matlab生成m序列的函数（本原多项式产生所有m序列）

后期更新：matlab中产生m序列最简单的方法是调用idinput()函数，关于idinput()的具体用法可以在matlab中查看说明，这里举两个简单的例子：

src = idinput(8191,'RBS')'; % 产生随机的二进制数据 1 -1
m = idinput(8191,'PRBS')';  % 产生长度为8192的m序列

m序列的基本生成原理这里就不做介绍了，今天闲着没事时候就行统计一下m序列中00和11的个数，结果有点失望，竟然是完全相等的（手动再最前面或者最后面补了一个0），并且00和11的个数是m序列长度的1/4（微小浮动）。我尝试了将m序列循环移位再统计，结果还是只有这两组值！！！下面是我通过本原多项式产生所有n=9和n=10的m序列并统计00和11个数的代码。其中 primpoly(9,'all')  这个函数可以获得所有n=9的m序列的本原多项式。

产生m序列的函数，输入参数为：m序列的本原多项式的系数矩阵

function[mseq]=m_sequence(fbconnection)
%     primpoly(9,'all')
    n=length(fbconnection);
    N=2^n-1; 
    newregister = zeros(1, n);
    mseq = zeros(1, N);
    register=[zeros(1,n-1) 1];  % 移位寄存器的初始状态
    mseq(1)=register(n);        % m序列的第一个输出码元
    for i=2:N      
        newregister(1)=mod(sum(fbconnection.*register),2);     
        for j=2:n          
            newregister(j)=register(j-1);     
        end    
    register=newregister;     
    mseq(i)=register(n); 
    end
end  

下面这代码是我统计m中00和11个数的代码

clear all;

syms D;
%     primpoly(9,'all')
if 0
    poly_str = [D^9+D^4+1, D^9+D^4+D^3+D^1+1, D^9+D^5+1, D^9+D^5+D^3+D^2+1, D^9+D^5+D^4+D^1+1, D^9+D^6+D^4+D^3+1, D^9+D^6+D^4+D^3+D^2+D^1+1, ...
    D^9+D^6+D^5+D^3+1, D^9+D^6+D^5+D^3+D^2+D^1+1, D^9+D^6+D^5+D^4+D^2+D^1+1, D^9+D^6+D^5+D^4+D^3+D^2+1, D^9+D^7+D^2+D^1+1,D^9+D^7+D^4+ ...
    D^2+1, D^9+D^7+D^5+D^1+1, D^9+D^7+D^5+D^2+1, D^9+D^7+D^5+D^3+D^2+D^1+1, D^9+D^7+D^5+D^4+D^2+D^1+1, D^9+D^7+D^5+D^4+D^3+D^2+1, D^9+ ...
    +D^7+D^6+D^3+D^2+D^1+1, D^9+D^7+D^6+D^4+1, D^9+D^7+D^6+D^4+D^3+D^1+1, D^9+D^7+D^6+D^5+D^4+D^2+1, D^9+D^7+D^6+D^5+D^4+D^3+1, D^9+D^8+ ...
    +D^4+D^1+1, D^9+D^8+D^4+D^2+1, D^9+D^8+D^4+D^3+D^2+D^1+1, D^9+D^8+D^5+D^1+1, D^9+D^8+D^5+D^4+1, D^9+D^8+D^5+D^4+D^3+D^1+1, D^9+D^8+ ...
    D^6+D^3+D^2+D^1+1, D^9+D^8+D^6+D^4+D^3+D^1+1, D^9+D^8+D^6+D^5+1, D^9+D^8+D^6+D^5+D^3+D^1+1, D^9+D^8+D^6+D^5+D^3+D^2+1 ,D^9+D^8+D^6+ ...
    D^5+D^4+D^1+1, D^9+D^8+D^6+D^5+D^4+D^3+D^2+D^1+1, D^9+D^8+D^7+D^2+1, D^9+D^8+D^7+D^3+D^2+D^1+1, D^9+D^8+D^7+D^5+D^4+D^2+1, D^9+D^8+ ...
    D^7+D^5+D^4+D^3+1, D^9+D^8+D^7+D^6+D^2+D^1+1, D^9+D^8+D^7+D^6+D^3+D^1+1, D^9+D^8+D^7+D^6+D^3+D^2+1, D^9+D^8+D^7+D^6+D^4+D^2+1, D^9+ ...
    D^8+D^7+D^6+D^4+D^3+1, D^9+D^8+D^7+D^6+D^5+D^1+1, D^9+D^8+D^7+D^6+D^5+D^3+1, D^9+D^8+D^7+D^6+D^5+D^4+D^3+D^1+1];
else
    poly_str = [D^10+D^3+1, D^10+D^4+D^3+D^1+1, D^10+D^5+D^2+D^1+1, D^10+D^5+D^3+D^2+1, D^10+D^6+D^5+D^2+1, D^10+D^6+D^5+D^3+D^2+D^1+1, ...
    D^10+D^7+1, D^10+D^7+D^3+D^1+1, D^10+D^7+D^6+D^2+1, D^10+D^7+D^6+D^4+D^2+D^1+1, D^10+D^7+D^6+D^5+D^2+D^1+1, D^10+D^7+D^6+D^5+D^4+D^1+...
    1, D^10+D^7+D^6+D^5+D^4+D^3+D^2+D^1+1, D^10+D^8+D^3+D^2+1, D^10+D^8+D^4+D^3+1, D^10+D^8+D^5+D^1+1, D^10+D^8+D^5+D^4+1, D^10+D^8+D^5+...
    D^4+D^3+D^2+1, D^10+D^8+D^6+D^1+1, D^10+D^8+D^6+D^4+D^2+D^1+1, D^10+D^8+D^6+D^5+D^3+D^1+1, D^10+D^8+D^7+D^2+1, D^10+D^8+D^7+D^3+D^2+...
    D^1+1, D^10+D^8+D^7+D^4+D^2+D^1+1, D^10+D^8+D^7+D^5+1, D^10+D^8+D^7+D^6+D^2+D^1+1, D^10+D^8+D^7+D^6+D^5+D^2+1, D^10+D^8+D^7+D^6+D^5+...
    D^4+D^2+D^1+1, D^10+D^8+D^7+D^6+D^5+D^4+D^3+D^1+1, D^10+D^9+D^4+D^1+1, D^10+D^9+D^4+D^2+1, D^10+D^9+D^5+D^2+1, D^10+D^9+D^5+D^4+D^2+...
    D^1+1, D^10+D^9+D^6+D^1+1, D^10+D^9+D^6+D^3+D^2+D^1+1, D^10+D^9+D^6+D^4+D^3+D^1+1, D^10+D^9+D^6+D^5+D^4+D^3+1, D^10+D^9+D^6+D^5+D^4+...
    D^3+D^2+D^1+1, D^10+D^9+D^7+D^3+1, D^10+D^9+D^7+D^5+D^4+D^2+1, D^10+D^9+D^7+D^6+1, D^10+D^9+D^7+D^6+D^4+D^1+1, D^10+D^9+D^7+D^6+D^4+...
    D^3+D^2+D^1+1, D^10+D^9+D^7+D^6+D^5+D^4+D^3+D^2+1, D^10+D^9+D^8+D^4+D^2+D^1+1, D^10+D^9+D^8+D^4+D^3+D^2+1, D^10+D^9+D^8+D^5+1, D^10+...
    D^9+D^8+D^5+D^4+D^3+1, D^10+D^9+D^8+D^6+D^2+D^1+1, D^10+D^9+D^8+D^6+D^3+D^2+1, D^10+D^9+D^8+D^6+D^4+D^2+1, D^10+D^9+D^8+D^6+D^4+D^3+...
    1, D^10+D^9+D^8+D^6+D^5+D^1+1, D^10+D^9+D^8+D^6+D^5+D^4+D^3+D^2+1, D^10+D^9+D^8+D^7+D^3+D^2+1, D^10+D^9+D^8+D^7+D^4+D^1+1, D^10+D^9+...
    D^8+D^7+D^5+D^4+1, D^10+D^9+D^8+D^7+D^6+D^4+D^3+D^1+1, D^10+D^9+D^8+D^7+D^6+D^5+D^4+D^1+1, D^10+D^9+D^8+D^7+D^6+D^5+D^4+D^3+1];
end

m00 = zeros(2, length(poly_str));
m11 = zeros(2, length(poly_str));

fd = fopen('m_Seq_Cnt.txt','a+');  % 保存数据结果到文本文件 
for i = 1 : 1 : length(poly_str)
    tmp = fliplr(sym2poly(poly_str(i)));
    s   = tmp(2 : length(tmp));
    
    m_seq_tmp = m_sequence(s);
    m_seq1 = [0 m_seq_tmp];
    
    m00_cnt = 0;
    m11_cnt = 0;
    t1 = m_seq1(1 : 2 : length(m_seq1));
    t2 = m_seq1(2 : 2 : length(m_seq1));
    for k = 1 : 1 : length(t1)
        tmp = t1(k) + t2(k);
        if(tmp == 0)
            m00_cnt = m00_cnt + 1;
        elseif(tmp == 2)
            m11_cnt = m11_cnt + 1;
        end
    end
    m00(1, i) = m00_cnt;
    m11(1, i) = m11_cnt;   
    fprintf(fd, '前置： 00 -> %d       11 -> %d            ', m00_cnt, m11_cnt);
    
    m00_cnt = 0;
    m11_cnt = 0;
    m_seq2 = [m_seq_tmp 0];
    t1 = m_seq2(1 : 2 : length(m_seq2));
    t2 = m_seq2(2 : 2 : length(m_seq2));
    for k = 1 : 1 : length(t1)
        tmp = t1(k) + t2(k);
        if(tmp == 0)
            m00_cnt = m00_cnt + 1;
        elseif(tmp == 2)
            m11_cnt = m11_cnt + 1;
        end
    end
    m00(2, i) = m00_cnt;
    m11(2, i) = m11_cnt;
    fprintf(fd, '后置： 00 -> %d       11 -> %d \n', m00_cnt, m11_cnt);
end

fclose(fd);

后来也统计了一下01和10的个数，这组的变化较大，总体浮动大概是00和11的两倍左右。