Wireless Propagation Characteristics Prof. Li Ping’an Tel: )

Mobile Commun. Environments Path loss Shadow Multi-path fading Time spread Doppler frequency shift (Doppler spread)

General 3-level Model

Path loss model is used for  system planning, cell coverage  link budget (what is the frequency reuse factor?) Shadowing is used for  power control design  2nd order interference and TX power analysis  more detailed link budget and cell coverage analysis Multipath fading is used for  physical layer modem design --- coder, modulator, interleaver, etc

Sky Wave Propagation LOS Propagation

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

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

Free Space Loss Consider an Isotropic point source fed by a trans- mitter of P t Watts The energy per unit area of the surface of the sphere with radius d Hence, at a distance d, an receive antenna with effective aperture A e obtain a total power

Free Space Loss Define an antenna gain as Hence, the received power : The wavelength

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 (» 3 ´ 10 8 m/s) where d and are in the same units (e.g., meters)

Free Space Loss Free space loss equation can be recast:

Path Loss Exponent Environmentsn Urban area cellular radio2.7 to 3.5 Shadowed urban cellular radio 3 to 5 In building LoS1.6 to 1.8 Obstructed in building4 to 6 Obstructed in factory2 to 3

Log-normal distribution

Shadowing Effects Variations around the median path loss line due to buildings, hills, trees, etc.  Individual objects introduces random attenuation of x dB.  As the number of these x dB factors increases, the combined effects becomes Gaussian (normal) distribution (by central limit theorem) in dB scale: “Lognormal” PL(dB) = PL avg (dB) + X where X is N(0,  2 ) where  PL avg (dB) is obtained from the path loss model   is the standard deviation of X in dB

Small-scale fading: Multipath Rayleigh Fading 100km/hr Delay=D 1 Delay=D 2 TX an impulse D 1 -D 2 RX impulse response

Small-scale channel

Time-varying and time-invariant channel

Why Convolution? x(t) x(t-1)x(t-2) x(t-4)h(4) x(t-0)h(0) x(t-1)h(1) At time t

Time-frequency analysis of the wireless channels 冲激响应 时延多普勒扩展时变传输函数 多普勒扩展

Time-Doppler couple Doppler frequency shift ( 由运动中不同时 间相位变化引起 )

Delay-Frequency couple At any time, auto- correlation of frequency only affects the power of the signal as a function of delay 由于各径中心频率相同，如 果时延扩展小，频率相关性 强，相干合并功率大 Power-delay spectrum

Fourier -couples 自相关功率谱 时间自相关 频率自相关 多普勒谱 时延谱

Coherent-Time: Fast/slow fading TcTc 小尺度信道

Coherent-Bandwidth:Flat fading and frequency selective fading 窄带信号 宽带信号 信道谱 BcBc

Flat Rayleigh fading Symbol Period >> Time Delay Spread Time Delay Spread aa aa aa aa aa aa aa t Equivalent Model: f f1f1 t y(t) =  x(t), t  [0,T] f f1f1

Rayleigh Fading (No Line of Sight) By Central Limit Theorem Independent zero mean Gaussian Phase is Uniform Magnitude is Rayleigh

Flat Rayleigh fading channel

Rician Distribution-with LoS N+1 paths with one LoS The amplitude of the received signal K factor Zero-means Gaussian each with variance

Rician Distribution Rician Factor Zero-order modified Bessel function

Effects of Racian Factor K

Channel model ： Flat fading

Channel Model: Frequency selective fading