5G-mm-wave simulations comparison and debuging.

Introduction

The purpose of this repository is to debug the code present in catproof/Localization-For-5G-MIMO-Using-Beam-Steering-and-Channel-Estimation. As it is a python translation of henkwymeersch/5GPositioning, both repositories are copied here and modified for debug purposes.

Method

To enable a reliable comparison between the two scripts, it is essential to eliminate any non-deterministic behavior. First, the sigma parameters in both scripts are set to zero, ensuring the absence of randomly generated noise. Additionally, predetermined values are assigned to the positions of scatter points, ensuring consistency across executions.

Another source of non-determinism arises from the population of the three-dimensional arrays y and F. To achieve deterministic behavior, the values of y and F are exported from the Matlab code, and the exported values are utilized in both Matlab and Python during subsequent executions. As direct import/export of three-dimensional structures is not supported by Matlab or Python's Numpy library, multiple export files are created, each containing two-dimensional structures. It is important to note that a minor modification is required before using the export files in Python due to the difference in the notation for the imaginary unit. In Matlab, the imaginary unit is denoted by i, while Python uses j.

In Matlab one time export is done

for i=1:N
    writematrix(y(:,:,i), sprintf('y_%d.csv', i));
    writematrix(F(:,:,i), sprintf('F_%d.csv', i));
end

Then the corresponding Matlab and Python imports are done

for i=1:N
    y(:,:,i) = readmatrix(sprintf('y_%d.csv', i));
    F(:,:,i) = readmatrix(sprintf('F_%d.csv', i));
end

for n in range(0, N):
    yFilename = os.path.join(DIR_PATH,'y_{}.csv'.format(n+1))
    y[:,:, n] = np.genfromtxt(yFilename, delimiter=",", dtype='complex_');

    FFilename = os.path.join(DIR_PATH,'F_{}.csv'.format(n+1))
    F[:,:, n]  = np.genfromtxt(FFilename,delimiter=",", dtype='complex_');

After eliminating all non-deterministic behavior, the scripts are executed, and each line is compared by examining corresponding variables. If any discrepancies are found, the corresponding line is debugged. This process is continued until the end of both scripts. Due to the large number of elements in certain structures, such as Omega with over 13 million entries, a selection of random positions is made to compare elements reliably. It is important to note that the indexing of structures differs between Python and Matlab. For instance, Omega[1,2,3] in Matlab corresponds to Omega[0,1,2] in Python.

By following this approach, the following discrepancies are identified and corrected: In Matlab, the ' operator is used in the initialization of H and Omega. The operator results in a complex conjugate transpose of a matrix. However, in the corresponding lines of the Python script, a normal transpose is used (equivalent to Matlab's ".'" operator). The necessary corrections are

H[:, :, n] += t1 * np.outer(t2, np.conjugate(t3))
...
omega[:, :, n] = np.kron((Ut.conjugate().transpose().dot(F[:, :, n])).transpose(), Ur) 

To initialize yb, the reshape function is utilized. It is important to note that Matlab follows a Fortran-like index order, while Python's Numpy library follows a C-like index order. In order to align with Matlab's behavior, the necessary correction are

yb[:, n] = 
    np.reshape(y[:, :, n],...
        [Nr * G, 1], order='F')[:,0] 

Another discrepancy is identified in the get_response_vector function. In the Matlab implementation, a minus sign is employed. To rectify this inconsistency, the correction is applied in the Python script as demonstrated

def get_response_vector(N,phi,d,lambda_n):
...
    response_vector = np.exp(-1j*antennas*2*math.pi*d*np.sin(phi)/lambda_n)/math.sqrt(N)

Additional tools and organization

All the export files for F and y are present correspondingly in 5GPositioning/debug_export_data and Localization-For-5G-MIMO-Using-Beam-Steering-and-Channel-Estimation/debug_export_data. A python script rewriting the complex number to j in the export files to be used in Python is present in Localization-For-5G-MIMO-Using-Beam-Steering-and-Channel-Estimation/debug_export_data/convert_i2j.py.

Conclusion

The simulation present in catproof/Localization-For-5G-MIMO-Using-Beam-Steering-and-Channel-Estimation was successfully debugged, therefore can be more reliably used.

Disclaimers

This repository does not claim any intelectual rights. The code provided here is only slightly modified version of the work present in catproof/Localization-For-5G-MIMO-Using-Beam-Steering-and-Channel-Estimation and henkwymeersch/5GPositioning. The code provided in this repository comes with no warranty. No claims about the accuracy of the simulation are made.