多径多普勒效应讲义(含matlab程序)20071228陈.pdf

【实例简介】
多径多普勒效应讲义(含matlab程序)，范例可以运行
-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 Part I: Multipath and Doppler effects After studying this note, students will be able to 1. Understand multipath channel cffccts in both time and frcqucncy domains 2. Understand Doppler effects in both time and frequency domains 3. Understand multipath and Doppler effects in both time and frequency domains 1. Multipath Channel effects: Time Invariant Case(No Doppler effects) In wireless communication environments, a signal transmitted from the transmitter reaches the rcccivcr through many diffcrent paths as illustrated in Figurc Figure 1: Multipath propagation Let s(t) is the transmitted signal. The received signal can then be written as a sum of multipath arrivals ()=∑a(-r),x≤ (1) Here, L is the total number of multipath arrivals, a; and t; are the amplitude and arrival time of the i ray respectively A s(t is a time harmonic(i. e, single frequency or sinusoidal signal Consider the transmitted signals(t)=e. Then, the received signal is y()=∑ a e/a(l-r =H(o) e/ot with H(a)=∑an Here, H(o) 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 a as the transmitted signal s(o. 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 H(a)l which is a function of angular frequency a We use the following matlab code to generate the figure 2 clear all %o amplitudes of 7 multipath arrivals a[061540.79190.92180.73820.1763040570.9355} %o arrival times of 7 multipath arrivals t[0.91690.41030.89360.05790.3529081320.0099]; 1=0; frequency index for omega=0: 0.05: 100: angular frcuencics multipath arrival=a. exp(*omega*t +1 abs h(i=abs (sum(multipath arrival)); the i-th transfer function ene omega-0:0.05:100 plot(omega, abs H) ylabel(amplitude of transfer function) xlabel(angular freuency,) title(frequency dependent multipath fading,) Here, we use 7 multipath arrivals. The amplitudes and arrival times of these seven multipath arrivals are randomly chosen from Figure 2, the magnitude of received signal fluctuates as angular frcqucncy changes. For somc frcqucncics, the 7 multipath arrivals interfere destructively and yield small H(o). For other frequencies, the 7 multipath arrivals interfere constructively and yield large H(o. This phenomenon is called multipath fading. Figure 2 shows that multipath fading is frequency dependent. Other kinds of fading will bc discusscd in future Icc frequency dependent multipath fading 45 35 5 70 10 ngular freuen y Figure 2: Multipath fading is a function of frequency Since the amplitudes and arrival times of multipath arrivals depend on locations of transmitter and receiver, the received signal strength will also depend on the locations of transmitter and receiver. s For example, consider a two ray model where line of sight (los) and reflected rays are the two multipath arrivals. Let the transmitter antenna height be h, and the receiver antenna height be hr. The horizontal distance between the transmitter and the receiver is denoted as d. From Figure 3 the travel distance for the los ray is +(h,-h,) and the travel distance for the reflected ray is d-+(h,+h) Then the transfer function is +R /c R :2 where r is the reflection coefficient and the coefficients bLos and bref are functions of antenna patterns, transmitted power, etc. For convenience, we choose bLosl, brefI and R=-1 in our example. Thus j2 LOS 10m Reflected 2m Figure 3: two-ray model We will first plot the magnitude of H(d) against the distance d using the following matlab code. If the frequency / 1GHz, the wave length is n=c//-03 m because the wave speed c-310'm/sec. Let h 10m, h =2m clear all ht=10: hr=2 c=Be8: fle9 lambda- c/f. R=-1: d=1:05:10000; dl=sqrt(d. 2+(ht-hry 2) d2=sqrt(d. 2+(ht+hr)2); al=expG*2 pi * d1/lambda). /d1 a2=R米exp(j*2米pi.*d2 lambda)./d2; a=abs(al+a2) ld=log 10(d);la=log10(a); figure(4 plot(ld, la) xlabel(loglo(distance),) labelclog10(magnitude)) title(two ray model") t口r -5 -35 4.5 5 15 loglO(distar Figure 4: Mutipath effects as a function of distance between source and receiver. Please see lecture 2 for detailed discussions Secondly, we plot the magnitude of H() against the frequency f for four distances d=50m, 300m, 800m and 2000m using the following matlab code clear all ht=10;hr=2; C=3e8;R=-1;f0-le8;f=[l:1:1000]:fd=50000010+fd*f; lambda=c/f; da=[50,300800,2000; for i=1: length( da) dl=sqrt(d. 2+(ht-hr)2) d2=sqrt(d. 2+(ht+hr)2 Td-(d2-d1)/c al-expg 2 pi*dl/ lambda)/dI a2=R*expgj 2 pi*d2 /lambda)/d2 a(i, =abs(al+a2) end figure(5) subplot(2, 2, 1); plot(f, a(l, ) title('d=50m); ylabelCmagnitude') subplot(2, 2, 2); plot(f, a(2, )) title('d=300m); ylabel(magnitude,) subplot(2, 2, 3 ); plot(f, a(3, )) titled'd=800m); xlabeld'frequency');ylabeld'magnitude') subplot(2, 2, 4): plot(f, a(4, ) titled'd=2000m); xlabel(frequency); ylabell'magnitude') C=50 10 d=300m 口4 03 02 三斗 001 d=doom d=20m 2 G0斗 上 5 斗 frequent trequency Figure 5 Frequency characteristics of Multipath fading at four locations From Figures 4 and 5, we conclude that frequency characteristics of multipath fading are location dependent. Note that the frequency separation of two adjacent deep fades is in each case in Figure 5 is 1/TD where TD is the travel time difference for the two rays TD=re B. so contains multiple frequency components As shown in equation(2), the transfer function of a wireless communication channel with multipath arrivals can be written as H()=∑an Here, an and t, are the amplitude and time-delay of the n"ray, respectively. As shown in (1), for an input signal s(t) with multiple frequencies, the output of the channel can bey written as y()=∑a1(t-zn) When the signal s(t) consists of multiple frequency components, S( (3) 2J-∞ where S(o)is the spectrum of s(o). The spectrum of y(o) can be written as Y()=H()小 a,s(oe (4) 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:zn:[O,lus,2μs,3us,4us,5μs Case2:zn:[0,0.1us,0.2us,0.3s,O,4μs.0.5us] The delay separation between the first arrival and the last arrival is 5us in Case l and is only 0.5 us in Case 2. For the time being, the delay separation is called as delay spread In future lectures, delay spread will be defined in other ways Consider the transmitted signal is a square pulse with pulse width equal to 5 us, 1. Time domain view Weusc the following matlab code to generate the time domain view of transmitted signals and received signals for both cases From Figure 6, we observe that multipath arrivals cause distortion. The larger the delay spread is, the worse the distortion becomes 10 【实例截图】
【核心代码】