Wireless Propagation Characteristics

1. Wireless Propagation Characteristics Prof. Li Ping’an Tel: )027-61282569 Email: pingan_liwhut@yahoo.com.cn

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

5. General 3-level Model

8. 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

11. Sky Wave Propagation LOS Propagation

12. 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

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

14. Free Space Loss • Consider an Isotropic point source fed by a trans-mitter of Pt 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 Ae obtain a total power

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

16. 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)

17. Free Space Loss • Free space loss equation can be recast:

18. Path Loss Exponent

19. Log-normal distribution

20. 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) = PLavg (dB) + X where X is N(0,s2) where • PLavg (dB) is obtained from the path lossmodel • s is the standard deviation of X in dB

22. Delay=D1 100km/hr Delay=D2 RX impulse response TX an impulse D1 -D2 Small-scale fading: Multipath Rayleigh Fading

23. Small-scale channel

24. Time-varying and time-invariant channel

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

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

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

28. 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

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

30. 小尺度信道 Tc Coherent-Time: Fast/slow fading

31. Bc Coherent-Bandwidth:Flat fading and frequency selective fading 信道谱 宽带信号 窄带信号

32. a1 Time Delay Spread a2 a4 a3 a5 a6 a7 f1 f t f1 f t Flat Rayleigh fading Symbol Period >> Time Delay Spread Equivalent Model: y(t) = a x(t), tÎ[0,T]

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

36. Flat Rayleigh fading channel

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

38. Rician Distribution Rician Factor Zero-order modified Bessel function

39. Effects of Racian Factor K

40. Channel model：Flat fading

41. Channel Model: Frequency selective fading