## 3 System Model
### Receiver Structure  
The receiver system, as depicted in Figure 2, conducts iterative multi-user detection along with frequency domain equalization to detect the received signal [19,20]. The received signal is converted from the time to the frequency domain after undergoing an N-point FFT. De-subcarrier mapping is performed corresponding to the transmitter sub-carrier mapping. The received sequence in vectorted form can be expressed as follows [19,20]. \[\mathrm{Y}=\sum_{\forall\mathrm{K}}\sqrt{\mathrm{P_{k}}}\wedge_{\mathrm{k}} \mathrm{X_{k}}+W \tag{4}\]  
Here, \(\mathrm{P_{k}}\) represents the assigned power to user \(\mathrm{k}\), \(\wedge_{\mathrm{k}}\) is the N \(\times\) N matrix of channel frequency response for the kth user. Additionally, the de-subcarrier mapped data vector in the frequency domain is denoted by \(\mathrm{X_{k}}\) as previously stated, along with \(W\) representing additive white gaussian noise (AWGN) with zero mean and variance \(\sigma_{\mathrm{w}}\)2. Following this, MUD is performed iteratively with FDE to retrieve the individual signal of the users from the combined signal. Multi-user interference cancellation (MIC), minimum mean square error (MMSE) equalization, and decoding processes are performed successively for every cycle of iteration [19,20]. While detecting the signals for individual users, users' signals are ordered according to their signal-to-noise ratio (SNR), with the detection of the highest SNR user first, followed by upcoming users' detection as per their SNR value from high to low. Cancellation of the user signal with the highest SNR from the combined signal offers less multiple access interference (MAI) for the rest of the users. Therefore, the minimum MAI will be offered to the user having the lowest SNR, resulting in better overall performance. Furthermore, minimum mean square error (MMSE) equalization is applied to all received symbols. To execute this, the mean \(\overline{\mathrm{x_{k}}}\) and variance \(\mathrm{v_{k}}\) of the transmitted symbols for each user \(\mathrm{k}\) can be expressed as [19,20]. \[\overline{\mathrm{x_{k}}}(\mathrm{n})\triangleq\mathrm{E}((\mathrm{x_{k}}( \mathrm{n}))=\sum_{\mathrm{r=0}}^{2^{\mathrm{R}}-1}\alpha_{\mathrm{r}}\mathrm{ P}(\mathrm{x_{k}}(\mathrm{n})=\alpha_{\mathrm{r}}) \tag{5}\]  
\[\mathrm{v_{k}}(\mathrm{n})\triangleq\mathrm{Cov}(\mathrm{x_{k}}(\mathrm{n}), \mathrm{x_{k}}(\mathrm{n}))=\sum_{\mathrm{r=0}}^{2^{\mathrm{R}}-1}|\alpha_{ \mathrm{r}}|^{2}\mathrm{.P}(\mathrm{x_{k}}(\mathrm{n})=\alpha_{\mathrm{r}})-| \overline{\mathrm{x_{k}}}(\mathrm{n})|^{2} \tag{6}\]  
Here, \(\mathrm{n}\) represents all symbols ranging from 0 to S. Depending on the modulation order \(\mathrm{R}\), \(\alpha_{\mathrm{r}}\) denotes the corresponding modulation level, ranging from \(\alpha_{0},\alpha_{1},\alpha_{2},\ldots\ldots,\alpha_{2^{\mathrm{R}}-1}\). The probability \(\mathrm{P}\) that a specific symbol has been assigned to a particular bit pattern is calculated as described in [19,20]. \[\mathrm{P}(\mathrm{x_{k}}(\mathrm{n})=\alpha_{\mathrm{r}})=\prod_{\mathrm{j=0 }}^{\mathrm{R}-1}\frac{1}{2}(1+\bar{\mathrm{x}}_{\mathrm{r,j}}\mathrm{.tanh}( \mathrm{L_{I}^{E}}(\mathrm{b_{k}}(\mathrm{Rn}+1)))) \tag{7}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Channel Delay Profiles** & **Path-1 (Direct)** & **Path-2** & **Path-3** & **Path-4** & **Path-5** & **Path 6** \\ \hline Delay (in n-sec) & 0 & 310 & 710 & 1090 & 1730 & 2510 \\ Power (in dB) & 0 & \(-1.0\) & \(-9.0\) & \(-10.0\) & \(-15.0\) & \(-20.0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Delay profiles for multipath channel. For each coded bit \(\{\mathrm{b}_{\mathrm{k}}(\mathrm{j})\}_{\mathrm{j}=0}^{\mathrm{RS-1}}\), where j ranges from 0 to \(\mathrm{RS-1}\), \(\mathrm{a}_{\mathrm{r}\mathrm{j}}\) and \(\mathrm{\bar{a}}_{\mathrm{r}\mathrm{j}}\) represent the inputs and outputs of the modulator, respectively, with the input to the modulator represented as 0 or 1 and the output from the modulator represented as 1 or \(-1\).