3 x 10 8 m/s

ECE 4710: Lecture #2 2 Propagation Modes  Three dominate types of propagation modes  Ground Wave » f < 2 MHz »Diffraction causes wave to propagate along Earth surface »Propagation beyond visual horizon (e.g. AM broadcast radio) with sufficient Tx power  Sky-Wave »2 MHz < f < 30 MHz »Refraction/Reflection off ionosphere ( mile alt.) »Intermittent coverage along Earth’s surface

ECE 4710: Lecture #2 3 Ground Wave With sufficient Tx power ground waves can propagate thousands of miles

ECE 4710: Lecture #2 4 Sky Wave International broadcasts (BBC, VOA, etc.) can be heard half-way around the world with modest Tx power Note that only certain locations on ground can receive Tx signal

ECE 4710: Lecture #2 5 Propagation Modes  Line of Sight = LOS » f > 30 MHz »Signal path must be free from obstructions »Earth’s curvature will determine LOS distance for antennas mounted on tall towers »LOS distance =  h f : antenna height in feet  h m : antenna height in meters »Two antenna towers/heights (Tx and Rx)

ECE 4710: Lecture #2 6 Line of Sight (LOS) Short range for reasonable antenna heights  h 1 = 30 m and h 2 = 50 m  D T = 52 km or 32 miles !!

ECE 4710: Lecture #2 7 Frequency Allocations

ECE 4710: Lecture #2 8 LOS Propagation  Why use high frequencies which have smaller propagation distances (LOS)?  High carrier frequencies ( f c ) support larger bandwidth (BW) signals which leads to higher data rates + more users »Practical Tx/Rx’s can have signal BWs  0.1 f c »Information data rate R d  BW  Antenna size must be at least 10% of for efficient propagation of EM wave thru atmosphere (~0.5 for RF) »f c = 10 kHz   km  antenna height = 3000 m !!  Must modulate most baseband signals with high frequency carrier for wireless transmission to have reasonable antenna size

ECE 4710: Lecture #2 9 Information Measure  How is information content measured?  Information sent from digital source from the j th message is where P j is the probability of transmitting the j th message  Information content will, in general, vary from one message to the next since P j is usually variable  Bit = unit of information and  Bit = unit of binary data (0,1) but they are not the same  Must use context to determine meaning

ECE 4710: Lecture #2 10 Information Measure  Since information content varies from message to message  must measure average information - where m is the number of possible source messages - H is also called the “entropy” of the source  Rate of Information

ECE 4710: Lecture #2 11 Information Measure Example: 8 digit word (message) with two possible states per digit (binary). Find the entropy if a) all words equally likely and b) if half the words have P j1 = 1/512 a) m = 2 8 = 256 and since all words equally likely P j = 1/ m = 1/256 b) Note: All  P j = 1 (definition of probability) so 128 P j P j2 = 1  P j2 = (1/128)(1-128 P j1 ) = (1/128)(3/4)= 3/512 must have equally likely for average information content = # digits

ECE 4710: Lecture #2 12 Channel Capacity  Ideal channel capacity shown by Shannon to be  Actual channel data rate R c < C

ECE 4710: Lecture #2 13 Channel Capacity  C  B so more bandwidth means higher data rate  PSD of rectangular pulse train is (sin x / x ) 2  As T b  data rate R c  since R c  ( T b ) -1, but B also  !!  Increasing signal BW will increase data rate if everything else remains the same f PSD 1 / T s = FNBW Symbol Period = T s = T b = Bit Period Signal BW = B s  1 / T b …

ECE 4710: Lecture #2 14 Channel Capacity  C is also  S/N  Higher signal power means larger channel capacity???  Larger S/N makes it easier to differentiate (detect) multiple states per digital symbol in presence of noise  higher data rate for same symbol period & bandwidth vs T s T s2 T s1 = T s2 but R 1 = 2R 2 **Note that ( S /N) 1 > ( S /N) 2 to achieve higher data rate with same bit error probability**

ECE 4710: Lecture #2 15 Digital System Performance  Critical Performance Measures:  Bit Error Rate (BER)  Channel BW = Transmitted Signal BW  Received S/ N  Signal Power  Channel Data Rate (R c )  Desire high data rate with small signal BW, low signal power, and low BER!!  Fundamental tradeoff between signal power and BW  Example: Error Coding  add coding bits to data stream but keep same data rate »For same R c  T s must  and  BW  »But coding will correct errors allowing weaker signal power for same BER

ECE 4710: Lecture #2 16 Error Coding  Errors occur due to corruption of Tx signal by noise and interference in channel  Reduce errors to improve performance  Two Coding Types  ARQ: Automatic Repeat Request  FEC: Forward Error Correction  ARQ : Add parity bits, Rx detects error, sends request for retransmission of data  FEC: Add coding bits, Rx detects and corrects for some (usually not all) of the errors

ECE 4710: Lecture #2 17 Error Coding  ARQ is used often for computer communications (internet)  Not possible with one-way communication  Not good for systems with large transmission delays  Leads to poor data throughput when retransmissions are frequent  FEC is widely used in wireless communication systems  Two major types: Block Codes & Convolutional Codes  Coding Performance: measure improvement in S/N before and after coding  Lower S/N can achieve same BER for signal with coding compared to signal without coding  “Coding Gain”  Coding Threshold: coded signal will have worse performance for S/N below some threshold value!!

ECE 4710: Lecture #2 18 Coding Performance