測試文獻Iterative MAP equalization %表達式(18)-(19)

%6. 測試文獻Iterative MAP equalization and decoding in wireless mobile coded ofdm
 %表達式(18)-(19)
 clc;clear;clc;
M = 8;   %在載波數
K = M
F = 1/sqrt(M) * fft(eye(M));   % unitary FFT matrix of size M
L =   2;       % CP length (same as channel order)
Q2 =   1;       %對角化用
q  =   Q2;

lambda = 0.6; 
pdp = exp( -lambda*(0:L).' ) / sum( exp( -lambda*(0:L).') ); % for exponential power-delay profile
normalized_Doppler_frequency = 0.05;     % with respect to the subcarrier spacing
f_d = normalized_Doppler_frequency / M; 

bit1=[0 1 1 1 1 1 0 1]';
bit2=[0 0 0 1 1 1 1 1]';   %數據源

d = 1/sqrt(2) * ((2*bit1-1)+sqrt(-1)*(2*bit2-1));  %星座點
n = 1/sqrt(2) * (randn(M,1)+sqrt(-1)*randn(M,1));
 % generation of the current channel realization
 ht = ltv_channel_gen_test(f_d,M,32,L+1,pdp); % time-varying CIR;
 Ht = zeros(M,M); % time-domain channel matrix (pre-allocation)
 for index_subcarrier = 1:M
      index_col = mod(((index_subcarrier-L):index_subcarrier)-1,M)+1;
      Ht(index_subcarrier,index_col) = fliplr(ht(1:(L+1),index_subcarrier).'); % time-domain channel matrix
 end

 % frequency-domain channel matrices (with mask to enforce banded matrices)
 Hf       = F * Ht * (F');

 %對角化
 mask2 = toeplitz([ones(Q2+1,1);zeros(M-(2*Q2+1),1);ones(Q2,1)]);
 mask2(M-1:M,1) = 0;
 mask2(M,2)     = 0;
 mask2(1,M-1:M) = 0;
 mask2(2,M)     = 0;

  Hf_banded     = Hf.* mask2;        %對角後的矩陣

  d_hat         = Hf*d + n;          %信道傳輸
  Hf_banded_hat = Hf_banded';
  temp1 = d_hat'* Hf_banded *d + d'*  Hf_banded_hat*d_hat;    %虛部和虛部約掉了，只剩下實部
  temp2 = 2*real( d'*  Hf_banded_hat*d_hat);                  %式(18) 第一項

  temp3 = d'*Hf_banded'*Hf_banded*d;                          %式(18) 第二項     


  %第一項
  temp_sum = 0;
  for m=1:K
      %mod(m-q:m+q,K)
      temp = 0;
      for k=(mod(m-q:m+q,K))                            %matlab下標從1開始，模掉K，再把0置爲K
          if (k == 0)
              k = K;
          end

          temp = temp +  Hf_banded_hat(m,k)*d_hat(k);
      end
      temp_d = (d(m))'*2*temp;
      temp_sum = temp_sum + real(temp_d);

  end

  %第二項
%   G = Hf_banded_hat*Hf_banded;                     %G
%   tempg_sum = 0;
%   for m=1:K
%       %mod(m-q:m+q,K)
%       tempg = 0;
%       for k=mod(1:2*q,K)                            %matlab下標從1開始，模掉K，再把0置爲K
%           if (k == 0)
%               k = K;
%           end
%           
%           if (m-k>0&&m-k<K)
%           tempg = temp +  G(m,m-k)*d(m-k);
%           end
%       end
%       temp_d = G(m,m)*d(m) + 2*tempg;
%       temp_gg = (d(m))'*  temp_d
%       tempg_sum = tempg_sum + real(temp_gg);
%       
%   end

  G = Hf_banded_hat*Hf_banded;                           %G
  tempg_sum = 0;
  for m=1:K
      %mod(m-q:m+q,K)
      tempg = 0;
      for k=mod(m-2*q:m+2*q,K)  %matlab下標從1開始，模掉K，再把0置爲K
          if (k == 0)
              k = K;            %用自己推的和原來的計算結果一致，
                                %但是用作者的計算與原表達式不一樣
          end

          tempg = tempg +  G(m,k)*d(k);
      end
          temp_gg = (d(m))'*  tempg;
          tempg_sum = tempg_sum + real(temp_gg);
  end