## 2 Materials and Methods  
### Multiuser MIMO-OFDM System  
MIMO-OFDM system contains \(T\) number of antennae having subcarrier frequencies in the BS of the transmitter side. The system considers \(I\) number of MSs and all users simultaneously transmit  
\begin{table}
\begin{tabular}{c l} \hline \hline
**Notation** & **Description** \\ \hline \(N_{R}\) & Number of receiver antennae \\ \hline \(L_{A}\) & Number of antennae \\ \hline \(B_{q_{x}}\) & Input data stream \\ \hline \(q_{x}\) & Transmitting antenna \\ \hline \(B_{q_{x}}^{T}\) a & The bit stream after the forward error correction encoder \\ \hline \(B_{q_{x}}^{I}\) & Output bit stream from the interleaver \(I\) \\ \hline \(\widehat{X}_{q_{x}}\) & Modulated data \\ \hline \(X_{q_{x}}[n,\,k]\) & Time domain (TD)-modulated signal \\ \hline \(n\) & Orthogonal frequency-division multiplexing (OFDM) symbol index \\ \hline \(K\) & Number of subcarriers \\ \hline \(B_{q_{x}}(n)\) & Transmitted user data \\ \hline \(K_{cp}\) & Cyclic prefix (CP) samples \\ \hline \(L_{CIR}\) & Length of the channel impulse responses \\ \hline \(\gamma^{j}[n,\,k]\) & Received signal for \(k\)-th subcarrier of the \(n\)-th orthogonal frequency-division multiplexing \\ \hline \(y_{q_{x}}\) & Received signals \\ \hline \(\bar{\Gamma}_{q_{x}}\) & Received pilot subcarriers \\ \hline \(H_{q_{x}}\) & Frequency-Domain Channel Transfer Functions \\ \hline \(X_{q_{x}}[n,k]\) & Frequency-domain channel transfer function (FD-CHTF) coefficient of the link between the \(x\)-th user and the \(q\)-th receiver antenna in the \(k\)-th subcarrier of the \(n\)-th orthogonal frequency-division multiplexing symbol \\ \hline \(W_{q}[n,k]\) & Frequency-domain additive white Gaussian noise (AWGN) \\ \hline \(H_{q}^{i}[n,k]\) & \(K\)-sparse channel impulse vector \\ \hline \(Y_{q}[n,k]\) & \(q\)-th receiver antenna element in the \(k\)-th subcarrier of the \(n\)-th orthogonal frequency-division multiplexing symbol \\ \hline \(\mu\Big{\{}\hat{h}_{q_{x}}\Big{\}}\) & Mutual Coherence \\ \hline \(\hat{h}_{q_{x}}\) & Overall system’s Channel Impulse Response vector \\ \hline \(H_{q_{x}}^{i}[n]\) & Impulse vector for the \(K\)-sparse channel \\ \hline \(Y_{q_{x}}[n]\) & Subcarrier-related signals \\ \hline \(X_{q_{x}}[n]\) & Diagonal elements \\ \hline \(F_{q_{x}}\) & Partial FFT matrix \\ \hline \(I_{q_{x},\,q_{x}}\) & Impulse vector of \(K\)-sparse channel \\ \hline \(K_{q_{x}}\) & Subcarriers position \\ \hline \hline \end{tabular}
\end{table}
Table 1: Nomenclature of the system architecture of the entire paper.  
their data streams to the BS, which can be denoted as \(B^{i}\)\(\forall\)\(1\leq i\leq I\). Furthermore, every user sends a unique ID along with the signal. Therefore, the user sends the data and pilot sequence as the inputs to the MIMO-OFDM system.  
The MUD and CE process is carried out on the receiver side for interference cancellation and noise reduction. An important aim of the suggested approach is to find the error bits among the received signals and correct them. The BER of the overall system is reduced in the joint MUD and CE. The received symbols and pilot over all subcarriers are collected at the receiver end for interference cancellation and noise reduction. The transmitted symbols are simultaneously received by the BS antenna. The MUD methods are used to separate the signals of various MSs depending on their unique user-specific channel impulse responses at BS. The frequency separation is measured in terms of the coherence bandwidth. The non-line-of-sight (NLOS) error is the major issue during transmissions that interferes with a path that is partially obstructed. The NLOS error exists if there is no visual line of sight (LOS) between the transmitting and receiving antennae. In the NLOS propagation case, it has a Rayleigh distribution. The uncorrelated fading experienced between the signal and the gain may be following a Rayleigh distribution.