hi , can help me in this problem "Invalid text character. Check for unsupported symbol, invisible character, or pasting of non-ASCII characters." i don't know the solution

H_zf = X_zf * inv(H_true) * Y  ;

or

H_zf = (X_zf ./ inv(H_true) )* Y  ;

[KSSV]

How did you get this error? Show us the whole code.

[Maha Saif]

%% MU-MIMO channel estimation 

clear all
close all
clc


N_r = 128;
K = 10; % number of UEs
L_k = 4; % number of paths per UE
no_sim = 10; % number of Monte Carlo runs


fade = 0;   % parameter for truncated Gaussian fading (if needed)
% fade - nature of fade. 
%       0 is pure Los (unit modulus path gains)
%       1 is Rayleigh fading
%       2 is arbitrary fading

dist_min = 0.5;
pd = makedist('Normal',0,sqrt(0.5));
trunc_pd = truncate(pd,dist_min,inf);
% Example: 
%     pd = makedist('Normal',0,sqrt(0.5));  trunc_pd = truncate(pd,dist_min,inf);
%     Results in real and imaginary parts of path gains (say, \alpha) to follow a
%     truncated Gaussian distribution with 0 <= |Re(\alpha)|,|Im(\alpha)| <= dist_min 


genie_aided_correlation = 0; 
% choose genie_aided_correlation = 1 to use the true channel correlation to
% compute the Bussgang decomposition. However, this is not practical in
% real life. 

OSR = 4; % spatial oversampling ratio at BS
delta = 0.5/OSR; % inter-element spacing at BS
N = K;  % Number of snapshots

aoa_grid = -90:1:90; % search grid for AoA
aspread_aoa = 60; % AoAs will be drawn from -aspread_aoa to aspread_aoa
spacing_aoa = 10; % minimum spacing between AoAs of same UE

aoa_grid_app = -aspread_aoa:1:aspread_aoa;
L_app = length(aoa_grid_app);

E_s = 1; % Signal power
SNR_dB = -12:4:25; 
SNR = 10.^(0.1.*SNR_dB);

tic

U = tril(ones(N_r));
V = U - eye(N_r);
U_inv = inv(U);


% Channel estimation errors
Channel_NMSE_uq_angular = zeros(1,length(SNR));

Channel_NMSE_sd = zeros(1,length(SNR));

Channel_NMSE_sd_zf = zeros(1,length(SNR));


for iter = 1:length(SNR)
    
    channel_err_uq_angular = 0;
    channel_err_sd = 0;
    channel_err_sd_zf = 0;
    
    ch_err_dr = 0;
    
    % selection of voltage level (b)
    b = 3*sqrt((SNR(iter)+1)/2);

    U = tril(ones(N_r));
    U_inv = inv(U);
    R_n = eye(N_r) + ((2*(b^2))/(3)).*U_inv*U_inv'; % Noise covariance
    R_n_pw = inv(sqrtm(R_n)); % pre-whitening matrix

    
    for loop_inner = 1:no_sim
        
        
       % Get channel matrix
         [H_true aoa_true alpha_true] = get_MUMIMO_channel(K,L_k,...
          N_r,delta,aspread_aoa, spacing_aoa, fade, trunc_pd);
       
        A_RX_temp = sqrt(1/L_app).*gen_a(N_r, delta, aoa_grid_app); 
      
        
        ch_err_dr = ch_err_dr + norm(H_true,'fro')^2;
        
        S = sqrt((SNR(iter))/K).*dftmtx(K); % pilot matrix
        N_noise = sqrt(1/2).*(randn(N_r,N) + (1j).*randn(N_r,N));
        
        X = H_true*S + N_noise; % unquantized received signal
        Y_q = sqrt(1/2).*sgn(X);  %One-bit 
        
        %% prameters for Bussgang decomposition based channel estimation [Ref. no]
        
        if(genie_aided_correlation == 0)
            C_G = A_RX_temp*A_RX_temp';
            C_g = kron(eye(K),C_G);
        elseif(genie_aided_correlation == 1)
            C_g = zeros(K*N_r);        
            for k=1:K
                range_consider = (k-1)*N_r+1:k*N_r;
                A_req = sqrt(1/L_k).*gen_a(N_r, delta, doa_true(:,k));
                C_g(range_consider,range_consider) = A_req*A_req';
            end 
        end

        P = kron(transpose(S), eye(N_r));
        C_x = P*C_g*P' + eye(N*N_r);
        beta = 1.05;

        C_r = zeros(N*N_r,N*N_r);


        sig_r_sq = zeros(N*N_r,1);
        sig_q_sq = zeros(N*N_r,1);
        sig_x_sq = diag(C_x);
        sig_y_sq = zeros(N*N_r,1);

        for k=1:N*N_r

            if(mod(k,N_r)==1)
                sig_r_sq(k) = sig_x_sq(k);
            else
                sig_r_sq(k) = sig_x_sq(k) + sig_q_sq(k-1);
            end

            sig_y_sq(k) = (pi/2)*(beta^2)*sig_r_sq(k);
            sig_q_sq(k) = sig_y_sq(k) - sig_r_sq(k);

        end

        r_t = sig_r_sq(1:N_r);
        a_m = zeros(N_r,1);
        a_m(1:N_r) = (beta/2).*sqrt(pi.*r_t(1:N_r)); % proposed voltage level in [Number]
        
        U_inv = kron(eye(N),inv(U));

        C_ql = diag(sig_q_sq);

        C_y = C_x + U_inv*C_ql*U_inv'; % Eq (31)

        Yl = sigma_delta_ADC_b(X,0,delta,a_m); % output of SD ADC proposed in []
        yl = reshape(Yl, N*N_r,1);

        C_gy = C_g*P';
        h_hat = C_gy*inv(C_y)*yl;
        

        %%%%%%%%%% Unquantized channel estimation - LMMSE
         x = reshape(X, N*N_r, 1);   
            
        C_gx = C_g*P';
        h_hat_lmmse = C_gx*inv(C_x)*x;
        H_est_lmmse = reshape(h_hat_lmmse, N_r, K); % LMMSE channel estimate    
        %%channel_err_uq_lmmse = channel_err_uq_lmmse + ((norm(H_true - H_est_lmmse,'fro'))^2);

        %% Proposed methods 
        
         T_s = 1 ;
        % UQ channel estimation        
        [H_est_uq_angular  aoa_est_uq_angular alpha_est_uq_angular] = MU_MIMO_est_UQ(H_true,S, T_s, delta, L_k, SNR(iter), aoa_grid );
        channel_err_uq_angular = channel_err_uq_angular + norm(H_true - H_est_uq_angular,'fro')^2;

        % SD channel estimation
        [H_est_sd  aoa_est_sd alpha_est_sd]  = MU_MIMO_est_SD(H_true, S, T_s, delta, L_k, SNR(iter), aoa_grid, b, R_n_pw );
        channel_err_sd = channel_err_sd + norm(H_true - H_est_sd,'fro')^2; 
      
             
        % zero forcing 
       Y = sigma_delta_ADC(X,0,delta,b); % output of sigma-delta quantizer
       H_true= zeros(N_r,K);
 
       estimated_symbols = ZF_receiver (Y , H_true , N_noise );
       X_zf = (Y./(H_true)) + N_noise ;
       %%[H_est_sd_zf] = MU_MIMO_est_SD_ZF(H_est, S, T_s ,X_zf,X , delta, L_k, SNR(iter), aoa_grid, b, R_n_pw ) ;
       h_zf = X_zf * inv(H_true) * Y  ;`

Invalid text character. Check for unsupported symbol, invisible character, or pasting of non-ASCII characters.

       H_est_sd_zf = reshape (h_zf * N_r * K) ;
       channel_err_sd_zf = channel_err_sd_zf + norm(H_true - estimated_symbols ,'fro')^2; 
        
        
        %% One bit BLMMSE channel estimation
            
         %% MRC combiner the outbut of SD
    %%% delete 
         
        [iter loop_inner];
        
    end
    
    
    
    Channel_NMSE_uq_angular(iter) = channel_err_uq_angular/ch_err_dr;
    Channel_NMSE_sd(iter) = channel_err_sd/ch_err_dr;
    Channel_NMSE_sd_zf(iter) = channel_err_sd_zf/ch_err_dr;

   
end

toc
%% Plotting Results
% 

figure
plot(SNR_dB , 10.*log10(Channel_NMSE_uq_angular), 'g-d','LineWidth', 1.2);
hold on
plot(SNR_dB ,  10.*log10(Channel_NMSE_sd), 'm-d','LineWidth', 1.2);
hold on
plot(SNR_dB , 10.*log10(Channel_NMSE_sd_zf), 'y-o','LineWidth',1.2);

grid on

legend('Unquantized-angular', 'SD-proposed', 'SD_ZF');
title('ZF WITH SIGMA DELTA Channel Estimation');
xlabel('SNR (dB)');
ylabel('NMSE (dB)');

%figure
%plot(SNR_dB ,  10.*log10(Channel_NMSE_zf), 'y-d','LineWidth', 1.2);

%xlabel('SNR (dB)');
%ylabel('NMSE (dB)');

[Maha Saif]

how i can solve the error ???

[Stephen23]

"how i can solve the error ???"

Exactly as the error message tells you, delete this invalid character:

[Maha Saif]

thank you

[Maha Saif]

in the result figure , i don't know why the curve about SD_ZF not show

[Walter Roberson]

%% MU-MIMO channel estimation 

clear all
close all
clc


N_r = 128;
K = 10; % number of UEs
L_k = 4; % number of paths per UE
no_sim = 10; % number of Monte Carlo runs


fade = 0;   % parameter for truncated Gaussian fading (if needed)
% fade - nature of fade. 
%       0 is pure Los (unit modulus path gains)
%       1 is Rayleigh fading
%       2 is arbitrary fading

dist_min = 0.5;
pd = makedist('Normal',0,sqrt(0.5));
trunc_pd = truncate(pd,dist_min,inf);
% Example: 
%     pd = makedist('Normal',0,sqrt(0.5));  trunc_pd = truncate(pd,dist_min,inf);
%     Results in real and imaginary parts of path gains (say, \alpha) to follow a
%     truncated Gaussian distribution with 0 <= |Re(\alpha)|,|Im(\alpha)| <= dist_min 


genie_aided_correlation = 0; 
% choose genie_aided_correlation = 1 to use the true channel correlation to
% compute the Bussgang decomposition. However, this is not practical in
% real life. 

OSR = 4; % spatial oversampling ratio at BS
delta = 0.5/OSR; % inter-element spacing at BS
N = K;  % Number of snapshots

aoa_grid = -90:1:90; % search grid for AoA
aspread_aoa = 60; % AoAs will be drawn from -aspread_aoa to aspread_aoa
spacing_aoa = 10; % minimum spacing between AoAs of same UE

aoa_grid_app = -aspread_aoa:1:aspread_aoa;
L_app = length(aoa_grid_app);

E_s = 1; % Signal power
SNR_dB = -12:4:25; 
SNR = 10.^(0.1.*SNR_dB);

tic

U = tril(ones(N_r));
V = U - eye(N_r);
U_inv = inv(U);


% Channel estimation errors
Channel_NMSE_uq_angular = zeros(1,length(SNR));

Channel_NMSE_sd = zeros(1,length(SNR));

Channel_NMSE_sd_zf = zeros(1,length(SNR));


for iter = 1:length(SNR)
    
    channel_err_uq_angular = 0;
    channel_err_sd = 0;
    channel_err_sd_zf = 0;
    
    ch_err_dr = 0;
    
    % selection of voltage level (b)
    b = 3*sqrt((SNR(iter)+1)/2);

    U = tril(ones(N_r));
    U_inv = inv(U);
    R_n = eye(N_r) + ((2*(b^2))/(3)).*U_inv*U_inv'; % Noise covariance
    R_n_pw = inv(sqrtm(R_n)); % pre-whitening matrix

    
    for loop_inner = 1:no_sim
        
        
       % Get channel matrix
         [H_true aoa_true alpha_true] = get_MUMIMO_channel(K,L_k,...
          N_r,delta,aspread_aoa, spacing_aoa, fade, trunc_pd);
       
        A_RX_temp = sqrt(1/L_app).*gen_a(N_r, delta, aoa_grid_app); 
      
        
        ch_err_dr = ch_err_dr + norm(H_true,'fro')^2;
        
        S = sqrt((SNR(iter))/K).*dftmtx(K); % pilot matrix
        N_noise = sqrt(1/2).*(randn(N_r,N) + (1j).*randn(N_r,N));
        
        X = H_true*S + N_noise; % unquantized received signal
        Y_q = sqrt(1/2).*sgn(X);  %One-bit 
        
        %% prameters for Bussgang decomposition based channel estimation [Ref. no]
        
        if(genie_aided_correlation == 0)
            C_G = A_RX_temp*A_RX_temp';
            C_g = kron(eye(K),C_G);
        elseif(genie_aided_correlation == 1)
            C_g = zeros(K*N_r);        
            for k=1:K
                range_consider = (k-1)*N_r+1:k*N_r;
                A_req = sqrt(1/L_k).*gen_a(N_r, delta, doa_true(:,k));
                C_g(range_consider,range_consider) = A_req*A_req';
            end 
        end

        P = kron(transpose(S), eye(N_r));
        C_x = P*C_g*P' + eye(N*N_r);
        beta = 1.05;

        C_r = zeros(N*N_r,N*N_r);


        sig_r_sq = zeros(N*N_r,1);
        sig_q_sq = zeros(N*N_r,1);
        sig_x_sq = diag(C_x);
        sig_y_sq = zeros(N*N_r,1);

        for k=1:N*N_r

            if(mod(k,N_r)==1)
                sig_r_sq(k) = sig_x_sq(k);
            else
                sig_r_sq(k) = sig_x_sq(k) + sig_q_sq(k-1);
            end

            sig_y_sq(k) = (pi/2)*(beta^2)*sig_r_sq(k);
            sig_q_sq(k) = sig_y_sq(k) - sig_r_sq(k);

        end

        r_t = sig_r_sq(1:N_r);
        a_m = zeros(N_r,1);
        a_m(1:N_r) = (beta/2).*sqrt(pi.*r_t(1:N_r)); % proposed voltage level in [Number]
        
        U_inv = kron(eye(N),inv(U));

        C_ql = diag(sig_q_sq);

        C_y = C_x + U_inv*C_ql*U_inv'; % Eq (31)

        Yl = sigma_delta_ADC_b(X,0,delta,a_m); % output of SD ADC proposed in []
        yl = reshape(Yl, N*N_r,1);

        C_gy = C_g*P';
        h_hat = C_gy*inv(C_y)*yl;
        

        %%%%%%%%%% Unquantized channel estimation - LMMSE
         x = reshape(X, N*N_r, 1);   
            
        C_gx = C_g*P';
        h_hat_lmmse = C_gx*inv(C_x)*x;
        H_est_lmmse = reshape(h_hat_lmmse, N_r, K); % LMMSE channel estimate    
        %%channel_err_uq_lmmse = channel_err_uq_lmmse + ((norm(H_true - H_est_lmmse,'fro'))^2);

        %% Proposed methods 
        
         T_s = 1 ;
        % UQ channel estimation        
        [H_est_uq_angular  aoa_est_uq_angular alpha_est_uq_angular] = MU_MIMO_est_UQ(H_true,S, T_s, delta, L_k, SNR(iter), aoa_grid );
        channel_err_uq_angular = channel_err_uq_angular + norm(H_true - H_est_uq_angular,'fro')^2;

        % SD channel estimation
        [H_est_sd  aoa_est_sd alpha_est_sd]  = MU_MIMO_est_SD(H_true, S, T_s, delta, L_k, SNR(iter), aoa_grid, b, R_n_pw );
        channel_err_sd = channel_err_sd + norm(H_true - H_est_sd,'fro')^2; 
      
             
        % zero forcing 
       Y = sigma_delta_ADC(X,0,delta,b); % output of sigma-delta quantizer
       H_true= zeros(N_r,K);
 
       estimated_symbols = ZF_receiver (Y , H_true , N_noise );
       X_zf = (Y./(H_true)) + N_noise ;
       %%[H_est_sd_zf] = MU_MIMO_est_SD_ZF(H_est, S, T_s ,X_zf,X , delta, L_k, SNR(iter), aoa_grid, b, R_n_pw ) ;
       h_zf = X_zf * inv(H_true) * Y  ;
       H_est_sd_zf = reshape (h_zf * N_r * K) ;
       channel_err_sd_zf = channel_err_sd_zf + norm(H_true - estimated_symbols ,'fro')^2; 
        
        
        %% One bit BLMMSE channel estimation
            
         %% MRC combiner the outbut of SD
    %%% delete 
         
        [iter loop_inner];
        
    end
    
    
    
    Channel_NMSE_uq_angular(iter) = channel_err_uq_angular/ch_err_dr;
    Channel_NMSE_sd(iter) = channel_err_sd/ch_err_dr;
    Channel_NMSE_sd_zf(iter) = channel_err_sd_zf/ch_err_dr;

   
end

Unrecognized function or variable 'get_MUMIMO_channel'.

toc
%% Plotting Results
% 

figure
plot(SNR_dB , 10.*log10(Channel_NMSE_uq_angular), 'g-d','LineWidth', 1.2);
hold on
plot(SNR_dB ,  10.*log10(Channel_NMSE_sd), 'm-d','LineWidth', 1.2);
hold on
plot(SNR_dB , 10.*log10(Channel_NMSE_sd_zf), 'y-o','LineWidth',1.2);

grid on

legend('Unquantized-angular', 'SD-proposed', 'SD_ZF');
title('ZF WITH SIGMA DELTA Channel Estimation');
xlabel('SNR (dB)');
ylabel('NMSE (dB)');

%figure
%plot(SNR_dB ,  10.*log10(Channel_NMSE_zf), 'y-d','LineWidth', 1.2);

%xlabel('SNR (dB)');
%ylabel('NMSE (dB)');

Answer 1

[Walter Roberson]

       h_zf = X_zf * inv(H_true) * Y  ;`

That line has a ` (back-quote) at the end of that you need to delete, making it

       h_zf = X_zf * inv(H_true) * Y  ;

[Maha Saif]

thanks alot

Answer 2

[Bruno Luong]

% Pasting the last line bellow in your code editor

H_true = rand(5);
X_zf = rand(5);
Y = rand(5);

H_zf = X_zf * inv(H_true) * Y

H_zf = 5×5

1.3314 3.7161 1.6341 0.0437 3.1849 3.4033 7.1076 3.1060 -0.1038 5.9743 0.8452 1.6774 0.9671 0.1583 2.0241 -0.6046 -0.3610 0.2176 0.3070 -0.2526 3.6896 7.7084 3.7287 0.0863 6.3431

[Maha Saif]

but each variable has different value

[Bruno Luong]

Pasting the last line

[Maha Saif]

N_r = 128 ;
K = 10 ;
H_true= zeros(N_r,K);
Y = sigma_delta_ADC(X,0,delta,b);
N_noise = sqrt(1/2).*( randn(N_r,K) + 1j.*randn(N_r,K) );
X_zf = (Y./(H_true)) + N_noise ;
H_zf = X_zf * inv(H_true) * Y

[Bruno Luong]

No I asked you to past the code here TO your code editor and run it, I suspect there is some non ascii code in your code source and by doing so you clean it.

I did not ask you to past your code here.

[Maha Saif]

ok , where i should put the code ?

there are many files and function