Chapter 2. Wireless Channels BASED ON CHAPTERS 4 & 5 OF WIRELESS COMMUNICATIONS PRINCIPLES AND PRACTICE, 2/E, T.S. RAPPPAPORT

Characteristics of Wireless Channels Path loss and white noises Multipath delay and spread Fading Doppler spread Co-channel and adjacent channel interference 11/7/2018 Chao GAO

Radio Propagations Depends on Frequency: Ground wave: frequencies lower than 2MHz can propagate alone the earth ground (because its super long wavelength can make large diffraction) Sky wave: frequency of 1MHz~30MHz, can be reflected by the ionosphere. Line-of-sight wave: at >30MHz frequencies, radio traveling in a straight line. Thus a "radio-horizon" exists for these frequencies. However, with a strong signal source the radio wave can penetrate through thin obstacles such as walls & trees, with around 10-20dB attenuation. Ground wave Sky wave 11/7/2018 Chao GAO

Line-of-Sight Calculation FM/TV tower height: depends on how far it will cover! Consider following: (𝑟≈𝑟′ when 𝛼 is small) 𝑟 2 + 𝑅 2 = 𝑅+𝐻 2 𝑟 2 = 𝐻 2 +2𝑅𝐻 For the fact that 𝑟≫𝐻, we have 𝑟= 2𝑅𝐻 or 𝐻= 𝑟 2 2𝑅 Line-of-sight wave H r r' R R 𝛼 Example: R=6400km, we have the radio coverage radius 30km, then 𝐻 = 𝑟2 2𝑅 = 0.07031km ≈ 70m

Radio Horizon From 𝑟= 2𝑅𝐻 = 2×6400× 10 3 ×𝐻 (m) 𝑟≈3.577 𝐻 (km) This is call optical horizon. Radio frequency can diffract a little bit and distance is longer: 𝑟≈3.577 𝐻 (km) 𝑟=3.577 𝐾𝐻 km , 𝐾=4/3 11/7/2018 Chao GAO

Radio Propagation in Free Space Consider an isotropic antenna which radiates in free space equally to all directions. The transmitted signal is cos⁡(2𝜋𝑓𝑡) The electric far field at distance 𝑟 is It is clear the signal power ( 𝐸 2 ) is inversely proportional to the distance (𝑟) square. 𝐸 𝑓,𝑡,𝑟 = cos⁡[2𝜋𝑓 𝑡− 𝑟 𝑐 ] 𝑟 11/7/2018 Chao GAO

Radio Propagation in Free Space The free space power received by a receiver antenna at a distance 𝑑 from transmitting antenna is given by Friis equation: 𝑃𝑡 is the transmitted power, Pr⁡(𝑑) is the received power. 𝐺𝑡, 𝐺𝑟 are transmitter/receiver gains, 𝑑 is the distance, 𝐿 is the system loss factor, and  is the wavelength. The Gain of an antenna is related to its effective aperture 𝐴 𝑒 : In practice, Effective Radiated Power (ERP) is used because real antennas are polarized, thus some gain is obtained by polarized antennas and we denote it in 𝑑𝐵𝑖 (to isotropic). 𝑃 𝑟 𝑑 = 𝑃 𝑡 𝐺 𝑡 𝐺 𝑟 𝜆 2 4𝜋 2 𝑑 2 𝐿 𝐺= 4𝜋 𝐴 𝑒 𝜆 2 11/7/2018 Chao GAO

Path Loss Path loss represents signal attenuation as a positive quantity measured in dB over the radio propagation path. defined as ratio of effective transmitted power and the received power. In free space, we have This equation doesn’t hold for 𝑑=0 (i.e., so-called Near Field). 𝑃𝐿 𝑑𝐵 =10log 𝑃 𝑡 𝑃 𝑟 =−10 log 𝐺 𝑡 𝐺 𝑟 𝜆 2 4𝜋 2 𝑑 2 𝐿 In free space, the signal power decreases by the square of distance. 11/7/2018 Chao GAO

Ground Two-ray Path Loss The earth is a good conductor/reflector 𝑃 𝑟 (𝑑)= 𝑃 𝑡 𝐺 𝑡 𝐺 𝑟 ℎ 𝑡 ℎ 𝑟 2 𝑑 4 In two-ray ground mode, the signal power decreases by power of 4 of the distance. The detailed derivation can be found in [Schwartz, pp.23-25]. d h t d 1 h r d 2 d’ d’’ 11/7/2018 Chao GAO

Power Calculation An isotropic antenna radiates 1W in free space. 𝐺 𝑡 = 𝐺 𝑟 =1 (0𝑑𝐵), frequency is 300MHz. What is the received power in watts at distance of 10m? What is the received power in watts at distance of 10km? An dipole antenna (omnidirectional horizontally) radiates 100W from a radio tower. ℎ 𝑡 =30𝑚, ℎ 𝑟 =2𝑚, 𝐺 𝑡 = 𝐺 𝑟 =1 (0𝑑𝐵). Find the answers for the same distances. As you see, the value becomes very small, therefore we always use decibel values. 11/7/2018 Chao GAO

Radiation Power Density Denoted as 𝜌 (mW/ cm 2 ). An isotropic antenna radiates 1W as the previous example. Find power density at 1m and 100m respectively. US FCC has specified a safety guideline for cellular radiations. 0.001𝑚𝑊/𝑐 𝑚 2 Typical near a celluar tower 0.5𝑚𝑊/𝑐 𝑚 2 FCC Public Exposure Standard (900MHz) 4𝑚𝑊/𝑐 𝑚 2 Unreproduced Reports of Effects 100𝑚𝑊/𝑐 𝑚 2 Clear Hazards 0.02𝑚𝑊/𝑐 𝑚 2 Maximum near a celluar tower 1𝑚𝑊/𝑐 𝑚 2 FCC Public Exposure Standard (2000MHz) 40𝑚𝑊/𝑐 𝑚 2 Reproducible Effects 11/7/2018 Chao GAO

SAR (Mobile phone) MMF (Mobile Manufacturer Forum) has adopted SAR (Specific Absorption Rate) 𝑆𝐴𝑅= 𝜎 𝐸 𝑟𝑚𝑠 2 𝑑 , where 𝜎 is conductivity of medium (brain ~0.6-0.9 S/m), 𝐸 𝑟𝑚𝑠 is the RMS value of Electric Field and 𝑑 is the density of medium (brain ~1040kg/ 𝑚 3 ) In EU the limit is 2W/kg for human being's head and trunk. Specific absorption rate (SAR) [W/kg] describes the possible biological effects of RF fields. The high energy of RF field exposure causes thermal effects in biological tissues and generates high SAR values. However, the so-called non-thermal effects, or the biological effects of RF fields at low energy levels have not been clarified yet. The basic concern of the present work is health hazard…… The depth of penetration is more in the child than the adult. The exposure of high intensity EM waves in the UHF (i.e., 300 MHz-3 GHz) range generates heat, which can cause thermal damage to the brain, specially of the children. This temperature may rise up to about 0.1℃ in 1𝑚 𝑚 3 after 33 hrs of continuous phone use. DNA breaks after receiving RF exposure. [Hoque et al, 2013] 11/7/2018 Chao GAO

Signal Propagation Ranges Because radio signal power decays by distance, there is a range for correct reception. Transmission range Communication range Low error rate Detecting range Detection of the signal is possible, but cannot correctly receive data because error rate is too high Interferencing range Signal cannot be detected but acts as a kind of noise to other systems Interference range Detection range Transmission range Distance from the transmitter. In practice there are irregular circles due to the variation of environment. 11/7/2018 Chao GAO

Multi-path propagation In practice the signal coming to the receiver is a combined signal with multiple components caused by reflection/diffraction/scattering, this is called multi-path propagation model. Two-ray ground model is the simplest multi-path example. 11/7/2018 Chao GAO

Effects of Multipath Reflection “Ghost image” on TV. GPS – incorrect position calculation. Intersymbol interference (ISI). Fading. 11/7/2018 Chao GAO

Intersymbol Interference Suppose that there are two paths. The shorter one has length d1, the longer one length d2. What is the difference in propagation delay between the two paths? 2 3 Symbols received over the shorter path 1 2 Symbols received over the longer path 3  1 Received signal – a combination of the two signals 11/7/2018 Chao GAO

Multipath delay vs Symbol rate Calculate: 3 multipath distances are 5km, 10km and 15km respectively, how much delay 𝛿 is between the 1st and 3rd path? If the symbol rate is 10kbps, how many symbols does 𝛿 equal to? How about the symbol rate is 10Mbps? Advanced homework: use Matlab to simulate this scenario. 11/7/2018 Chao GAO

Random Channel Characterization Caused by the multi-path, the radio signal presents a random feature in both long-term (slow) and short-term (fast) loss. We name this kind of loss as fading. Fading happens in a random fashion, because it is caused by the random movement of user mobile, and/or uncertain changes of environments. Received power Average in long time (slow fading) Fast fading time 11/7/2018 Chao GAO

Fading in Time: Slow Fadings Long-term fading is caused by the movement of user device so that the signal may come from different reflecting/diffracting/scattering path. This change is slow because the mobile needs to have a relatively long distance to move. One special long-term fading is called shadowing, caused by the mobile moves into a shadow area of radio. It is also called slow fading. Poor signal Strong signal 11/7/2018 Chao GAO

Fading in Time: Fast Fadings Short-term fading is caused by the movement of user mobile (usually in a magnitude of wavelength) so that the combined signal at the receiver changes its phase and magnitude in short time.. It is also called fast fading. Several mathematical models have been established for short-term fading, they are Nakagami fading Weibull fading Rayleigh fading (open field, non-line-of-sight) Rician fading (open field, line-of-sight) 11/7/2018 Chao GAO

Fast Fading: an example Simplest 2-path scenario: 𝐸 𝑓,𝑡 = cos 2𝜋𝑓 𝑡− 𝑟 𝑐 𝑟 − cos⁡[2𝜋𝑓 𝑡− 2𝑑−𝑟 𝑐 ] 2𝑑−𝑟 reflected 𝑟 𝑑 11/7/2018 Chao GAO

Fast Fading: an Example If the mobile is close to the wall, 𝑑≈𝑟, 2𝑑−𝑟≈𝑟 𝐸 𝑓,𝑡 = cos 2𝜋𝑓 𝑡− 𝑟 𝑐 −cos⁡[2𝜋𝑓 𝑡− 2𝑑−𝑟 𝑐 ] 𝑟 The phase difference is Δ𝜃= 2𝜋𝑓 2𝑑−𝑟 𝑐 +𝜋 − 2𝜋𝑓𝑟 𝑐 = 4𝜋𝑓 𝑐 𝑑−𝑟 +𝜋 If the phase difference Δ𝜃 is a multiple of 2𝜋, two waves add constructively, if it is an odd integer of 𝜋, two waves add distructively. Thus a standing wave is formed, and the distance between a node to an anti-node is Δ𝑟= 𝜆 4 . 11/7/2018 Chao GAO

Fast Fading: an Example So, if the mobile terminal moves either towards the Tx tower or towards the wall, it will be encountering nodes and anti-nodes every Δr (which is also called as coherent distance). At an anti-node, the signal fades. The radio frequency used by cellular system is around 1~2GHz, 𝜆≈ 15~30𝑐𝑚. Therefore, even the mobile terminal moves at a relatively low speed, fast fading occurs. E.g., 𝑓=2𝐺𝐻𝑧, 𝜆=15𝑐𝑚, mobile velocity 𝑣=2𝑚/𝑠. It will take 𝜆/4 𝑣 = 0.0187 sec. from a node to an antinode. 11/7/2018 Chao GAO

Fast Fading at High Mobility If the mobility is high, e,g., on a moving vehicle or train (speed is about 60~200km/h), the time from a node to antinode becomes much smaller. As a result, fast fading occurs at a time scale of milliseconds, slow fading occurs at a time scale of seconds or minutes. Fast fading is caused by standingwave, so it occurs only in an environment with strong reflections. 11/7/2018 Chao GAO

Effects of Fading for digital modulation BER: the lower the better Fig. 2.13 SNR: the higher the worse 11/7/2018 Chao GAO

A Result from WINIQSIM 11/7/2018 Chao GAO

Result Comparison No multipath, no white noise No multipath, Gaussian noise Multipath, Gaussian noise 11/7/2018 Chao GAO

Irreducible BER due to fading Probability of error Fig. 2.16 Signal-to-Noise Ratio 11/7/2018 Chao GAO

Irreducible BER due to fading The lower the mobility, the lower the BER Fig. 2.16 11/7/2018 Chao GAO

Fading in Frequency Domain In frequency domain, fading can be classified as "flat fading" and "selective fading". Flat fading means fading occurs at the whole frequency band of a communication system. It's typical for most narrow-band communication systems. Selective fading occurs at certain frequencies or subbands of the whole frequency band of a communication system. It's typically a wideband system feature. 11/7/2018 Chao GAO

Mitigation Using diversity channels is a way to mitigate fading results, because fading is random and different channels fade at different time. Diversity can be done in time, frequency, and space. There are several techniques: Diversity reception and transmission (against fast fading) OFDM (against ISI, doppler) Rake receivers (against ISI) Space–time codes/Interleaving (against fast fading) MIMO (against fast fading) 11/7/2018 Chao GAO