multipath arrivals can be written as ‫ܪ‬ሺ߱ሻ ൌ ෍ ܽ௡ ݁ ି௝ఠఛ೙ Here, ܽ௡ and ߬௡ are the amplitude and time-delay of the nth ray, respectively. When the signal ‫ݏ‬ሺ‫ݐ‬ሻ consists of multiple frequency components, ‫ݏ‬ሺ‫ݐ‬ሻ ൌ
ଵ ஶ ‫ܵ ׬‬ሺ߱ሻ݁ ௝ఠ௧ ݀߱ ଶగ ିஶ ௡ୀଵ ௅
(3)
Where ܵሺ߱ሻ is the spectrum of ‫ݏ‬ሺ‫ݐ‬ሻ. The spectrum of ‫ݕ‬ሺ‫ݐ‬ሻ can be written as ି௝ఠఛ೙ ܻሺ߱ሻ ൌ ‫ܪ‬ሺ߱ሻܵሺ߱ሻ ൌ ∑௅ ௡ୀଵ ܽ௡ ܵሺ߱ሻ݁ Consider the following 6-ray model as an example. The amplitudes are defined as an: [1, 0.3, -0.8, 0.5, -0.4, 0.2]. We will consider two kinds of arrival time distributions: Case 1: n τ : [0, 1µs, 2µs, 3µs, 4µs, 5µs] Case 2: n τ : [0, 0.1µs, 0.2µs, 0.3µs, 0.4µs, 0.5µs]
思考: （1） 记录并分析仿真结果； （2） 改变多径参数，观察仿真结果的变化； （3） 总结当多径路数相同时，时延扩展大小的不同对信号的影响的变化。
2. Frequency Domain View: We use the following matlab code to generate the frequency domain view of transmitted signals and received signals for both cases. At first, FFT is employed to implement (3) to find the input spectrum. Secondly, (2) is used to compute the channel transfer functions. Finally, (4) is used to compute the output spectrum. Test3.m clear all; s=[ones(1,10),zeros(1,90)]; % transmitted signal s_f=fft(s); x=s_f([1:50]); y=s_f([51:100]); signal_f=[y,x]; %input spectrum dt=5/10; % each time interval is 0.01 micro sec df=1/(100*dt); f_s=df*([0:99]-50);% frequecy vector an=[1,0.3,-0.8,0.5,-0.4,0.2]; %amplitudes f=f_s; w=2*pi*f; tn_1=[0,1,2,3,4,5]; % arrival times for case 1 for i=1:6; h1(i,:)=an(i)*exp(-j*w*tn_1(i)); end h_1=sum(h1(:,1:end));%transfer function y_1=h_1.*signal_f;%output spectrum tn_2=[0,0.1,0.2,0.3,0.4,0.5]; % arrival times for case 2 for i=1:6;
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.
title('case 1: large delay spread') subplot(2,2,4); plot(t,y(2,:)); xlabel('Time(us)'); ylabel('received signal y(t)'); title('case 2: small delay spread') ===============================================================================
无线通信原理（ 无线通信原理（双语） 双语）实验指导说明
课程名称：无线通信原理（双语） 实验名称：多径效应与多普勒效应 实验报告内容包括： 1 实验名称: 多径效应与多普勒频移 2 实验目的和任务: 无线信道某些固有的特性直接制约着无线通信质量和速率的提高， 对于无线信道的研究 有助于寻找更多新的思路和切入点去解决这一瓶颈问题。 本次软件实验将帮助学生认识无线信道的基本特征（多径效应、多普勒效应）和分类， 促进学生对无线通信技术和应用的理解与思考。 要求： (1) 理解多径效应和多普勒效应的概念及它们对信号的影响； (2) 认识信道的分类，平坦衰落信道和频率选择性信道，快衰落信道与慢衰落信道的区别。 (3) 查找资料，举例说明实际系统采用哪些技术来克服频率选择性衰落所带来的负面影响。 3 实验过程与结果（含实验程序、运行的图形结果） ； 4 实验分析（回答实验任务中提出的思考编程问题，实验结果分析、设计与调试中出现的问 题及解决方法、实验心得、改进的设想）
(4)
The delay separation between the first arrival and the last arrival is 5µs in Case 1 and is only 0.5 µs in Case 2. For the time being, the delay separation is called as delay spread. Consider the transmitted signal is a square pulse with pulse width equal to 5µs, 1. Time Domain View: We use the following matlab code to generate the time domain view of transmitted signals and received signals for both cases. Test2.m clear all; an=[1,0.3,-0.8,0.5,-0.4,0.2];tn=[0,1,2,3,4,5;0,0.1,0.2,0.3,0.4,0.5]; signal=[0, zeros(1,0),ones(1,501),zeros(1,1000)]; % transmitted signal for k=1:2; %for two cases for i=1:6; ray(i,:)=an(i)*[0, zeros(1,(100*tn(k,i))),ones(1,501),zeros(1,(1000-100*tn(k,i)))]; end y(k,:)=sum(ray(:,1:end)); end t=((1:1:length(y(1,:)))-1)*10^(-2); subplot(2,2,1);plot(t,signal); ylabel('transmitted signal s(t)'); title('case 1 & case 2') axis([ 0 20 -0.5 1.5]) subplot(2,2,2);plot(t,y(1,:)); ylabel('received signal y(t)');
思考: （1） 记录仿真结果； （2） 将程序中的 7 路多径分别改为 1 路和 2 路多径，观察比较结果的变化； （3） 由此仿真结果可得出怎样的结论？
B. s(t) contains multiple frequency components As shown in equation (2), the transfer function of a wireless communication channel with
Let s(t) is the transmitted signal. The received signal can then be written as a sum of multipath arrivals: ‫ݕ‬ሺ‫ݐ‬ሻ ൌ ∑௅ (1) ௜ୀଵ ܽ௜ ‫ݏ‬ሺ‫ ݐ‬െ ߬௜ ሻ
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 Consider the transmitted signal ‫ݏ‬ሺ‫ݐ‬ሻ ൌ ݁ ௝ఠ௧ . Then, the received signal is ௝ఠሺ௧ିఛ೙ ሻ ି௝ఠఛ೙ ‫ݕ‬ሺ‫ݐ‬ሻ ൌ ∑௅ ൌ ‫ܪ‬ሺ߱ሻ݁ ௝ఠ௧ with ‫ܪ‬ሺ߱ሻ ൌ ∑௅ (2) ௡ୀଵ ܽ௡ ݁ ௡ୀଵ ܽ௡ ݁ Here, ‫ܪ‬ሺ߱ሻ is defined as the tranth environment. Note that the receiver signal ‫ݕ‬ሺ‫ݐ‬ሻremains as a time harmonic signal with the same angular frequency ω as the transmitted signal s(t). Thus, no distortion in wave shape has occurred during the transmission of s(t) through a time invariant multipath environment. However, the magnitude of the signal has been modified. The new magnitude is |‫ܪ‬ሺ߱ሻ| which is a function of angular frequency ω . Test1.m =============================================================================== clear all; %a=[0.6154]; %t=[0.9169]; %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 frequencies 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 frequency') title('frequency dependent multipath fading')