1. Stallings charts modified and added to
Antennas, Electromagnetic Propagation, Fading Effects, and Channel Coding
Session 4
Nilesh Jha
Stallings charts modified and added to

2. General Frequency Ranges
Microwave and Millimeter Wave frequency range
Roughly 1 GHz to 20 GHz; 20 GHz to 300 GHz
The higher the frequency the higher the beam directionality (antenna gain) for a given antenna size
Used for point to point and satellite communications, but also in lower ranges for PCS (so far up to 2GHz) and WLAN (so far up to 6 GHz)
Radio frequency range --- VHF and UHF (plus)
30 MHz to 1 GHz
Easier to do omni transmission
Broadcasting, radio mobile services, cellular
Infrared frequency range --- short range
Roughly, 3x1011 to 2x1014 Hz
Useful in local point-to-point and to multipoint applications within confined areas

3. Fixed Terrestrial Microwave
Description of common microwave antenna
Parabolic dish, a few feet or meters in diameter
Fixed rigidly and focuses a narrow beam
Achieves line-of-sight transmission to receiving antenna
Located at substantial heights above ground level
Applications --- Fixed Wireless
Long haul telecommunications service
Short point-to-point links between buildings
Wireless Local Loop --- to Homes or Businesses

4. Satellite Microwave Description of communication satellite
Microwave relay station
Used to link two or more ground-based microwave transmitter/receivers
Receives transmissions on one frequency band (uplink), amplifies or repeats the signal, and transmits it on another frequency (downlink)
Applications
Television distribution
Long-distance telephone transmission
Private business networks

5. Broadcast Radio Description of broadcast radio antennas Applications
Omnidirectional
Antennas not required to be dish-shaped
Antennas need not be rigidly mounted to a precise alignment
Receive antennas often dipoles
Applications
Broadcast radio
VHF and part of the UHF band; 30 MHZ to 1GHz
Covers FM radio and UHF and VHF television

6. Cellular, PCS and WLAN
Frequencies in the 800 MHz to 1000 MHz range for cellular --- also called First Generation or 1G
PCS and DCS called 2G --- Frequencies around 1800 to 2000 MHz range
WLAN around 2400 MHz, also around 5.5 GHz
Cell phone antennas are short dipoles, base station antennas longer dipoles and combinations for some gains
Finding more spectrum
Some around 1700 MHz, also down at TV UHF bands
Up to around 2700 MHz
Lower frequencies propagate better and penetrate buildings more, but less spectrum

7. Antennas -- Basic
An antenna is an electrical conductor or system of conductors
Transmission - radiates electromagnetic energy into space
Reception - collects electromagnetic energy from space
In two-way communication, the same antenna can be used for transmission and reception

8. Radiation Patterns Radiation pattern
Graphical representation of radiation properties of an antenna
Depicted as two-dimensional cross section
Beam width (or half-power beam width)
Measure of directivity of antenna
Reception pattern
Receiving antenna’s equivalent to radiation pattern

9. Types of Antennas Isotropic antenna (idealized) Dipole antennas
Radiates power equally in all directions
Dipole antennas
Half-wave dipole antenna (or Hertz antenna)
Quarter-wave vertical antenna (or Marconi antenna)
Parabolic Reflective Antenna

10. Antenna Gain Antenna gain Effective area
Power output, in a particular direction, compared to that produced in any direction by a perfect omnidirectional antenna (isotropic antenna)
Effective area
Related to physical size and shape of antenna

11. Antenna Gain Relationship between antenna gain and effective area
G = antenna gain
Ae = effective area
f = carrier frequency
c = speed of light (» 3 ´ 108 m/s)
 = carrier wavelength

12. Propagation Modes Ground-wave propagation Sky-wave propagation
Line-of-sight propagation

13. Ground Wave Propagation

14. Ground Wave Propagation
Follows contour of the earth
Can Propagate considerable distances
Frequencies up to 2 MHz
Example
AM radio

15. Sky Wave Propagation

16. Sky Wave Propagation
Signal reflected from ionized layer of atmosphere back down to earth
Signal can travel a number of hops, back and forth between ionosphere and earth’s surface
Reflection effect caused by refraction
Examples
Amateur radio
CB radio

17. Line-of-Sight Propagation

18. Line-of-Sight Propagation
Transmitting and receiving antennas must be within line of sight
Satellite communication – signal above 30 MHz not reflected by ionosphere
Ground communication – antennas within effective line of site due to refraction
Refraction – bending of microwaves by the atmosphere
Velocity of electromagnetic wave is a function of the density of the medium
When wave changes medium, speed changes
Wave bends at the boundary between mediums

19. Line-of-Sight Equations
Optical line of sight
Effective, or radio, line of sight
d = distance between antenna and horizon (km)
h = antenna height (m)
K = adjustment factor to account for refraction, rule of thumb K = 4/3

20. Line-of-Sight Equations
Maximum distance between two antennas for LOS propagation:
h1 = height of antenna one
h2 = height of antenna two

21. LOS Wireless Transmission Impairments
Attenuation and attenuation distortion
Free space loss
Noise
Atmospheric absorption
Multipath
Refraction
Thermal noise

22. Attenuation
Strength of signal falls off with distance over transmission medium
Attenuation factors for unguided media:
Received signal must have sufficient strength so that circuitry in the receiver can interpret the signal
Signal must maintain a level sufficiently higher than noise to be received without error
Attenuation is greater at higher frequencies, causing distortion

23. Free Space Loss Free space loss, ideal isotropic antenna
Pt = signal power at transmitting antenna
Pr = signal power at receiving antenna
 = carrier wavelength
d = propagation distance between antennas
c = speed of light (= 3x10^ 8 m/s)
where d and  are in the same units (e.g., meters)

24. Free Space Loss
Free space loss equation can be recast:

25. Free Space Loss Free space loss accounting for gain of other antennas
Gt = gain of transmitting antenna
Gr = gain of receiving antenna
At = effective area of transmitting antenna
Ar = effective area of receiving antenna

26. Free Space Loss + Antenna Gains
Free space loss accounting for gain of other antennas can be recast as (Note: usually the antenna gains/losses are added separately)

27. Real Distance Dependence
20xlog(d) comes from 1/d^2 propagation, spherical propagation of wavefront
In reality propagation is through many multipath channels, with fading effects, scattering around obstacles, etc
Effective distance dependence is xnxlog(d)
n is propagation index, environment dependent
n is usually 3-5, 4 is not too far off

28. From Rappaport and Ref. there

30. Categories of Noise Thermal Noise Intermodulation noise Crosstalk
Impulse Noise

31. Thermal Noise Thermal noise due to agitation of electrons
Present in all electronic devices and transmission media
Cannot be eliminated
Function of temperature
Particularly significant for satellite communication

32. Thermal Noise
Amount of thermal noise to be found in a bandwidth of 1Hz in any device or conductor is:
N0 = noise power density in watts per 1 Hz of bandwidth
k = Boltzmann's constant = x10-23 J/K
T = temperature, in kelvins (absolute temperature)

33. Thermal Noise Noise is assumed to be independent of frequency
Thermal noise present in a bandwidth of B Hertz (in watts):
or, in decibel-milliwatts (dBm)
Where T=NFxTsub0, and Tsub0=290 degrees K
NF is effective noise figure of device

34. Noise Terminology
Intermodulation noise – occurs if signals with different frequencies share the same medium
Interference caused by a signal produced at a frequency that is the sum or difference of original frequencies
Crosstalk – unwanted coupling between signal paths
Impulse noise – irregular pulses or noise spikes
Short duration and of relatively high amplitude
Caused by external electromagnetic disturbances, or faults and flaws in the communications system

35. Expression Eb/N0
Ratio of signal energy per bit to noise power density per Hertz
B=bandwidth
So SNR and Eb/N0 related through B/R
The bit error rate for digital data is a function of Eb/N0
Given a value for Eb/N0 to achieve a desired error rate, parameters of this formula can be selected
As bit rate R increases, transmitted signal power must increase to maintain required Eb/N0

36. Other Impairments and Effects
Atmospheric absorption – water vapor and oxygen make it worse at higher frequencies --- typically some GHz, worse higher, some ‘windows’ around GHz and 95 GHz
Multipath – obstacles reflect signals so that multiple copies with varying delays are received -- see fig 5.10 next
Particularly important in cellular or any path that does not have a direct line of sight, or where objects near LOS path
Diffraction -- Bending of radio waves around obstacles and corners
Refraction -- Bending by atmosphere (like lenses) due to varying index of refraction at different heights, places

37. Multipath Propagation

38. Multipath Propagation
Reflection - occurs when signal encounters a surface that is large relative to the wavelength of the signal
Diffraction - occurs at the edge of an impenetrable body that is large compared to wavelength of radio wave
Scattering – occurs when incoming signal hits an object whose size in the order of the wavelength of the signal or less

39. The Effects of Multipath Propagation
Multiple copies of a signal may arrive at different phases
If phases add destructively, the signal level relative to noise declines, making detection more difficult --- Fading
Intersymbol interference (ISI)
One or more delayed copies of a pulse may arrive at the same time as the primary pulse for a subsequent bit

40. Types of Fading
Due to multiple paths arriving at receiver and adding constructively and destructively in a random basis
Fast fading
due to small variations in path lengths as one moves or as scatterers move -- often modeled as Rayleigh
Slow fading -- shadow fading
Slower, as one moves and blockage and objects in between change -- often modeled as a log normal distribution

41. Figure showing fading, similar to fig. 5.12 in Stallings

42. Error Control Process --and Error Minimization
Error control process has three components
Error minimization
Error detection
Error correction --- FEC (Forward Error Correction)
Error minimization: modulation/coding techniques to minimize effects of noise/fading, interleaving to scramble bits (fight off effects of error ‘bursts’), equalization vs fading effects, and diversity vs fading effects
Coding done for error detection (eg, CRC) and for error correction (FEC codes: convolutional, block)
Automatic repeat request (ARQ) protocols
Block of data with error is discarded, data retransmitted -- not for voice
Requires error detection

43. Wireless Re-transmission
ARQ Protocols
Often inadequate for wireless applications
Error rate on wireless link can be high, results in a large number of retransmissions
Long propagation delay compared to transmission time --- lots of frames in transit
Not good for voice, possible for data if FEC is used first to have errors less often

44. Forward Error Correction (FEC)
Required to offset channel induced errors
Sometimes referred to as ‘channel coding’
Transmitter adds error-correcting code to data block
Code is a function of the data bits
Receiver calculates error-correcting code from incoming data bits
If calculated code matches incoming code, no error occurred
If error-correcting codes don’t match, receiver attempts to determine bits in error and correct
Codes are in fact able to correct

45. Channel Coding
FEC used to code to offset effects of propagation -- eg multipath fading
Since fading goes in and out, when power down FEC used to try to offset the lower SNR
Involves insertion of additional FEC bits
Block Codes -- similar to CRC, but are able to correct 1, 2 or more errors, depending on size of block (number of bits added) and code strength (Hamming distance)
Convolutional Codes -- combines the the bits to be corrected ---- uses Viterbi decoding
Interleaving --- used to mix bits in to minimize the effects of error bursts

46. Error Detection Probabilities
Definitions
Pb : Probability of single bit error (BER)
P1 : Probability that a frame arrives with no bit errors
P2 : While using error detection, the probability that a frame arrives with one or more undetected errors
P3 : While using error detection, the probability that a frame arrives with one or more detected bit errors but no undetected bit errors (ie, all errors detected)

47. Error Detection Probabilities
With no error detection
F = Number of bits per frame

48. Error Detection Process
Transmitter
For a given frame, an error-detecting code (check bits) is calculated from data bits
Check bits are appended to data bits
Receiver
Separates incoming frame into data bits and check bits
Calculates check bits from received data bits
Compares calculated check bits against received check bits
Detected error occurs if mismatch

49. Error Detection Process
Decoder

50. Parity Check Parity bit appended to a block of data Even parity
Added bit ensures an even number of 1s
Odd parity
Added bit ensures an odd number of 1s
Example, 7-bit character [ ]
Even parity [ ]
Odd parity [ ]

51. Cyclic Redundancy Check (CRC)
Transmitter
For a k-bit block, transmitter generates an (n-k)-bit frame check sequence (FCS)
Resulting frame of n bits is exactly divisible by predetermined number
Receiver
Divides incoming frame by predetermined number
If no remainder, assumes no error

52. CRC using Modulo 2 Arithmetic
Exclusive-OR (XOR) operation
Parameters:
T = n-bit frame to be transmitted
D = k-bit block of data; the first k bits of T
F = (n – k)-bit FCS; the last (n – k) bits of T
P = pattern of n–k+1 bits; this is the predetermined divisor
Q = Quotient
R = Remainder

53. CRC using Modulo 2 Arithmetic
For T/P to have no remainder, start with
Divide 2n-kD by P gives quotient and remainder
Use remainder as FCS

54. CRC using Modulo 2 Arithmetic
Does R cause T/P have no remainder?
Substituting,
No remainder, so T is exactly divisible by P

55. CRC using Polynomials Widely used versions of P(X) CRC–12 CRC–16
X12 + X11 + X3 + X2 + X + 1
CRC–16
X16 + X15 + X2 + 1
CRC – CCITT
X16 + X12 + X5 + 1
CRC – 32
X32 + X26 + X23 + X22 + X16 + X12 + X11 + X10 + X8 + X7 + X5 + X4 + X2 + X + 1

56. Digital Logic CRC

57. Block Error Correction Codes
Transmitter
Forward error correction (FEC) encoder maps each k-bit block into an n-bit block codeword
Codeword is transmitted; analog for wireless transmission
Receiver
Incoming signal is demodulated
Block passed through an FEC decoder

58. Forward Error Correction Process

59. FEC Decoder Outcomes No errors present
Codeword produced by decoder matches original codeword
Decoder detects and corrects bit errors
Decoder detects but cannot correct bit errors; reports uncorrectable error
Decoder detects no bit errors, though errors are present

60. Block Code Principles
Hamming distance – for 2 n-bit binary sequences, the number of different bits
E.g., v1=011011; v2=110001; d(v1, v2)=3
Redundancy – ratio of redundant bits to data bits
Code rate – ratio of data bits to total bits
Coding gain – the reduction in the required Eb/N0 to achieve a specified BER of an error-correcting coded system

61. Hamming Code Designed to correct single bit errors
Family of (n, k) block error-correcting codes with parameters:
Block length: n = 2m – 1
Number of data bits: k = 2m – m – 1
Number of check bits: n – k = m
Minimum distance: dmin = 3
Single-error-correcting (SEC) code
SEC double-error-detecting (SEC-DED) code

62. Cyclic Codes
Can be encoded and decoded using linear feedback shift registers (LFSRs)
For cyclic codes, a valid codeword (c0, c1, …, cn-1), shifted right one bit, is also a valid codeword (cn-1, c0, …, cn-2)
Takes fixed-length input (k) and produces fixed-length check code (n-k)
In contrast, CRC error-detecting code accepts arbitrary length input for fixed-length check code

63. BCH Codes
For positive pair of integers m and t, a (n, k) BCH code has parameters:
Block length: n = 2m – 1, m greater than 2
Number of check bits: n – k  mt
Minimum distance:dmin  2t + 1
Can correct combinations of t or fewer errors
Flexibility in choice of parameters
Block length, code rate

64. Reed-Solomon Codes Subclass of nonbinary BCH codes
Data processed in chunks of m bits, called symbols
An (n, k) RS code has parameters:
Symbol length: m bits per symbol
Block length: n = 2m – 1 symbols = m(2m – 1) bits
Data length: k symbols
Size of check code: n – k = 2t symbols = m(2t) bits
Minimum distance: dmin = 2t + 1 symbols
Can correct t or fewer errors

65. Convolutional Codes Generates redundant bits continuously
Error checking and correcting carried out continuously
(n, k, K) code
Input processes k bits at a time
Output produces n bits for every k input bits
K = constraint factor
k and n generally very small
n-bit output of (n, k, K) code depends on:
Current block of k input bits
Previous K-1 blocks of k input bits

66. Convolutional Encoder

67. Decoding Trellis diagram – expanded encoder diagram
Viterbi code – error correction algorithm
Compares received sequence with all possible transmitted sequences
Algorithm chooses path through trellis whose coded sequence differs from received sequence in the fewest number of places
Once a valid path is selected as the correct path, the decoder can recover the input data bits from the output code bits

68. Some Use of Codes
CRC used often to detect uncorrectable errors in a frame, for an ARQ function on data as last choice
Reed-Solomon code used in CDPD
Coding gain is determined by change in Eb/Nsub0 that gives same BER -- few dB
eg, 2.77 dB in Fig 8.6 Stallings at ber of 10^-5
IS-95 uses convolutional codes, as do most cellular systems, using Viterbi decoding
Bit error rates : Raw channel BER is about 10^-1 or 10^ -2
Voice needs 10^-2 or 10^-3, so coding needs to do this
For data one often needs about 10^ in 3G a concatenated coding scheme, with RS block coding and convolutional coding

69. From Stallings

70. Block Interleaving -- Time Diversity
Data written to and read from memory in different orders
Data bits and corresponding check bits are interspersed with bits from other blocks
At receiver, data are deinterleaved to recover original order
A burst error that may occur is spread out over a number of blocks, making error correction possible
Used in 2G and 3G systems --- speech coders produce important bits in succession, interleaving spreads them out over time, codes can correct them

71. Block Interleaving

72. Automatic Repeat Request
Mechanism used in data link control and transport protocols
Relies on use of an error detection code (such as CRC)
Flow Control
Error Control

73. Multipath Induced Effects
Causes fading (amplitude variations and deep ‘nulls’) and ISI (copies of symbols come in delayed and overlap next symbol) -- fading is both fast (msec) and slow (seconds)
Fast is rapid variations, slow is shadowing
Flat fading is for narrowband channels
BW (signal)<(Coherence) BW of channel, eg, AMPS
Fast fading, ‘handled’ somewhat with coding and diversity
Frequency selective fading
BW (signal)>(Coherence) BW of channel, eg, TDMA, GSM, CDMA
Causes ISI, some fading but not as bad as it averages out some
Fast fading ‘handled’ well with coding and diversity
Time diversity in Rake receivers for CDMA (combines multi path energies
ISI handled with equalizers in TDMA/GSM
CDMA codes separate multi path returns so no mixing, can combine

74. Adaptive Equalization for ISI
Used to combat intersymbol interference (ISI) caused by multipath
Involves gathering dispersed symbol energy back into its original time interval
Dispersion determined by maximum time delay spread
Represents the time over which one symbol will affect other symbols
Large variation, environment dependent
Outdoors in 5-20 usecs range, maybe to 100 usec
Indoors smaller, maybe to .1 to 1 usec
At 30kbps one bit is 33 usec long, so if delay spread is 100 usec it causes interference with 3 bits
Even if delay spread is 10 usec it interferes with first third of next bit
At 200 kbps one bit is 5 usec long so 10 usec spread interferes with 2 bits
The higher the data rate the worse the ISI effect is -- A BROADBAND EFFECT
Channel coherence bandwidth Bc=(approx) 1/5x(RMS delay spread)
For delay spread = 4 usec (say), Bc=50 KHz, so AMPS at 30 KHz (so less) does NOT need equalizer but GSM at 200 KHz DOES

75. From Rappaport

76. Equalization Techniques
Need to be adaptive since channel is unknown -- at receiver
Digital signal processing algorithms, called equalizers, that estimate the channel transfer function and reverse its effects --- involves an estimate of the channel via a known symbol sequence transmitted which is then compared at receiver with stored replica
Estimate channel: training and tracking
Equalizer is a time varying filter whose weights are adapted based on channel estimate --- often implemented as adaptive transversal (FIR) filter
Algorithms: weights to minimize estimated error, eg, least mean squares
Linear and nonlinear -- nonlinear needed if deep nulls due to multipath
NL: Decision feedback (subtracts detected symbol), maximum likelihood (tests all possible data sequences and picks best --- lots of computation)
Also possible but not as robust: blind algorithms, based on eg, keeping envelope constant on constant envelope modulations (eg, GSM)

77. Diversity Techniques
Diversity is based on the fact that individual channels experience independent fading events
Space diversity – techniques involving multiple physical transmission paths -- eg, multiple antennas
Most base stations have two diversity receive antennas for this reason
Rapaport p.327, can go from 90% prob. of not fading to 99% w/2, or 99.99% w/4 diversity antennas, by selecting the strongest one
Smart antennas can collect most of the energy from different multipaths
Frequency diversity – techniques where the signal is spread out over a larger frequency bandwidth or carried on multiple frequency carriers --- CDMA DS spreads energy over a larger BW, affects frequency diversity
Time diversity – techniques aimed at spreading the data out over time --- eg, bit repetition, interleaving, Rake processing (in CDMA)
FEC coding often thought of as a form of time diversity

78. Sample
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79. Sample
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