Week3筆記_Signal Propagation

1.Signal Propagation 的效應
• Path loss(Large-Scale Fading):在一給定的propagation path中，RX相較於(ratio)TX收到的power，關係如下
PR-received signal power,PT-transmitted power,f-carrier frequency,d-propagation distance,
G-power gain from the transmit and receive antennas,α = 2(free-space propagation時))

具體公式:

• Shadowing(Large-Scale Fading):Due to random shadowing, the actual path loss is also
random，其公式為

**
• Multipath fading(Small-Scale Fading):無線通訊必須考慮的

1. flat/frequency-selective fading:不同路徑抵達的時間差
2. slow/fast fading:TX和RX的相對移動速度

總結:可以從下圖(非依比例畫的)看出來
(1)Path loss穩定隨距離增加而成比例下降
(2)Shadowing即使距離不動(TX和RX距離固定，但是位置改變)都會有此效應，因為Same T-R distance usually have different path loss
(3)Multipath Fading:變化很快且浮動範圍較shadowing大，只要移動一點點，就會變動很快

2.Multipath Channel Parameters:Baseband complex impulse response of a multipath channel

3.
•Power delay profile(PDP-功率延遲曲線):gives the intensity of a signal received through a multipath
channel as a function of time delay，這堂課主要藉由PDP知道能量的離散程度，平均值沒有很重要，重要的是離散程度
•RMS delay spread:此值越大代表越分散，反之亦然，且其值的倒數意義就是和Coherence Bandwidth成正比，也就是PDP在time domain上越分散，RMS越大，Coherence Bandwidth就越小
•Coherence Bandwidth:Bc=1/(KτRMS),K=5~50
Signal bandwidth (SB) vs. coherence bandwidth (CB)
• SB < CB : Flat fading
• SB > CB : Frequency-selective fading
是Flat fading或Frequency-selective fading都也和signal 的bandwidth有關
• Doppler Spread:
RMS Doppler spread:公式如下圖
The models behind Rayleigh or Rician fading假設說訊號是uniformly distributed within
[0, 2p]，以此假設可以推導出Spectral_Power_Density的分布

(我又另外用matlab去繪圖，證實說以此假設得出的公式，確實shiftting的訊號集中在離Fc正負Fm的地
方，Fm是指maximum Doppler shift)
matlab code如下:

clc 
clear all
close all
fm = 100;
f_minus_fc = -fm : fm/100 :fm;

% Spectral_Power_Density = (1 )./ ((fm^2-(f_minus_fc^2))^0.5);
Spectral_Power_Density = 1./((fm^2-(f_minus_fc.^2)).^0.5);
plot(f_minus_fc,Spectral_Power_Density)

得出的圖形如下

4.Coherence Time:公式為Tc=K/fm,fm : maximum Doppler frequency; Rule of thumb: K=0.423
Symbol time (ST) vs. coherence time (CT)
• ST<CT: slow fading
• ST>CT: fast fading (time-selective fading)
物理意義:
•若為slow fading 代表一個coherence time內可以傳多個symbol
•若為fast fading (time-selective fading)，則每次傳完一個symbol就要去重測channel