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1、3.8题的仿真结果al = -0.195 a2 = 0.95)1.510.50-0.50100 200 300 400 500 600 700 800 900 1000a1 = -1.5955 a2 = 0.950100 200 300 400 500 600 700 800 900 1000-10.40.20-0.2-0.4-0.6-0.8-1iterative times niterative times nx io305a1 = -1.9114 a2 = 0.9521曰0 _- 11n-2 - 3 - 4 -,- 5 - 6 L，- 7 |1c11-''J10100200
2、3004005006007008009001000iterative times na1 = -0.195 a2 = 0.955.4题的仿真结果0.80.60.40.2 0n -0.2- 0.4- 0.6- 0.8-1-1.201002003004005006007008009001000iterative times niterative times niterative times n10.4题的仿真结果空间方向10 10 10 1010 10 10 1010 10 10 1010 10 10 10Rj 1000.4337 0.90110.6238 0.78160.9748 0.22320
3、.4337 0.901110.4337 0.90110.6238 0.78160.6238 0.78160.4337 0.901110.4337 0.90110.9748 0.22320.6238 0.78160.4337 0.90111Rnn111-33.369+90.106iRxx-52.383-78.156i107.48-22.316iRss + Rjj的特征值为：-33.369-90.106j 111-33.369+90.106i-52.383-78.156i402.35 , 37.65 ,-52.383+78.156j-33.369-90.106i111-33.369+90.106i
4、107.48+22.316j-52.383+78.156i-33.369-90.106i1110, 0相应的特征向量为:v= V1 ,V2 ,V3 ,V40.50950.3742 - 0.0860i 0.7131-0.0072 - 0.2192i-0.2042 + 0.4458i 0.5524 - 0.2177i -0.3155-0.1028i -0.3384+0.5176i v-0.2963 - 0.3906i 0.59380.1271+0.2572i 0.63140.4973 - 0.1109i 0.3797 - 0.0572i -0.5247-0.1545i -0.2859 - 0.29
5、84i最佳权向量为：H 111Wopta( s) Rxxa( s)Rxxa( s)0.2036 - 0.0068i 0.2964 - 0.0515i 0.2964+0.0515i 0.2036+0.0068T附：程序1、题 3.8clc; clear all; close all;% Using AR module generate signaldisp('Using Steepest Descent algorithm estimate the weight vector ') column = input('column =');a1 = input(
6、9;a1 =');a2 = input('a2 =');row = 1;ns = 1;n = 1 : column;u = AR_module(a1, a2, ns, row, column);% Compute Rxx and rxdr = xcorr(u, 500, 'biased');Rxx = r(501), r(502); r(500), r(501);rxd = r(500); r(499);% Using Steepest Descent algorithm compute the weight vector omega = Steepes
7、t_descent(Rxx, rxd, column);% Draw the weight vectorplot(n, omega(1, 1 : column);xlabel('n');hold on;plot(n, omega(2, 1 : column), '-');xlabel('iterative times n');ylabel('omega(n)');title('a1 = ', num2str(a1),' a2 = ',num2str(a2);legend('omega0
8、9;,'omega1',0);%最陡下降法的程序function omega = Steepest_descent(Rxx, rxd, column)% Steep descent algorithmomega = zeros(2, column);for n = 1 : columnomega( :, n+1) = omega(:, n) + 0.02 * (rxd - Rxx * omega( :, n);end3.8题和5.4题共用的AR模型function signal = AR_module(a1, a2, ns, row, column)% Using AR mod
9、ule generate signal v0 = randn(column,row);v = sqrt(ns) * v0; %generate noise u0 = 0 0;num = 1;den = 1 al a2;Zi = filtic(num,den,u0);signal, Zf = filter(num, den, v, Zi);2、5.4 题% initialclc; clear all; close all;disp('Using RLS algorithm estimate the weight vector')a1 = input('a1 =')
10、;a2 = input('a2 =');row = input('row =');column = input('column =');ns = input('ns =');signal = AR_module(a1, a2, ns, row, column);omega_ave, omega, mse_ave, mse = recursive_least_squares(signal, row, column); % draw the weight vector and mean square errorn = 1 : colu
11、mn;figure。)；plot(n, omega(1, :);hold onplot(n, omega(2, :),'-');hold onplot(n, omega_ave(1, :);hold onplot(n, omega_ave(2, :),'-');legend('omega0','omega1',0);title('a1 = ', num2str(a1),' a2 = ',num2str(a2);xlabel('iterative times n');ylabel(&#
12、39;omega(n)');figure(2);plot(n, mse);xlabel('iterative times n');ylabel('单次学习曲线');figure(3);plot(n, mse_ave);xlabel('iterative times n');ylabel('100 平均学习曲线');RLS算法的程序function omega_ave, omega, mse_ave, mse = recursive_least_squares(signal, row, column)% Recursive
13、Least Squares Algorithmomega_a = zeros (2,column,row);omega = zeros(2,column);ee_ave = zeros(1,column,row);ee = zeros(1,column);mse = zeros(1,column);u = zeros(2, column);k = zeros(2, column);P = zeros(2, 2, column);P(:, :, 2) = eye(2) / 0.02;for r = 1 : rowfor n = 3 : columnu(:, n) = signal(n-1, r)
14、; signal(n-2, r);k(:, n) = P(:, :, n-1) * u(:, n)/ (0.9+ u(:, n)' * P(:, :, n-1) * u(:, n);ee(n) = signal(n, r) - u(:, n)' * omega(:, n-1);omega(:, n) = omega(:, n-1) + k(:, n) * ee(n);P(:, :, n) = (P(:, :, n-1) - k(:, n) *u(:, n)' * P(:, :, n-1) /0.9;mse(n) = ee(n)A2;endee_ave(:, :, r)
15、= mse;omega_a(:, :, r) = omega;endomega_ave = sum(omega_a, 3) ./ row;mse_ave = sum(ee_ave, 3) ./ row;3、10.4 题clc; clear all;close all;aj = 1; exp(j*pi*sin(40*pi/180);.exp(j*2*pi*sin(40*pi/180); exp(j*3*pi*sin(40*pi/180);as = ones(4, 1);Rss = 10 * as * as'Rjj = 100 * aj * aj'Rnn = eye(4)Rxx =
16、 Rss + Rjj + Rnnv, d = eig(Rss + Rjj)wopt = inv(as' * inv(Rxx) *as) * inv(Rxx) * ass = -100 : 100;a = ones(size(s); exp(j * pi * sin(s * pi / 180);exp(j * 2 * pi * sin(s * pi/180); exp(j * 3 * pi * sin(s * pi /180);m = abs(wopt' * a);plot(s, m);title('幅度波束图');xlabel('空间方向');ylabel('增益');