%%
%Adaptive?Filter?Test
%Copyright?By?popwaic
%2019.11
%In?ZhengZhou
%%
%
clc;
clear;

d=randn（110000）‘;


h=[0.2?0.66?0.31?0.77?0.91?0.65?0?0?0?0?0?0?0];
N=11;
h1=[0?0?0?0.3?0.6?0.3?0.7?0.9??0?0?0];

w=zeros（113）;??%init
w1=zeros（12*N+3）;??%init
w1（N+2）=1;

r=zeros（1length（d））;

u=0.2;
u1=0.015;

?Lmin=7000;

%%
%System?Identification
????for?i=1:length（d）-13
????????xx=d（i+12:-1:i）;??
????????dr=h*xx;???????
????????r（i）=dr;????
????end

????%LMS
????[w_est_Lee_L]=LMS_t（rdwu1）;
????
?????%use?RLS
?????R=eye（length（w））;
?????t=0.0001;
?????R=t*R;
?????R=inv（R）;
?????j=0.995;

?????[w_est_Ree_R]=RLS_t（d（1:Lmin）rwRj）;
????
%drow?picture
????subplot（221）;
????stem（h）;?
????title（‘h（n）‘）;
????subplot（222）;
????stem（w_est_L）;?
????hold?on;
????stem（w_est_R）;
????hold?off;
????title（‘w（n）‘）;
????subplot（223）;
????stem（h-w_est_L）;
????hold?on;
????stem（h-w_est_R‘）;
????hold?off;
????title（‘h（n）-w（n）‘）;
????subplot（224）;
????plot（ee_L（1:Lmin-100））;?
????hold?on?
?????plot（ee_R（1:Lmin-100））;?
????title（‘MSE?of?e*e‘）;
????

%%
%System?inverse?identification

for?i=1:length（d）-N
????xx=d（i+N-1:-1:i）;??
????dr=h1*xx;???????
????r（i）=dr;????
end

r=r*0.7359;?????????%Normalization

eee=zeros（1length（r））;
?
?%use?LMS
?[w_est_Lee_L]=LMS_t（d（17:Lmin）rw1u10）;
?
?%use?RLS
?R=eye（length（w1））;
?t=0.0001;
?R=t*R;
?R=inv（R）;
?j=0.995;
?
?[w_est_Ree_R]=RLS_t（rd（17:Lmin）w1Rj）;
?
figure;

subplot（221）;
stem（h1）;?
title（‘h1（n）‘）;
subplot（222）;
%stem（w1）
stem（w_est_L）;?
hold?on;
stem（w_est_R）;
hold?off;

title（‘w1（n）‘）;

subplot（223）;
stem（conv（h1w_est_L（:）））;?
hold?on;
stem（conv（h1w_est_R（:）））;?
hold?off;

%stem（conv（h1w1（:）））;?
title（‘h1（n）*w1（n）‘）;
subplot（224）;
plot（ee_L（1:Lmin-100））;?
hold?on;
plot（ee_R（1:Lmin-100））;?
hold?off;
title（‘MSE?of?e*e‘）;


%%noise?


%%
%functrion?of?LMS
%?r:y
%?d:d
%?w:estimate?of?h
%?u:?step?length
%?mod?:?0:basic?LMS???1:normalzial?LMS

function?[w_estee]=LMS_t（rdwumod）
????N=length（w）;
????n=30;
????for?i=1:length（r）-2*N
????????xx=d（i+N-1:-1:i）;?%
????????
????????%
????????[m?h]=size（xx）;????????
????????if?m==1
????????????xx=xx‘;
????????end
????????
????????y=w*xx;????????
????????e=r（i）-y;
???????
????????if?mod==1
????????????w=w+（u/（sum（xx.^2）+0.01）*xx*e）‘;?
????????elseif?mod==0
????????????w=w+（u*xx*e）‘;????
????????end

????%calculate??MSE
????Le=i;
????eee（i）=e.^2;??
????if?i?????ee（i）=10*log10（sum（eee（1:Le）.^2）/Le）;???
????else
????????ee（i）=10*log10（sum（eee（Le-n+1:Le）.^2）/Le）;???
????end
???????
????end
????
????w_est=w;???
end

%%function
%RLS?
%?x:?x???????????N*1?D
%?d:?d???????????N*1?D
%?w:?w（n-1）??????N*1?D
%?R:??the?inverse?of?square?matrix??Rxx（n-1）????N*N?D

%?t:?????????????a?very?small?param
%?I:?????????????N*N?D??R（0）=t*I
%?j:?????????????forget?param

%init:?w（0）=0?R0?jt

f

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????3855??2019-12-08?15:05??Adaptive_Filter_LSM_RLS_SysIdent_SysEqu.m