faster than Nyquist OFDM implementation

for almost a month I have been trying to replicate the performance of this paper "https://ieeexplore.ieee.org/document/10225298", it MIMO-FTN implementation my focus is on the OFDM-SISO-FTN. I tried implementing my concern is that I implemented H_isi and phi (noise covariance ) in the wrong way , can you give me your feed back on the code :

represents the channel matrix including the effects of ISI induced by FTN signaling and the multipath fading, and ηq​ is the sampled version of ηq​(t). Specifically, the (k,m)-th entries of HISI​ can be calculated by:

g(t) is pulse shaping

​ to reduce the computation loading, whose n-th diagonal entry is calculated by

my code :

N = 128;        % FFT size
G = 30;          % Cyclic prefix length


% FTN parameters
rolloff = 0.3;       % RRC roll-off factor
zeta =0.9;          % FTN time compression factor (0 < zeta < 1) - Set to < 1 for true FTN
filter_span =12; % Filter span in symbols
sps = 10;           % Samples per symbol for pulse shaping
sps_ftn = round(sps*zeta); % Effective samples per symbol (FTN acceleration)

%% Step 1: Generate random bits and BPSK modulation
% Generate random bits for all antennas
bit_streams = randi([0 1], N, Nt);     % N x Nt

% BPSK modulation (0 -> -1, 1 -> +1)
S = 2 * bit_streams - 1;               % N x Nt

%% Step 2: implement Precoding, 
x_cp_p = zeros(N+G, Nt);

% process data steam
x_cp_p = A_cp * F_H * P * S;

%% Step 3: PULSE SHAPING
    
tx_upsampled = zeros(((length(x_cp_p))-1)*sps_ftn + 1,Nt ); %upsample T=tau*T0;
tx_upsampled(1:sps_ftn:end,Nt) = x_cp_p;

% Apply the FTN shaping filter to the transmitted signal
Tx_shaped = conv(tx_upsampled, rrc_filter);
    
tx_signal = Tx_shaped;

%% Generate ISI matrix properly (using first loop)  ????
ac = conv(rrc_filter,rrc_filter);
ac_center = (length(ac) + 1) / 2;

% Generate ISI matrix H (NxN) with multipath effects
H_ISI = zeros(N+G, N+G);
for i = 1:N+G
    for j = 1:N+G
        val = 0;
        for l = 0:L-1
            dist = i - (j + l);
            ac_idx = round(ac_center + dist * sps_ftn);
            if ac_idx >= 1 && ac_idx <= length(ac)
                val = val + h_channel(l+1) * ac(ac_idx);
            end
        end
        H_ISI(i, j) = val;
    end
end

%% Compute noise covariance using pulse autocorrelation (R_n) ????
phi = zeros(N, 1);            % Initialize the noise covariance matrix
for n = 0:N-1
    sum_val = 0;
for i = 0:N-1
    for j = 0:N-1
        lag = i - j;  
        ac_idx = ac_center + lag;
        if ac_idx >= 1 && ac_idx <= length(ac)
            sum_val =  sum_val + ac(ac_idx) * exp((1i * 2*pi * lag * n )/ N); % Use N0/2 for proper scaling
        end
    end
end
    phi(n+1) = sum_val / N;
end
% Scalar noise power (diagonal covariance)


Noise_var=phi*N0;
Noise_var=diag(Noise_var);

[sadeq ebrahimi]

Hello Ahmed I am also working on FTN could you give me your contacts to connect each other?

[Dokman Djaaroun]

Hello Ahmed and Sadeq I am lokman I am also working on FTN this my email [e-mail]