1. Wireless NETWORKS NET 434 Topic # 3 Wireless Transmission and Channel
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2.  The McGraw-Hill Companies, Inc., 1998
Figure 4-6
Sine Wave
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3.  The McGraw-Hill Companies, Inc., 1998
Figure 4-8
Amplitude Change
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Figure 4-9
Frequency Change
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Figure 4-10
Phase Change
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6. Time and Frequency Domain
Figure 4-11
Time and Frequency Domain
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7.  The McGraw-Hill Companies, Inc., 1998
Figure 4-12
Examples
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8. Signal with DC Component
Figure 4-13
Signal with DC Component
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9.  The McGraw-Hill Companies, Inc., 1998
Figure 4-14
Complex Waveform
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Figure 4-15
Bandwidth
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11.  The McGraw-Hill Companies, Inc., 1998
Figure 4-16
Digital Signal
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12. Amplitude, Period, and Phase
Figure 4-17
Amplitude, Period, and Phase
for a Digital Signal
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13. Bit Rate and Bit Interval
Figure 4-18
Bit Rate and Bit Interval
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14. Harmonics of a Digital Signal
Figure 4-19
Harmonics of a Digital Signal
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15. Exact and Significant Spectrums
Figure 4-20
Exact and Significant Spectrums
However, most of the energy in the signal is contained in a relatively narrow band of frequencies. This band is referred to as the effective bandwidth, or just bandwidth.
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16. Corruption Due to Insufficient Bandwidth
Figure 4-22
Corruption Due to Insufficient Bandwidth
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17. Bandwidth and Data Rate
Figure 4-23
Bandwidth and Data Rate
How fast we can send the data in bits per second. It depends upon the bandwidth, the noise and the number of levels used to encode the data.
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18. Relationship between Data Rate and Bandwidth
Nyquist theorem
In information theory, Nyquist theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the absence of noise. Theoretical maximum data rate over a channel of Bandwidth B is given by
𝐶=2𝐵 𝑙𝑜𝑔 2 (𝑀) (bits/sec)
Where 𝐵 is the bandwidth of the channel. M is the number of discrete signal or voltage levels.
Shannon’s Capacity
In information theory, shannon theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise.
𝐶=𝐵 𝑙𝑜𝑔 2 (1+𝑆𝑁𝑅) (bits/sec)
Where 𝑆𝑁𝑅 is given by
𝑆𝑁𝑅 𝑑𝐵 =10 𝑙𝑜𝑔 10 ( 𝑆𝑖𝑔𝑛𝑎𝑙 𝑃𝑜𝑤𝑒𝑟 𝑁𝑜𝑖𝑠𝑒 𝑃𝑜𝑤𝑒𝑟 )
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19. 𝑑𝐵, 𝑑𝐵 𝑚
The decibel (dB) measures the relative strengths of two signals or one signal at two different points.
The (dB) is negative if a signal is attenuated and positive if the signal is amplified.
𝑑𝐵=10 𝑙𝑜𝑔 10 ( 𝑃 2 / 𝑃 1 )
The dB tells if power is lost or gained.
Signal to noise (decibels) 1 dB = 10 log10 S/N.
Ex: S/N = 10 => 10 dB; S/N =100 => 20 dB,1000 is 30dB
Decibel is used to measure signal power in milli watt. In this case it is referred to as 𝑑𝐵 𝑚 .
𝑑𝐵 𝑚 =10 𝑙𝑜𝑔 10 ( 𝑃 𝑚 )
Example:
-3dB+7dB-3dB=1dB.
There is an overall gain in the system

20. The expression 𝐸 𝑏 / 𝑁 𝑜 𝐸 𝑏 𝑁 𝑜
𝐸 𝑏 𝑁 𝑜
The expression 𝐸 𝑏 𝑁 𝑜 is the equivalent of 𝑆𝑁𝑅 for digital communication. The parameter is the ratio of signal energy per bit to noise power density per Hertz.
𝑅 is the bit rate.
𝐸 𝑏 , the energy per bit can be represented 𝑆𝑇 𝑏 . Where 𝑆 is the signal power and 𝑇 𝑏 is the time to send one bit. Watt=1J/s. 𝑅=1/ 𝑇 𝑏 .
𝐸 𝑏 𝑁 𝑜 = 𝑆/𝑅 𝑁 𝑜 ,
The metric of performance in digital communication systems is a plot of the bit error probability ( 𝑃 𝑏 ) versus 𝐸 𝑏 𝑁 𝑜 . The graph is a waterfall curve.

21. The expression 𝐸 𝑏 / 𝑁 𝑜
The ratio 𝐸 𝑏 𝑁 𝑜 is important because the bit error rate is a decreasing function of this ratio.
System describes a permissible probability of error.
There is a given 𝐸 𝑏 𝑁 𝑜 for a given probability of error that has to
be achieved.
As the bit rate 𝑅 increases, the signal power must increase
or the bandwidth of the channel W must be increased to maintain
the same 𝐸 𝑏 𝑁 𝑜 .
Received Eb/No. The SNR can degrade in three ways. Decrease in signal power (Loss), Increase in the noise power noise, Interference from other sources. We look into the different sources of loss and noise next.

22. Transmission impairments
With any communications system, the received signal may differ from the signal that is transmitted due to various transmission impairments.
For analog signals, these impairments can degrade the signal quality. For digital signals, bit errors may be introduced, such that a binary 1 is transformed into a binary 0 or vice versa.

23. Transmission impairments
Common types of transmission impairments:
Attenuation
Delay distortion
Noise
The strength of a signal falls off with distance over any transmission medium.
For guided media, this reduction in strength, or attenuation, is generally exponential and thus is typically expressed as a constant number of decibels per unit distance. For twisted-pair and coaxial cable, loss varies exponentially with distance (linear in decibels).

24. Transmission impairments
For microwave (and radio frequencies), the loss is expressed as
𝐿=10 𝑙𝑜𝑔 10 ( 4𝜋𝑑 λ ) 2
where d is the distance and λ is the wavelength, in the same units. Loss varies as the square of the distance.
Repeaters or amplifiers may be placed farther apart for microwave systems—10 to 100 km is typical.
Attenuation introduces three considerations for the transmission engineer.
First, a received signal must have sufficient strength so that the electronic circuitry in the receiver can detect the signal.
Second, the signal must maintain a level sufficiently higher than noise to be received without error.
Third, attenuation varies with frequency.
The first and second problems are dealt with by attention to signal strength and the use of amplifiers or repeaters.
For a point-to-point link, the signal strength of the transmitter must be strong enough to be received intelligibly.
Another source of impairment is interference. With the growing popularity of microwave, transmission areas overlap and interference is always a danger. Thus the assignment of frequency bands is strictly regulated.
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25. Transmission impairments
Distortion Delay spread
Delay distortion occurs because the velocity of propagation of a signal through a guided medium varies with frequency.
For a band-limited signal, the velocity tends to be highest near the center frequency and fall off toward the two edges of the band.
Thus various frequency components of a signal will arrive at the receiver at different times, resulting in phase shifts between the different frequencies.
This effect is referred to as delay distortion because the received signal is distorted due to varying delays experienced at its constituent frequencies.

26. Transmission impairments
Delay distortion (Inter symbol interference) is particularly critical for digital data.
Consider that a sequence of bits is being transmitted. Because of delay distortion, some of the signal components of one bit position will spill over into other bit positions, causing inter symbol interference, which is a major limitation to maximum bit rate over a transmission channel.
Noise
For any data transmission event, the received signal will consist of the transmitted signal, modified by the various distortions imposed by the transmission system, plus additional unwanted signals that are inserted somewhere between transmission and reception.
Undesired signals are referred to as noise.
Noise is the major limiting factor in communications system performance.
Noise may be divided into four categories:
Thermal noise
Intermodulation noise

27. Transmission impairments
Crosstalk
Impulse noise
Thermal noise
Thermal agitation of electrons. It is present in all electronic devices and transmission media and is a function of temperature.
Thermal noise is uniformly distributed across the bandwidths typically used in communications systems and hence is often referred to as white noise.
Thermal noise cannot be eliminated and therefore places an upper bound on communications system performance.
Because of the weakness of the signal received by satellite earth stations, thermal noise is particularly significant for satellite communication.
The amount of thermal noise to be found in a bandwidth of 1 Hz in any device or conductor is
𝑁𝑜𝑖𝑠𝑒 𝑃𝑜𝑤𝑒𝑟 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑁 𝑜 =𝐾𝑇( 𝑊𝑎𝑡𝑡 𝐻𝑧 )
𝐾=1.38× 10 −23 is the Boltzman constant. T is the temperature in Kelvin.

28. Transmission impairments
The noise is assumed to be independent of frequency. Thus the thermal noise in watts present in a bandwidth of B Hertz can be expressed as: N=KTB.
Intermodulation noise
Intermodulation noise arises when signals at different frequencies share the same transmission medium.
The effect of intermodulation noise is to produce signals at a frequency that is the sum or difference of the two original frequencies or multiples of those frequencies.
For example, the mixing of signals at frequencies and might produce energy at the frequency This derived signal could interfere with an intended signal at the frequency.
Cross talk
It is an unwanted coupling between signal paths. It can occur by electrical coupling between nearby twisted pairs or, rarely, coax cable lines carrying multiple signals.
Crosstalk has been experienced by anyone who, while using the telephone, has been able to hear another conversation;
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29. Transmission impairments
Crosstalk can also occur when microwave antennas pick up unwanted signals; although highly directional antennas are used.
microwave energy does spread during propagation.
Typically, crosstalk is of the same order of magnitude as, or less than, thermal noise.
Impulse Noise
Impulse noise, non-continuous, consisting of irregular pulses or noise spikes of short duration and of relatively high amplitude.
Causes, including external electromagnetic disturbances, such as lightning, and faults and flaws in the communications system.
Impulse noise is a minor annoyance for analog data. Example, voice transmission may be corrupted by short clicks and crackles with no loss of intelligibility.
Impulse noise the primary source of error in digital data communication. Example, a sharp spike of energy of 0.01 s duration would not destroy any voice data but would wash out about 560 bits of digital data being transmitted at 56 kbps.

30. Transmission Impairments Wireless Line of sight
Impairments specific to wireless line-of-sight transmission
Free Space Loss
Atmospheric Absorption
Multipath
Refraction
For any type of wireless communication the signal disperses with distance. Antenna with a fixed area farther away from the antenna will receive less power.
Even if no other sources of attenuation or impairment are assumed, a transmitted signal attenuates over distance because the signal is being spread over a larger and larger area. This form of attenuation is known as free space loss.

31. Transmission Impairments Wireless Line of sight
Free space loss is expressed as a ratio of the power transmitted from the antenna 𝑃 𝑡 to the power received at the receiving antenna 𝑃 𝑟 . For an isotropic antenna it is given by the following expression:
For an antenna with a gain
Reference William Stallings

32. Transmission impairments
Interference
Another source of impairment is interference. With the growing popularity of microwave, transmission areas overlap and interference is always a danger. Thus the assignment of frequency bands is strictly regulated.
Atmospheric Absorption
An additional loss between the transmitting and receiving antennas is atmospheric absorption. Water vapor and oxygen contribute most to attenuation.
Attenuation is increased with rainfall. The effects of rainfall become especially noticeable above 10 GHz.
At frequencies below 15 GHz, the attenuation is less.
Rain and fog (suspended water droplets) cause scattering of radio waves that results in attenuation. In this context, the term scattering refers to the production of waves of changed direction or frequency when radio waves encounter matter.
This can be a major cause of signal loss. Thus, in areas of significant precipitation, either path lengths have to be kept short or lower-frequency bands should be used.

33. Transmission impairments
Multipath
For wireless (Satellite/Point to point microwave), there is a relatively free choice of where antennas are to be located, they can be placed so that if there are no nearby interfering obstacles, there is a direct line-of-sight path from transmitter to receiver.
Mobile telephony, there are obstacles in abundance.
The signal reflected by obstacles resulting in multiple copies of the signal with varying delays. Extreme cases, there may be no direct signal.
The composite signal can be either larger or smaller than the direct signal.(depending on diff in the path lengths of the direct and reflected waves)
Depending on the differences in the path lengths of the direct and reflected waves. Reinforcement and cancellation of the signal resulting from the signal following multiple paths can be controlled for communication between fixed, well-sited antennas, and between satellites and fixed ground stations
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34. WIRELESS PROPAGATION Wireless Propagation Modes
A signal radiated from an antenna travels along one of three routes:
Ground wave
Sky wave,
Line of sight (LOS).
Ground Wave Propagation
Ground wave propagation follows the contour of the earth.
This effect is found in frequencies up to about 2 MHz.
Electromagnetic waves in this frequency range are scattered by the atmosphere and they do not penetrate the upper atmosphere.
The best-known example of ground wave communication is AM radio.

35. Ground Wave Propagation

36. Sky Wave Propagation

37. Line of Sight Propagation

38. WIRELESS PROPAGATION Sky Wave propagation
Sky wave propagation, a signal from an earth-based antenna is reflected from the ionized layer of the upper atmosphere (ionosphere) back down to earth due to refraction.
A sky wave signal can travel through a number of hops, bouncing back and forth between the ionosphere and the earth’s surface.
This effect is found in frequencies from 2-30 MHz
With this propagation mode, a signal can be picked up thousands of kilometers from the transmitter.
Amateur radio, BBC world service, Voice of America
Line of Sight propagation
Mode of propagation above above 30 MHz,
Neither ground wave nor sky wave propagation modes operate,
Communication must be by line of sight.
For satellite communication, a signal above 30 MHz is not reflected by the ionosphere and therefore a signal can be transmitted between an earth station and a satellite overhead.

39. WIRELESS PROPAGATION Optical and Radio Line of Sight
For ground-based communication, the transmitting and receiving antennas must be within an effective line of sight of each other.
Optical and Radio Line of Sight
With no intervening obstacles, the optical line of sight can be expressed as
𝑑=3.57 ℎ
where d is the distance between an antenna and the horizon in kilometers and h is the antenna height in meters. The effective, or radio, line of sight to the horizon is expressed by
𝑑=3.57 𝐾ℎ
where K is an adjustment factor generally taken as 𝐾=4/3 to account for the refraction.
The maximum distance between two antennas for LOS propagation is
3.57 𝐾 ℎ 𝐾 ℎ 2
where ℎ 1 and ℎ 2 and are the heights of the two antennas.

40. Optical and Radio Horizons

41. Refraction
Velocity of electromagnetic wave is a function of density of material
~3 x 108 m/s in vacuum, less in anything else
As wave moves from one medium to another, its speed changes
Causes bending of direction of wave at boundary
Towards more dense medium
Causes sudden change of direction at transition between media
May cause gradual bending if medium density is varying
Density of atmosphere decreases with height
Results in bending towards earth of radio waves