1. Wireless NETWORKS NET 434 Topic # 3 Wireless Transmission and Channel
Lte Capacity Workstream RMEA | Ericsson Internal | Uen, Rev DRAFT | 18-May | Page ‹#›

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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4.  The McGraw-Hill Companies, Inc., 1998
Figure 4-9
Frequency Change
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5.  The McGraw-Hill Companies, Inc., 1998
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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10.  The McGraw-Hill Companies, Inc., 1998
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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Lte Capacity Workstream RMEA | Ericsson Internal | Uen, Rev DRAFT | 18-May | Page ‹#›

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 )
Lte Capacity Workstream RMEA | Ericsson Internal | Uen, Rev DRAFT | 18-May | Page ‹#›

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. 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.

23. Optical and Radio Horizons

24. 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

25. LINE OF SIGHT TRANSMISSION

26. Transmission Impairments Wireless Line of sight
Impairments specific to wireless line-of-sight transmission
Free Space Loss
Atmospheric Absorption
Multipath
Refraction

27. Transmission impairments
Free space loss
For any type of wireless communication the signal disperses with distance.
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.
An antenna with a fixed area will receive less signal power the farther it is from the transmitting antenna.
For satellite communication this is the primary mode of signal loss. 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. The free space loss can be defined by the ratio of the transmit to the received power.

28. Transmission impairments
For the ideal isotropic antenna, free space loss is given by

29. Transmission Impairements

30. 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.

31. 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
Lte Capacity Workstream RMEA | Ericsson Internal | Uen, Rev DRAFT | 18-May | Page ‹#›

32. 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