多径多普勒效应仿真和对信号的影响-高铁通信核心技术
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Multipath and Doppler Effects and Models
There are two parts in this lecture. • In Part I, we will first introduce the mutipath propagation effects and Doppler frequency shift/spread effects. • In Part II, we will briefly introduce multipath and Doppler channel models.
which is a function of angular frequency ω . We use the following matlab code to generate the Figure 2: ======================================================== clear all; % amplitudes of 7 multipath arrivals a=[0.6154 0.7919 0.9218 0.7382 0.1763 0.4057 0.9355]; % arrival times of 7 multipath arrivals t=[0.9169 0.4103 0.8936 0.0579 0.3529 0.8132 0.0099]; i=0; % frequency index for omega=0:0.05:100; % angular freuencies multipath_arrival=a.*exp(j*omega*t); i=i+1; abs_H(i)=abs(sum(multipath_arrival)); % the i-th transfer function end omega=0:0.05:100; plot(omega, abs_H) ylabel('amplitude of transfer function') xlabel('angular freuency') title('frequency dependent multipath fading')
1
Background: Overviews on Wireless Channel Modeling We need to ask the following three important questions while designing a wireless communication link: 1. Fading & Power Loss: Is the signal to interference plus noise ratio (SINR) large enough for the receiver to detect the transmitted signal? 失真 2. Signal Distortion: Can the signal distortion be ignored, predicted or removed so that we know how to recover the transmitted information at the receiver? 3. Time Variation: Can the receiver adapt faster enough to the variations of the above two features (SINR & signal distortion)?
n =1
L
(2)
4
Here, H (ω ) is defined as the transfer function of the multipath environment. Note that the receiver signal y(t) remains as a time harmonic signal with the same angular frequency ω as the transmitted signal s(t). Thus, no distortion in wave shape has 失真 occurred during the transmission of s(t) through a time invariant multipath environment. 无变化的 However, the magnitude of the signal has been modified. The new magnitude is H (ω )
3
Part I: Multipath and Doppler Effects
After studying this note, students will be able to 1. Understand multipath channel effects in both time and frequency domains 2. Understand Doppler effects in both time and frequency domains 3. Understand multipath and Doppler effects in both time and frequency domains
I. Multipath Channel Effects: Time Invariant Case (No Doppler effects) In wireless communication environments, a signal transmitted from the transmitter reaches the receiver through many different paths as illustrated in Figure 1.
Figure 1: Multipath propagation Let s(t) is the transmitted signal. The received signal can then be written as a sum of multipath arrivals:
y (t ) = ∑ ai s (t − τ i ), τ 1 ≤ τ 2 ≤ τ 3 ≤ .... ≤ τ L
数量的 A complete wireless channel model should provide quantitative measures of SINR, signal distortion and timNR (referred in question 1), we need only to consider the time invariant transmission loss at a single frequency (that is the RF carrier frequency). The frequency and time dependent properties of signal can be addressed in answering questions 2 and 3. Signal distortion (referred in question 2) is caused by the frequency dependent variations of the received signal strength and phase. The primary source of frequency dependent variations is multipath propagation. Here, we need only to consider time invariant situations and leave the time varying features to question 3. Motions of receivers, transmitters or wireless environments generate Doppler effects. With Doppler effects, signal frequencies shift and spread. These Doppler effects will cause time variations in the received signal strength and wave shape. This kind of time varying features is usually random and can be modeled as stochastic processes. 随机过程 In order to addressing these three important issues, we divide wireless channel modeling into three parts: • Transmission loss -single frequency (or narrowband signal) -time invariant environment (or short observation time period) 不变 • Frequency dependent channel impulse response or transfer function -multiple frequencies (or broadband signal) -time invariant environment (or short observation time period) • Time varying channel impulse response or transfer function -multiple frequencies (or broadband signal)
Consider the transmitted signal s (t ) = e jωt . Then, the received signal is
y (t ) = ∑ an e jω ( t −τ n ) = H (ω )e jωt
n =1
L
with H (ω ) = ∑ an e− jωτ n
i =1
L
(1)
Here, L is the total number of multipath arrivals, ai and τi are the amplitude and arrival time of the ith ray, respectively.
A. s(t) is a time harmonic (i.e., single frequency or sinusoidal) signal
2
-time varying environment (or long observation time period) We have discussed transmission loss (including path loss, short term fading and long term fading) of a single frequency response in time invariant environments in the previous lecture. Both frequency dependent and time varying features of a channel impulse response (or transfer function) will be introduced in this lecture.
There are two parts in this lecture. • In Part I, we will first introduce the mutipath propagation effects and Doppler frequency shift/spread effects. • In Part II, we will briefly introduce multipath and Doppler channel models.
which is a function of angular frequency ω . We use the following matlab code to generate the Figure 2: ======================================================== clear all; % amplitudes of 7 multipath arrivals a=[0.6154 0.7919 0.9218 0.7382 0.1763 0.4057 0.9355]; % arrival times of 7 multipath arrivals t=[0.9169 0.4103 0.8936 0.0579 0.3529 0.8132 0.0099]; i=0; % frequency index for omega=0:0.05:100; % angular freuencies multipath_arrival=a.*exp(j*omega*t); i=i+1; abs_H(i)=abs(sum(multipath_arrival)); % the i-th transfer function end omega=0:0.05:100; plot(omega, abs_H) ylabel('amplitude of transfer function') xlabel('angular freuency') title('frequency dependent multipath fading')
1
Background: Overviews on Wireless Channel Modeling We need to ask the following three important questions while designing a wireless communication link: 1. Fading & Power Loss: Is the signal to interference plus noise ratio (SINR) large enough for the receiver to detect the transmitted signal? 失真 2. Signal Distortion: Can the signal distortion be ignored, predicted or removed so that we know how to recover the transmitted information at the receiver? 3. Time Variation: Can the receiver adapt faster enough to the variations of the above two features (SINR & signal distortion)?
n =1
L
(2)
4
Here, H (ω ) is defined as the transfer function of the multipath environment. Note that the receiver signal y(t) remains as a time harmonic signal with the same angular frequency ω as the transmitted signal s(t). Thus, no distortion in wave shape has 失真 occurred during the transmission of s(t) through a time invariant multipath environment. 无变化的 However, the magnitude of the signal has been modified. The new magnitude is H (ω )
3
Part I: Multipath and Doppler Effects
After studying this note, students will be able to 1. Understand multipath channel effects in both time and frequency domains 2. Understand Doppler effects in both time and frequency domains 3. Understand multipath and Doppler effects in both time and frequency domains
I. Multipath Channel Effects: Time Invariant Case (No Doppler effects) In wireless communication environments, a signal transmitted from the transmitter reaches the receiver through many different paths as illustrated in Figure 1.
Figure 1: Multipath propagation Let s(t) is the transmitted signal. The received signal can then be written as a sum of multipath arrivals:
y (t ) = ∑ ai s (t − τ i ), τ 1 ≤ τ 2 ≤ τ 3 ≤ .... ≤ τ L
数量的 A complete wireless channel model should provide quantitative measures of SINR, signal distortion and timNR (referred in question 1), we need only to consider the time invariant transmission loss at a single frequency (that is the RF carrier frequency). The frequency and time dependent properties of signal can be addressed in answering questions 2 and 3. Signal distortion (referred in question 2) is caused by the frequency dependent variations of the received signal strength and phase. The primary source of frequency dependent variations is multipath propagation. Here, we need only to consider time invariant situations and leave the time varying features to question 3. Motions of receivers, transmitters or wireless environments generate Doppler effects. With Doppler effects, signal frequencies shift and spread. These Doppler effects will cause time variations in the received signal strength and wave shape. This kind of time varying features is usually random and can be modeled as stochastic processes. 随机过程 In order to addressing these three important issues, we divide wireless channel modeling into three parts: • Transmission loss -single frequency (or narrowband signal) -time invariant environment (or short observation time period) 不变 • Frequency dependent channel impulse response or transfer function -multiple frequencies (or broadband signal) -time invariant environment (or short observation time period) • Time varying channel impulse response or transfer function -multiple frequencies (or broadband signal)
Consider the transmitted signal s (t ) = e jωt . Then, the received signal is
y (t ) = ∑ an e jω ( t −τ n ) = H (ω )e jωt
n =1
L
with H (ω ) = ∑ an e− jωτ n
i =1
L
(1)
Here, L is the total number of multipath arrivals, ai and τi are the amplitude and arrival time of the ith ray, respectively.
A. s(t) is a time harmonic (i.e., single frequency or sinusoidal) signal
2
-time varying environment (or long observation time period) We have discussed transmission loss (including path loss, short term fading and long term fading) of a single frequency response in time invariant environments in the previous lecture. Both frequency dependent and time varying features of a channel impulse response (or transfer function) will be introduced in this lecture.