1、暑期实习报告一、 实习题目用正弦波模拟仿真瑞利信道和莱斯信道二、 实习背景在移动通信中，移动台与基站之间的通信往往受到各种障碍物和其他移动物体的影响，作为载体的电磁波会在传输过程中有直射波、反射波、绕射波和散射波之分，以致移动台接收到的信号是由经过不同延时不同路径到达的多路信号合并而成，而这些信号受阴影效应、多普勒效应等的影响，他们的幅度受到不同程度的衰减，同时在存在频移和相移。三、 实习原理瑞利衰落信道是一种无线电信号传播环境的统计模型，这种模型表现为在发射机和接收机之间不存在直射信号，假设信号通过无线信道后，其幅度是随机的。并且接收机信号的包络服从瑞利分布。莱斯衰落信道与瑞利信道的区别就是
2、在发射机和接收机之间存在直射波。瑞利信道模型为：1()cos(2)NRtCnftFtTheatCn、 F、Theata 是相互独立的随机变量，Cn 表示信号幅度，F 为频移系数，Theata 表示相移。莱斯信道模型为： 1()cos(2)cos(2)nRtftCfttTheatCn、F 、Theata 是相互独立的随机变量，Cn 表示信号幅度，F 为频移系数，Theata 表示相移四、 仿真结果：瑞利信道 1代码：function rayleight=sym(t);n=input(n=);f=8*108;%取信号频率为800MhzC=rand(1,n);Theata=-2*pi+4*pi.*r
3、and(1,n);F=-1+2.*rand(1,n);Zx=cos(2*pi*f.*t+2*pi*f.*F*t+Theata);RS=Zx*C当仿真路数为30路时，得到的接收信号时域图为：0 10 20 30 40 50 60 70 80 90 10-8-6-4-20246810当仿真路数为30路时，接收信号的包络：代码：t=0:.2:100;N=501;%采样点总数R=0:0.024:12;%包络幅度范围m=zeros(1,N);q=(8226958330713791*cos(14738544651813039.*t)/2097152 - 6420982962695317/112589990
4、6842624)/9007199254740992 + (8624454854533211*cos(3147546321980441.*t)/2097152 + 1592488907343941/281474976710656)/9007199254740992 + (153933462881711*cos(2922601302899569.*t)/2097152 - 1293881763019091/562949953421312)/281474976710656 + (109820732902227*cos(5056154441375673.*t)/524288 + 57205439508
5、5517/140737488355328)/1125899906842624 + (770956303438939*cos(11971310637107755.*t)/2097152 - 976910002155657/281474976710656)/4503599627370496 + (7648276850999985*cos(24678095153207873.*t)/4194304 + 1097200154976001/562949953421312)/9007199254740992 + (55201045594335*cos(15890773575148387.*t)/20971
6、52 - 1129149318181027/562949953421312)/140737488355328 + (3798887910549989*cos(4144792385309751.*t)/2097152 - 384936153162253/562949953421312)/9007199254740992 + (1143795557080799*cos(682689757498656039.*t)/134217728 - 6312399365597953/2251799813685248)/9007199254740992 + (1802071410739743*cos(48978
7、86369182033.*t)/524288 - 8860550568223013/2251799813685248)/2251799813685248 + (8690943295155051*cos(2714506704779073.*t)/1048576 - 823359778227783/140737488355328)/9007199254740992 + (6825116339432507*cos(753288409837281.*t)/262144 - 23146170456561/1125899906842624)/9007199254740992 + (295200998195
8、3243*cos(501305679469463.*t)/131072 + 603204343011701/562949953421312)/4503599627370496 + (525791455320933*cos(46359008585863987.*t)/8388608 - 2386764799977513/562949953421312)/562949953421312 + (3567784634204585*cos(25975981384114555.*t)/4194304 + 740548295201613/281474976710656)/4503599627370496 +
9、 (257756635625713*cos(165424021614621.*t)/65536 + 1035053019742027/562949953421312)/281474976710656 + (638999261770491*cos(7378662735005679.*t)/2097152 - 72409097729717/562949953421312)/4503599627370496 + (354913107955861*cos(138474482834837.*t)/16384 - 54167120430423/70368744177664)/225179981368524
10、8 + (7338378580900475*cos(15838866808400863.*t)/2097152 + 1457619014526091/562949953421312)/9007199254740992 + (2953193568373273*cos(926749021084891.*t)/262144 - 49514120493885/17592186044416)/4503599627370496 + (4321169733967891*cos(39913151771089687.*t)/8388608 + 1801714140618479/562949953421312)/
11、4503599627370496 + (8621393422876569*cos(4291865570455739.*t)/524288 + 939164443260505/281474976710656)/9007199254740992 + (1423946432832521*cos(18782798714916921.*t)/2097152 - 712496390568455/140737488355328)/2251799813685248 + (8158648460577917*cos(672267189674085.*t)/262144 - 3311925752416549/562
12、949953421312)/9007199254740992 + (6693542213068579*cos(1995494383059311.*t)/262144 + 1626169033800729/281474976710656)/9007199254740992 + (4371875181445801*cos(5134205601560665.*t)/2097152 + 522078571254719/140737488355328)/9007199254740992 + (6113502781001449*cos(4834269018907937.*t)/524288 - 53906
13、01969460187/1125899906842624)/9007199254740992 + (160831102319495*cos(8758126564219489.*t)/1048576 + 635629730369417/281474976710656)/4503599627370496 + (2185580645132801*cos(2680499240977253.*t)/1048576 - 1675767268482273/1125899906842624)/2251799813685248 + (627122237356493*cos(92294997228769907.*
14、t)/16777216 + 172282999978905/70368744177664)/2251799813685248;y=hilbert(q);%希尔伯特变换z=q+j*y;%解析信号a=z.*exp(-j*16*pi*108.*t);%复包络r=abs(a);%包络for l=1:501for n=1:501if r(n)R(l)m(l)=m(l)+1;endendendmP=m./N;%概率函数figure(1),plot(R,P)figure(2),plot(t,r)包络时域图为：0 10 20 30 40 50 60 70 80 90 100024681012tr概率函数图为：
15、0 2 4 6 8 10 1200.10.20.30.40.50.60.70.80.91rP然后对概率函数进行拟合再微分得到概率密度函数：代码为：stan=sqrt(var(r)P_theory=(R./stan2).*exp(-R.2./(2*stan2);coef=polyfit(R,P,10);P_density=polyder(coef);P_density_practice=polyval(P_density,R);plot(R,P_density_practice,b),hold on plot(R,P_theory,r)蓝色表示仿真结果，红色代表理论结果。当拟合阶数为10时，对比
16、结果为： 10 2 4 6 8 10 1200.050.10.150.20.250.30.35当拟合阶数为20时对比结果为： 20 2 4 6 8 10 12-0.15-0.1-0.0500.050.10.150.20.250.3莱斯信道 2莱斯信道可以看成是在瑞利信道上叠加有直射波，故按照相同的思路可得到仿真结果。仿真路数为 30 路时，t=sym(t);n=input(n=);f=8*108;C=rand(1,n);F=-1+2.*rand(1,n);Zx=cos(2*pi*f.*t+2*pi*f.*F*t+Theata);RS=cos(2*pi*f*t)+Zx*C时域信号图为：0 10
17、20 30 40 50 60 70 80 90 100-8-6-4-202468包络图为：0 10 20 30 40 50 60 70 80 90 1000246810121416tr概率图为：0 2 4 6 8 10 12 14 1600.10.20.30.40.50.60.70.80.91rP理论莱斯分布图为：stan=sqrt(var(r)I0=BesselJ(0,R./stan2);P_theory=(R./stan2).*exp(-(R.2+1)./(2*stan2).*I0；当拟合阶数为15时，仿真结果对比图为：红色代表理论概率分布图，蓝色代表仿真概率分布图0 2 4 6 8 10 12 14 16-0.1-0.0500.050.10.150.20.25五、 总结从对比结果来看，仿真结果与理论结果存在一定的误差，这其中有仿真路数不适中，计算概率时采样点不够多，拟合时所取的阶数不够恰当等原因造成的。但可以得到这样的结论：用正弦波叠加来模拟瑞利信道和莱斯信道是合适的。
