## 3 Results  
The performance estimation of the suggested method is in the fading channel. The bandwidth of the system is 5 MHz with 32, 128 and 512 subcarriers. A MIMO-OFDM with dimensions of 4 \(\times\) 4 is considered for performance evaluation. The input simulation parameters are given in Table 2.  
The simulation results for the suggested method are demonstrated in terms of the BER, SER and MSE compared to the signal-to-noise ratio (SNR). When compared to existing algorithms, the loss due to the joint MUD and CE is decreased. The suggested MIMO-assisted multi-user detection algorithm compromises and attains a greater throughput than the traditional MMSE scheme. The optimum pilot pattern \(\lambda_{iTR},iTR=1,\,2,\,\ldots,\,N_{TR}\) is selected through a mutual coherence of 0.1872. The performance evaluation of SER can be illustrated in Figures 2 and 3 for 20 users and 100 users. The comparative analysis of various MUD techniques presented in [23] is compared with the existing approach. SER is minimized for our proposed approach. The proposed technique is compared with the existing zero-forcing (ZF) detector, minimum mean square error (MMSE) detector, ridge detector (RD), lasso detector (LD), sparse Bayesian learning (SBL), block sparse Bayesian learning (BSBL) and pattern-coupled sparse Bayesian learning (PCSBL). The SER is calculated based on the detected errors. The low and high users' activity is detected by finding the error bits. The graph significantly shows that the proposed method has a minimum SER in terms of the SNR (dB) for 20 and 100 users. The rate of SER is declined with an increase in SNR. BER can estimate the altered bits transmitted over the channel. The same problem discussed in [23] for activity detection is used but the performance of the proposed approach outperforms their methods (SBL, BSBL and PCSBL). Furthermore, it is not well suited for MAI compared to our proposed methods. The BER and SNR performance of LS and MMSE in Figure 4 shows the efficiency of CE. The CSO based optimization for attaining the minimized mutual coherence attains a minimized BER in terms of SNR compared with LS and MMSE. The existing comparison chart for BER is presented in reference [13]. The comparative analysis of the proposed work represented in Figures 4-7 and the existing works are taken from reference [15]. The entire bandwidth of the channel is divided by 128 subcarriers with a symbol duration of 160 \(\upmu\)s in the LS based pilot allocation. To avoid inter-symbol interference, we chose 40 \(\upmu\)s for the delay spread in the channel, 40 Hz for the Doppler shift and 100 Hz of the Doppler spread. The simulations were completed for two dissimilar channels (delay and power profiles). The results were estimated for 500 OFDM simulated blocks based on each antenna. The average SNR was less than or equal to 25 dB and the average delay was 260 ns for 10 to 20 iterations. Due to ignored channel taps, the proposed estimator has a larger MSE than the other estimators for SNR = 25 dB. For SNR = 15 dB, the smallest MSE was achieved with nine-tap. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Users & 20, 100, 500 \\ No. of cell & 7 \\ No. of users per cell & 10 \\ Number of transmitters & 4 \\ Total pilots to each transmitter & 24 \\ Cell radius & 1000 m \\ Guard interval & \(\frac{1}{4}\) \\ Total receivers & 4 \\ Number of Subcarriers \(N\) & 32, 128, 512 \\ Cyclic prefix & 16 \\ Signal Constellation & 16 QAM modulation \\ Path loss exponent & 4 \\ Bandwidth & 5 MHz \\ Channel & Frequency selective Rayleigh fading \\ FFT size & 2048 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation Parameters. Figure 4: Performance of bit error rate (BER) vs. signal-to-noise ratio (SNR). Figure 3: Performance of SER vs. SNR (dB) with 100 users. Figure 2: Performance of symbol error rate (SER) vs. signal-to-noise ratio (SNR) (dB) with 20 users. Figure 5: Performance of Uplink sum rate. Figure 6: Performance of Downlink sum rate.