Wireless NETWORKS NET 434 Topic # 3 Wireless Transmission and Channel Lte Capacity Workstream RMEA | Ericsson Internal | Uen, Rev DRAFT | 18-May-2014 | Page ‹#›

 The McGraw-Hill Companies, Inc., 1998 Figure 4-6 Sine Wave WCB/McGraw-Hill  The McGraw-Hill Companies, Inc., 1998

 The McGraw-Hill Companies, Inc., 1998 Figure 4-8 Amplitude Change WCB/McGraw-Hill  The McGraw-Hill Companies, Inc., 1998

 The McGraw-Hill Companies, Inc., 1998 Figure 4-9 Frequency Change WCB/McGraw-Hill  The McGraw-Hill Companies, Inc., 1998

 The McGraw-Hill Companies, Inc., 1998 Figure 4-10 Phase Change WCB/McGraw-Hill  The McGraw-Hill Companies, Inc., 1998

Time and Frequency Domain Figure 4-11 Time and Frequency Domain WCB/McGraw-Hill  The McGraw-Hill Companies, Inc., 1998

 The McGraw-Hill Companies, Inc., 1998 Figure 4-12 Examples WCB/McGraw-Hill  The McGraw-Hill Companies, Inc., 1998

Signal with DC Component Figure 4-13 Signal with DC Component WCB/McGraw-Hill  The McGraw-Hill Companies, Inc., 1998

 The McGraw-Hill Companies, Inc., 1998 Figure 4-14 Complex Waveform WCB/McGraw-Hill  The McGraw-Hill Companies, Inc., 1998

 The McGraw-Hill Companies, Inc., 1998 Figure 4-15 Bandwidth WCB/McGraw-Hill  The McGraw-Hill Companies, Inc., 1998

 The McGraw-Hill Companies, Inc., 1998 Figure 4-16 Digital Signal WCB/McGraw-Hill  The McGraw-Hill Companies, Inc., 1998

Amplitude, Period, and Phase Figure 4-17 Amplitude, Period, and Phase for a Digital Signal WCB/McGraw-Hill  The McGraw-Hill Companies, Inc., 1998

Bit Rate and Bit Interval Figure 4-18 Bit Rate and Bit Interval WCB/McGraw-Hill  The McGraw-Hill Companies, Inc., 1998

Harmonics of a Digital Signal Figure 4-19 Harmonics of a Digital Signal WCB/McGraw-Hill  The McGraw-Hill Companies, Inc., 1998

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. WCB/McGraw-Hill  The McGraw-Hill Companies, Inc., 1998 Lte Capacity Workstream RMEA | Ericsson Internal | Uen, Rev DRAFT | 18-May-2014 | Page ‹#›

Corruption Due to Insufficient Bandwidth Figure 4-22 Corruption Due to Insufficient Bandwidth WCB/McGraw-Hill  The McGraw-Hill Companies, Inc., 1998

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. WCB/McGraw-Hill  The McGraw-Hill Companies, Inc., 1998

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-2014 | Page ‹#›

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

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.

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.

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 1 +3.57 𝐾 ℎ 2 where ℎ 1 and ℎ 2 and are the heights of the two antennas.

Optical and Radio Horizons

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

LINE OF SIGHT TRANSMISSION

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

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.

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

Transmission Impairements

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.

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-2014 | Page ‹#›

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